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CONTRIBUTING.md
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@ -24,8 +24,8 @@ The list of topics for which we are looking for content are provided below along
- Web Scrapping - [Link](https://github.com/animator/learn-python/tree/main/contrib/web-scrapping)
- API Development - [Link](https://github.com/animator/learn-python/tree/main/contrib/api-development)
- Data Structures & Algorithms - [Link](https://github.com/animator/learn-python/tree/main/contrib/ds-algorithms)
- Python Mini Projects - [Link](https://github.com/animator/learn-python/tree/main/contrib/mini-projects)
- Python Question Bank - [Link](https://github.com/animator/learn-python/tree/main/contrib/question-bank)
- Python Mini Projects - [Link](https://github.com/animator/learn-python/tree/main/contrib/mini-projects) **(Not accepting)**
- Python Question Bank - [Link](https://github.com/animator/learn-python/tree/main/contrib/question-bank) **(Not accepting)**
You can check out some content ideas below.

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contrib/advanced-python/dates_and_times.md 100644
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## Working with Dates and Times in Python
Handling dates and times is an essential aspect of many programming tasks.
Python provides robust modules to work with dates and times, making it easier to perform operations like formatting, parsing, and arithmetic.
This guide provides an overview of these modules and their key functionalities.
## 1. 'datetime' Module
The datetime module supplies classes for manipulating dates and times. The main classes in the datetime module are:
* date: Represents a date (year, month, day).
* time: Represents a time (hour, minute, second, microsecond).
* datetime: Combines date and time information.
* timedelta: Represents the difference between two dates or times.
* tzinfo: Provides time zone information objects.
**Key Concepts:**
* Naive vs. Aware: Naive datetime objects do not contain time zone information, while aware datetime objects do.
* Immutability: date and time objects are immutable; once created, they cannot be changed.
Example:
```bash
import datetime
# Get the current date and time
now = datetime.datetime.now()
print("Current date and time:", now)
```
## 2. Formatting Dates and Times
Formatting involves converting datetime objects into human-readable strings. This is achieved using the strftime method, which stands for "string format time."
You can specify various format codes to dictate how the output string should be structured.
**Common Format Codes:**
* %Y: Year with century (e.g., 2024)
* %m: Month as a zero-padded decimal number (e.g., 01)
* %d: Day of the month as a zero-padded decimal number (e.g., 15)
* %H: Hour (24-hour clock) as a zero-padded decimal number (e.g., 13)
* %M: Minute as a zero-padded decimal number (e.g., 45)
* %S: Second as a zero-padded decimal number (e.g., 30)
Example:
```bash
import datetime
now = datetime.datetime.now()
formatted_now = now.strftime("%Y-%m-%d %H:%M:%S")
print("Formatted current date and time:", formatted_now)
```
## 3. Parsing Dates and Times
Parsing is the process of converting strings representing dates and times into datetime objects. The strptime method, which stands for "string parse time,"
allows you to specify the format of the input string.
Example:
```bash
import datetime
date_string = "2024-05-15 13:45:30"
date_object = datetime.datetime.strptime(date_string, "%Y-%m-%d %H:%M:%S")
print("Parsed date and time:", date_object)
```
## 4. Working with Time Differences
The timedelta class is used to represent the difference between two datetime objects. This is useful for calculations involving durations, such as finding the
number of days between two dates or adding a certain period to a date.
Example:
```bash
import datetime
date1 = datetime.datetime(2024, 5, 15, 12, 0, 0)
date2 = datetime.datetime(2024, 5, 20, 14, 30, 0)
difference = date2 - date1
print("Difference:", difference)
print("Days:", difference.days)
print("Total seconds:", difference.total_seconds())
```
## 5. Time Zones
Time zone handling in Python is facilitated by the pytz library. It allows you to convert naive datetime objects into timezone-aware objects and perform
operations across different time zones.
**Key Concepts:**
* Timezone-aware: A datetime object that includes timezone information.
* Localization: The process of associating a naive datetime with a time zone.
Example:
```bash
import datetime
import pytz
# Define a timezone
tz = pytz.timezone('Asia/Kolkata')
# Get the current time in a specific timezone
now = datetime.datetime.now(tz)
print("Current time in Asia/Kolkata:", now)
```
## 6. Date Arithmetic
Date arithmetic involves performing operations like addition or subtraction on date or datetime objects using timedelta. This is useful for calculating future
or past dates based on a given date.
Example:
```bash
import datetime
today = datetime.date.today()
future_date = today + datetime.timedelta(days=10)
print("Date after 10 days:", future_date)
```
## Summary
Python’s datetime module and the pytz library provide comprehensive tools for working with dates, times, and time zones. They enable you to perform a wide range
of operations, from basic date manipulations to complex time zone conversions.

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# Understanding the `eval` Function in Python
## Introduction
The `eval` function in Python allows you to execute a string-based Python expression dynamically. This can be useful in various scenarios where you need to evaluate expressions that are not known until runtime.
## Syntax
```python
eval(expression, globals=None, locals=None)
```
### Parameters:
* expression: String is parsed and evaluated as a Python expression
* globals [optional]: Dictionary to specify the available global methods and variables.
* locals [optional]: Another dictionary to specify the available local methods and variables.
## Examples
Example 1:
```python
result = eval('2 + 3 * 4')
print(result) # Output: 14
```
Example 2:
```python
x = 10
expression = 'x * 2'
result = eval(expression, {'x': x})
print(result) # Output: 20
```
Example 3:
```python
x = 10
def multiply(a, b):
return a * b
expression = 'multiply(x, 5) + 2'
result = eval(expression)
print("Result:",result) # Output: Result:52
```
Example 4:
```python
expression = input("Enter a Python expression: ")
result = eval(expression)
print("Result:", result)
#input= "3+2"
#Output: Result:5
```
Example 5:
```python
import numpy as np
a=np.random.randint(1,9)
b=np.random.randint(1,9)
operations=["*","-","+"]
op=np.random.choice(operations)
expression=str(a)+op+str(b)
correct_answer=eval(expression)
given_answer=int(input(str(a)+" "+op+" "+str(b)+" = "))
if given_answer==correct_answer:
print("Correct")
else:
print("Incorrect")
print("correct answer is :" ,correct_answer)
#2 * 1 = 8
#Incorrect
#correct answer is : 2
#or
#3 * 2 = 6
#Correct
```
## Conclusion
The eval function is a powerful tool in Python that allows for dynamic evaluation of expressions.

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# Exception Handling in Python
Exception Handling is a way of managing the errors that may occur during a program execution. Python's exception handling mechanism has been designed to avoid the unexpected termination of the program, and offer to either regain control after an error or display a meaningful message to the user.
- **Error** - An error is a mistake or an incorrect result produced by a program. It can be a syntax error, a logical error, or a runtime error. Errors are typically fatal, meaning they prevent the program from continuing to execute.
- **Exception** - An exception is an event that occurs during the execution of a program that disrupts the normal flow of instructions. Exceptions are typically unexpected and can be handled by the program to prevent it from crashing or terminating abnormally. It can be runtime, input/output or system exceptions. Exceptions are designed to be handled by the program, allowing it to recover from the error and continue executing.
## Python Built-in Exceptions
There are plenty of built-in exceptions in Python that are raised when a corresponding error occur.
We can view all the built-in exceptions using the built-in `local()` function as follows:
```python
print(dir(locals()['__builtins__']))
```
|**S.No**|**Exception**|**Description**|
|---|---|---|
|1|SyntaxError|A syntax error occurs when the code we write violates the grammatical rules such as misspelled keywords, missing colon, mismatched parentheses etc.|
|2|TypeError|A type error occurs when we try to perform an operation or use a function with objects that are of incompatible data types.|
|3|NameError|A name error occurs when we try to use a variable, function, module or string without quotes that hasn't been defined or isn't used in a valid way.|
|4|IndexError|A index error occurs when we try to access an element in a sequence (like a list, tuple or string) using an index that's outside the valid range of indices for that sequence.|
|5|KeyError|A key error occurs when we try to access a key that doesn't exist in a dictionary. Attempting to retrieve a value using a non-existent key results this error.|
|6|ValueError|A value error occurs when we provide an argument or value that's inappropriate for a specific operation or function such as doing mathematical operations with incompatible types (e.g., dividing a string by an integer.)|
|7|AttributeError|An attribute error occurs when we try to access an attribute (like a variable or method) on an object that doesn't possess that attribute.|
|8|IOError|An IO (Input/Output) error occurs when an operation involving file or device interaction fails. It signifies that there's an issue during communication between your program and the external system.|
|9|ZeroDivisionError|A ZeroDivisionError occurs when we attempt to divide a number by zero. This operation is mathematically undefined, and Python raises this error to prevent nonsensical results.|
|10|ImportError|An import error occurs when we try to use a module or library that Python can't find or import succesfully.|
## Try and Except Statement - Catching Exception
The `try-except` statement allows us to anticipate potential errors during program execution and define what actions to take when those errors occur. This prevents the program from crashing unexpectedly and makes it more robust.
Here's an example to explain this:
```python
try:
# Code that might raise an exception
result = 10 / 0
except:
print("An error occured!")
```
Output
```markdown
An error occured!
```
In this example, the `try` block contains the code that you suspect might raise an exception. Python attempts to execute the code within this block. If an exception occurs, Python jumps to the `except` block and executes the code within it.
## Specific Exception Handling
You can specify the type of expection you want to catch using the `except` keyword followed by the exception class name. You can also have multiple `except` blocks to handle different exception types.
Here's an example:
```python
try:
# Code that might raise ZeroDivisionError or NameError
result = 10 / 0
name = undefined_variable
except ZeroDivisionError:
print("Oops! You tried to divide by zero.")
except NameError:
print("There's a variable named 'undefined_variable' that hasn't been defined yet.")
```
Output
```markdown
Oops! You tried to divide by zero.
```
If you comment on the line `result = 10 / 0`, then the output will be:
```markdown
There's a variable named 'undefined_variable' that hasn't been defined yet.
```
## Important Note
In this code, the `except` block are specific to each type of expection. If you want to catch both exceptions with a single `except` block, you can use of tuple of exceptions, like this:
```python
try:
# Code that might raise ZeroDivisionError or NameError
result = 10 / 0
name = undefined_variable
except (ZeroDivisionError, NameError):
print("An error occured!")
```
Output
```markdown
An error occured!
```
## Try with Else Clause
The `else` clause in a Python `try-except` block provides a way to execute code only when the `try` block succeeds without raising any exceptions. It's like having a section of code that runs exclusively under the condition that no errors occur during the main operation in the `try` block.
Here's an example to understand this:
```python
def calculate_average(numbers):
if len(numbers) == 0: # Handle empty list case seperately (optional)
return None
try:
total = sum(numbers)
average = total / len(numbers)
except ZeroDivisionError:
print("Cannot calculate average for a list containing zero.")
else:
print("The average is:", average)
return average #Optionally return the average here
# Example usage
numbers = [10, 20, 30]
result = calculate_average(numbers)
if result is not None: # Check if result is available (handles empty list case)
print("Calculation succesfull!")
```
Output
```markdown
The average is: 20.0
```
## Finally Keyword in Python
The `finally` keyword in Python is used within `try-except` statements to execute a block of code **always**, regardless of whether an exception occurs in the `try` block or not.
To understand this, let us take an example:
```python
try:
a = 10 // 0
print(a)
except ZeroDivisionError:
print("Cannot be divided by zero.")
finally:
print("Program executed!")
```
Output
```markdown
Cannot be divided by zero.
Program executed!
```
## Raise Keyword in Python
In Python, raising an exception allows you to signal that an error condition has occured during your program's execution. The `raise` keyword is used to explicity raise an exception.
Let us take an example:
```python
def divide(x, y):
if y == 0:
raise ZeroDivisionError("Can't divide by zero!") # Raise an exception with a message
result = x / y
return result
try:
division_result = divide(10, 0)
print("Result:", division_result)
except ZeroDivisionError as e:
print("An error occured:", e) # Handle the exception and print the message
```
Output
```markdown
An error occured: Can't divide by zero!
```
## Advantages of Exception Handling
- **Improved Error Handling** - It allows you to gracefully handle unexpected situations that arise during program execution. Instead of crashing abruptly, you can define specific actions to take when exceptions occur, providing a smoother experience.
- **Code Robustness** - Exception Handling helps you to write more resilient programs by anticipating potential issues and providing approriate responses.
- **Enhanced Code Readability** - By seperating error handling logic from the core program flow, your code becomes more readable and easier to understand. The `try-except` blocks clearly indicate where potential errors might occur and how they'll be addressed.
## Disadvantages of Exception Handling
- **Hiding Logic Errors** - Relying solely on exception handling might mask underlying logic error in your code. It's essential to write clear and well-tested logic to minimize the need for excessive exception handling.
- **Performance Overhead** - In some cases, using `try-except` blocks can introduce a slight performance overhead compared to code without exception handling. Howerer, this is usually negligible for most applications.
- **Overuse of Exceptions** - Overusing exceptions for common errors or control flow can make code less readable and harder to maintain. It's important to use exceptions judiciously for unexpected situations.

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# Generators
## Introduction
Generators in Python are a sophisticated feature that enables the creation of iterators without the need to construct a full list in memory. They allow you to generate values on-the-fly, which is particularly beneficial for working with large datasets or infinite sequences. We will explore generators in depth, covering their types, mathematical formulation, advantages, disadvantages, and implementation examples.
## Function Generators
Function generators are created using the `yield` keyword within a function. When invoked, a function generator returns a generator iterator, allowing you to iterate over the values generated by the function.
### Mathematical Formulation
Function generators can be represented mathematically using set-builder notation. The general form is:
```
{expression | variable in iterable, condition}
```
Where:
- `expression` is the expression to generate values.
- `variable` is the variable used in the expression.
- `iterable` is the sequence of values to iterate over.
- `condition` is an optional condition that filters the values.
### Advantages of Function Generators
1. **Memory Efficiency**: Function generators produce values lazily, meaning they generate values only when needed, saving memory compared to constructing an entire sequence upfront.
2. **Lazy Evaluation**: Values are generated on-the-fly as they are consumed, leading to improved performance and reduced overhead, especially when dealing with large datasets.
3. **Infinite Sequences**: Function generators can represent infinite sequences, such as the Fibonacci sequence, allowing you to work with data streams of arbitrary length without consuming excessive memory.
### Disadvantages of Function Generators
1. **Single Iteration**: Once a function generator is exhausted, it cannot be reused. If you need to iterate over the sequence again, you'll have to create a new generator.
2. **Limited Random Access**: Function generators do not support random access like lists. They only allow sequential access, which might be a limitation depending on the use case.
### Implementation Example
```python
def fibonacci():
a, b = 0, 1
while True:
yield a
a, b = b, a + b
# Usage
fib_gen = fibonacci()
for _ in range(10):
print(next(fib_gen))
```
## Generator Expressions
Generator expressions are similar to list comprehensions but return a generator object instead of a list. They offer a concise way to create generators without the need for a separate function.
### Mathematical Formulation
Generator expressions can also be represented mathematically using set-builder notation. The general form is the same as for function generators.
### Advantages of Generator Expressions
1. **Memory Efficiency**: Generator expressions produce values lazily, similar to function generators, resulting in memory savings.
2. **Lazy Evaluation**: Values are generated on-the-fly as they are consumed, providing improved performance and reduced overhead.
### Disadvantages of Generator Expressions
1. **Single Iteration**: Like function generators, once a generator expression is exhausted, it cannot be reused.
2. **Limited Random Access**: Generator expressions, similar to function generators, do not support random access.
### Implementation Example
```python
# Generate squares of numbers from 0 to 9
square_gen = (x**2 for x in range(10))
# Usage
for num in square_gen:
print(num)
```
## Conclusion
Generators offer a powerful mechanism for creating iterators efficiently in Python. By understanding the differences between function generators and generator expressions, along with their mathematical formulation, advantages, and disadvantages, you can leverage them effectively in various scenarios. Whether you're dealing with large datasets or need to work with infinite sequences, generators provide a memory-efficient solution with lazy evaluation capabilities, contributing to more elegant and scalable code.

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contrib/advanced-python/index.md
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# List of sections
- [OOPs](oops.md)
- [Decorators/\*args/**kwargs](decorator-kwargs-args.md)
- ['itertools' module](Itertools_module.md)
- ['itertools' module](itertools.md)
- [Type Hinting](type-hinting.md)
- [Lambda Function](lambda-function.md)
- [Working with Dates & Times in Python](dates_and_times.md)
- [Regular Expressions in Python](regular_expressions.md)
- [JSON module](json-module.md)
- [Map Function](map-function.md)
- [Protocols](protocols.md)
- [Exception Handling in Python](exception-handling.md)
- [Generators](generators.md)
- [List Comprehension](list-comprehension.md)
- [Eval Function](eval_function.md)

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# The 'itertools' Module in Python
The itertools module in Python provides a collection of fast, memory-efficient tools that are useful for creating and working with iterators. These functions
allow you to iterate over data in various ways, often combining, filtering, or extending iterators to generate complex sequences efficiently.
## Benefits of itertools
1. Efficiency: Functions in itertools are designed to be memory-efficient, often generating elements on the fly and avoiding the need to store large intermediate results.
2. Conciseness: Using itertools can lead to more readable and concise code, reducing the need for complex loops and temporary variables.
3. Composability: Functions from itertools can be easily combined, allowing you to build complex iterator pipelines from simple building blocks.
## Useful Functions in itertools <br>
Here are some of the most useful functions in the itertools module, along with examples of how to use them:
1. 'count': Generates an infinite sequence of numbers, starting from a specified value.
```bash
import itertools
counter = itertools.count(start=10, step=2)
for _ in range(5):
print(next(counter))
# Output: 10, 12, 14, 16, 18
```
2. 'cycle': Cycles through an iterable indefinitely.
```bash
import itertools
cycler = itertools.cycle(['A', 'B', 'C'])
for _ in range(6):
print(next(cycler))
# Output: A, B, C, A, B, C
```
3.'repeat': Repeats an object a specified number of times or indefinitely.
```bash
import itertools
repeater = itertools.repeat('Hello', 3)
for item in repeater:
print(item)
# Output: Hello, Hello, Hello
```
4. 'chain': Combines multiple iterables into a single iterable.
```bash
import itertools
combined = itertools.chain([1, 2, 3], ['a', 'b', 'c'])
for item in combined:
print(item)
# Output: 1, 2, 3, a, b, c
```
5. 'islice': Slices an iterator, similar to slicing a list.
```bash
import itertools
sliced = itertools.islice(range(10), 2, 8, 2)
for item in sliced:
print(item)
# Output: 2, 4, 6
```
6. 'compress': Filters elements in an iterable based on a corresponding selector iterable.
```bash
import itertools
data = ['A', 'B', 'C', 'D']
selectors = [1, 0, 1, 0]
result = itertools.compress(data, selectors)
for item in result:
print(item)
# Output: A, C
```
7. 'permutations': Generates all possible permutations of an iterable.
```bash
import itertools
perms = itertools.permutations('ABC', 2)
for item in perms:
print(item)
# Output: ('A', 'B'), ('A', 'C'), ('B', 'A'), ('B', 'C'), ('C', 'A'), ('C', 'B')
```
8. 'combinations': Generates all possible combinations of a specified length from an iterable.
```bash
import itertools
combs = itertools.combinations('ABC', 2)
for item in combs:
print(item)
# Output: ('A', 'B'), ('A', 'C'), ('B', 'C')
```
9. 'product': Computes the Cartesian product of input iterables.
```bash
import itertools
prod = itertools.product('AB', '12')
for item in prod:
print(item)
# Output: ('A', '1'), ('A', '2'), ('B', '1'), ('B', '2')
```
10. 'groupby': Groups elements of an iterable by a specified key function.
```bash
import itertools
data = [{'name': 'Alice', 'age': 25}, {'name': 'Bob', 'age': 25}, {'name': 'Charlie', 'age': 30}]
sorted_data = sorted(data, key=lambda x: x['age'])
grouped = itertools.groupby(sorted_data, key=lambda x: x['age'])
for key, group in grouped:
print(key, list(group))
# Output:
# 25 [{'name': 'Alice', 'age': 25}, {'name': 'Bob', 'age': 25}]
# 30 [{'name': 'Charlie', 'age': 30}]
```
11. 'accumulate': Makes an iterator that returns accumulated sums, or accumulated results of other binary functions specified via the optional func argument.
```bash
import itertools
import operator
data = [1, 2, 3, 4, 5]
acc = itertools.accumulate(data, operator.mul)
for item in acc:
print(item)
# Output: 1, 2, 6, 24, 120
```
## Conclusion
The itertools module is a powerful toolkit for working with iterators in Python. Its functions enable efficient and concise handling of iterable data, allowing you to create complex data processing pipelines with minimal memory overhead.
By leveraging itertools, you can improve the readability and performance of your code, making it a valuable addition to your Python programming arsenal.

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# JSON Module
## What is JSON?
- [JSON]("https://www.json.org/json-en.html") (JavaScript Object Notation) is a format for structuring data.
- JSON is a lightweight, text-based data interchange format that is completely language-independent.
- Similar to XML, JSON is a format for structuring data commonly used by web applications to communicate with each other.
## Why JSON?
- Whenever we declare a variable and assign a value to it, the variable itself doesn't hold the value. Instead, the variable holds an address in memory where the value is stored. For example:
```python
age = 21
```
- When we use `age`, it gets replaced with `21`. However, *age doesn't contain 21, it contains the address of the memory location where 21 is stored*.
- While this works locally, transferring this data, such as through an API, poses a challenge. Sending your computer’s entire memory with the addresses is impractical and insecure. This is where JSON comes to the rescue.
### Example JSON
- JSON supports most widely used data types including String
, Number, Boolean, Null, Array and Object.
- Here is an example of JSON file
```json
{
"name": "John Doe",
"age": 21,
"isStudent": true,
"address": null,
"courses": ["Math", "Science", "History"],
"grades": {
"Math": 95,
"Science": 89,
"History": 76
}
}
```
# Python JSON
Python too supports JSON with a built-in package called `json`. This package provides all the necessary tools for working with JSON Objects including `parsing, serializing, deserializing, and many more`.
## 1. Python parse JSON string.
- To parse JSON string Python firstly we import the JSON module.
- JSON string is converted to a Python object using `json.loads()` method of JSON module in Python.
- Example Code:
```python
# Python program to convert JSON to Python
import json
# JSON string
students ='{"id":"01", "name": "Yatharth", "department":"Computer Science Engineering"}'
# Convert string to Python dict
students_dict = json.loads(students)
print(students_dict)
print(students_dict['name'])
```
- Ouput:
```json
{"id": "01", "name": "Yatharth", "department": "Computer Science Engineering"}
```
## 2. Python load JSON file.
- JSON data can also be directly fetch from a json file
- Example:
```python
import json
# Opening JSON file
f = open('input.json',)
# Returns JSON object as a dictionary
data = json.load(f)
# Iterating through the json file
for i in data['students']:
print(i)
# Closing file
f.close()
```
- JSON file
```json
{
"students":{
{
"id": "01",
"name": "Yatharth",
"department": "Computer Science Engineering"
},
{
"id": "02",
"name": "Raj",
"department": "Mechanical Engineering"
}
}
}
```
- Ouput
```json
{"id": "01", "name": "Yatharth", "department": "Computer Science Engineering"}
{"id": "02", "name": "Raj", "department": "Mechanical Engineering"}
```
- `json.load()`: Reads JSON data from a file object and deserializes it into a Python object.
- `json.loads()`: Deserializes JSON data from a string into a Python object.
## Addtiotnal Context
Relation between python data types and json data types is given in table below.
| Python Object | JSON Object |
|-----------------|-------------|
| Dict | object |
| list, tuple | array |
| str | string |
| int, long, float | numbers |
| True | true |
| False | false |
| None | null |
## 3. Python Dictionary to JSON String
- Parsing python dictionary to json string using `json.dumps()`.
- Example Code:
```python
import json
# Data to be written
dictionary ={
"id": "03",
"name": "Suraj",
"department": "Civil Engineering"
}
# Serializing json
json_object = json.dumps(dictionary, indent = 4)
print(json_object)
```
- Output:
``` json
{
"department": "Civil Engineering",
"id": "02",
"name": "Suraj"
}
```
## 4. Python Dictionary to JSON file.
- - Parsing python dictionary to json string using `json.dump()`.
- Example Code:
``` python
import json
# Data to be written
dictionary ={
"name" : "Satyendra",
"rollno" : 51,
"cgpa" : 8.8,
"phonenumber" : "123456789"
}
with open("sample.json", "w") as outfile:
json.dump(dictionary, outfile)
```
- Ouput: `sample.json`
``` json
{
"name" : "Satyendra",
"rollno" : 51,
"cgpa" : 8.8,
"phonenumber" : "123456789"
}
```
## 5. Append Python Dictionary to JSON String.
- Append to an already existing string using `json.update()`.
- Example :
```python
import json
# JSON data:
x = {
"id": "03",
"name": "Suraj"
}
# python object to be appended
y = { "department": "Civil Engineering"}
# parsing JSON string:
z = json.loads(x)
# appending the data
z.update(y)
# the result is a JSON string:
print(json.dumps(z))
```
- Ouput:
```json
{"id": "03", "name": "Suraj", "department": "Civil Engineering"}
```
## 6. Append Python Dictionary to JSON File.
- There is no direct function to append in file. So, we will load file in a dictionary, update dictionary then update content and convert back to json file format.
- `data.json`
``` json
{
"students":{
{
"id": "01",
"name": "Yatharth",
"department": "Computer Science Engineering"
},
{
"id": "02",
"name": "Raj",
"department": "Mechanical Engineering"
}
}
}
```
- Example Code:
``` python
import json
# function to add to JSON
def write_json(new_data, filename='data.json'):
with open(filename,'r+') as file:
# First we load existing data into a dict.
file_data = json.load(file)
# Join new_data with file_data inside students
file_data["students"].append(new_data)
# Sets file's current position at offset.
file.seek(0)
# convert back to json.
json.dump(file_data, file, indent = 4)
# python object to be appended
y = {
"id": "03",
"name": "Suraj",
"department": "Civil Engineering"
}
write_json(y)
```
- Output:
```json
{
"students":{
{
"id": "01",
"name": "Yatharth",
"department": "Computer Science Engineering"
},
{
"id": "02",
"name": "Raj",
"department": "Mechanical Engineering"
},
{
"id": "03",
"name": "Suraj",
"department": "Civil Engineering"
}
}
}
```
The Python json module simplifies the handling of JSON data, offering a bridge between Python data structures and JSON representations, vital for data exchange and storage in modern applications.

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# Lambda Function
Lambda functions in Python are small, anonymous functions that can be created on-the-fly. They are defined using the `lambda` keyword instead of the `def` keyword used for regular functions. Lambda functions are typically used for simple tasks where a full-blown function definition is not necessary.
Here's an example of a lambda function that adds two numbers:
```python
add = lambda x, y: x + y
print(add(3, 5)) # Output: 8
```
The above lambda function is equivalent to the following regular function:
```python
def add(x, y):
return x + y
print(add(3, 5)) # Output: 8
```
The difference between a regular function and a lambda function lies mainly in syntax and usage. Here are some key distinctions:
1. **Syntax**: Lambda functions are defined using the `lambda` keyword, followed by parameters and a colon, while regular functions use the `def` keyword, followed by the function name, parameters, and a colon.
2. **Name**: Lambda functions are anonymous; they do not have a name like regular functions. Regular functions are defined with a name.
3. **Complexity**: Lambda functions are suitable for simple, one-liner tasks. They are not meant for complex operations or tasks that require multiple lines of code. Regular functions can handle more complex logic and can contain multiple statements and lines of code.
4. **Usage**: Lambda functions are often used in situations where a function is needed as an argument to another function (e.g., sorting, filtering, mapping), or when you want to write concise code without defining a separate function.
Lambda functions are used primarily for convenience and brevity in situations where a full function definition would be overkill or too cumbersome. They are handy for tasks that require a small, one-time function and can improve code readability when used judiciously.
## Use Cases
1. **Sorting**: Lambda functions are often used as key functions for sorting lists, dictionaries, or other data structures based on specific criteria. For example:
```python
students = [
{"name": "Alice", "age": 20},
{"name": "Bob", "age": 18},
{"name": "Charlie", "age": 22}
]
sorted_students = sorted(students, key=lambda x: x["age"])
```
2. **Filtering**: Lambda functions can be used with filter() to selectively include elements from a collection based on a condition. For instance:
```python
numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
even_numbers = list(filter(lambda x: x % 2 == 0, numbers))
```
3. **Mapping**: Lambda functions are useful with map() to apply a transformation to each element of a collection. For example:
```python
numbers = [1, 2, 3, 4, 5]
squared_numbers = list(map(lambda x: x**2, numbers))
```
4. **Event Handling**: In GUI programming or event-driven systems, lambda functions can be used as event handlers to execute specific actions when an event occurs. For instance:
```python
button.clicked.connect(lambda: self.on_button_click(argument))
```
5. **Callback Functions**: Lambda functions can be passed as callback functions to other functions, especially when a simple operation needs to be performed in response to an event. For example:
```python
def process_data(data, callback):
# Process data
result = ...
# Execute callback function
callback(result)
process_data(data, lambda x: print("Result:", x))
```
6. **Anonymous Functions in Higher-Order Functions**: Lambda functions are commonly used with higher-order functions such as reduce(), which applies a rolling computation to sequential pairs of values in a list. For example:
```python
from functools import reduce
numbers = [1, 2, 3, 4, 5]
sum_of_numbers = reduce(lambda x, y: x + y, numbers)
```
These are just a few examples of how lambda functions can be applied in Python to simplify code and make it more expressive. They are particularly useful in situations where a small, one-time function is needed and defining a separate named function would be excessive.
In conclusion, **lambda functions** in Python offer a concise and powerful way to handle simple tasks without the need for full function definitions. Their versatility, especially in scenarios like sorting, filtering, and event handling, makes them valuable tools for improving code readability and efficiency. By mastering lambda functions, you can enhance your Python programming skills and tackle various tasks with elegance and brevity.

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# List Comprehension
Creating lists concisely and expressively is what list comprehension in Python does. You can generate lists from already existing iterables like lists, tuples or strings with a short form.
This boosts the readability of code and reduces necessity of using explicit looping constructs.
## Syntax :
### Basic syntax
```python
new_list = [expression for item in iterable]
```
- **new_list**: This is the name given to the list that will be created using the list comprehension.
- **expression**: This is the expression that defines how each element of the new list will be generated or transformed.
- **item**: This variable represents each individual element from the iterable. It takes on the value of each element in the iterable during each iteration.
- **iterable**: This is the sequence-like object over which the iteration will take place. It provides the elements that will be processed by the expression.
This list comprehension syntax `[expression for item in iterable]` allows you to generate a new list by applying a specific expression to each element in an iterable.
### Syntax including condition
```python
new_list = [expression for item in iterable if condition]
```
- **new_list**: This is the name given to the list that will be created using the list comprehension.
- **expression**: This is the expression that defines how each element of the new list will be generated or transformed.
- **item**: This variable represents each individual element from the iterable. It takes on the value of each element in the iterable during each iteration.
- **iterable**: This is the sequence-like object over which the iteration will take place. It provides the elements that will be processed by the expression.
- **if condition**: This is an optional part of the syntax. It allows for conditional filtering of elements from the iterable. Only items that satisfy the condition
will be included in the new list.
## Examples:
1. Generating a list of squares of numbers from 1 to 5:
```python
squares = [x ** 2 for x in range(1, 6)]
print(squares)
```
- **Output** :
```python
[1, 4, 9, 16, 25]
```
2. Filtering even numbers from a list:
```python
nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
even = [x for x in nums if x % 2 == 0]
print(even)
```
- **Output** :
```python
[2, 4, 6, 8, 10]
```
3. Flattening a list of lists:
```python
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
flat = [x for sublist in matrix for x in sublist]
print(flat)
```
- **Output** :
```python
[1, 2, 3, 4, 5, 6, 7, 8, 9]
```
List comprehension is a powerful feature in Python for creating lists based on existing iterables with a concise syntax.
By mastering list comprehension, developers can write cleaner, more expressive code and leverage Python's functional programming capabilities effectively.

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The `map()` function in Python is a built-in function used for applying a given function to each item of an iterable (like a list, tuple, or dictionary) and returning a new iterable with the results. It's a powerful tool for transforming data without the need for explicit loops. Let's break down its syntax, explore examples, and discuss various use cases.
### Syntax:
```python
map(function, iterable1, iterable2, ...)
```
- `function`: The function to apply to each item in the iterables.
- `iterable1`, `iterable2`, ...: One or more iterable objects whose items will be passed as arguments to `function`.
### Examples:
#### Example 1: Doubling the values in a list
```python
# Define the function
def double(x):
return x * 2
# Apply the function to each item in the list using map
original_list = [1, 2, 3, 4, 5]
doubled_list = list(map(double, original_list))
print(doubled_list) # Output: [2, 4, 6, 8, 10]
```
#### Example 2: Converting temperatures from Celsius to Fahrenheit
```python
# Define the function
def celsius_to_fahrenheit(celsius):
return (celsius * 9/5) + 32
# Apply the function to each Celsius temperature using map
celsius_temperatures = [0, 10, 20, 30, 40]
fahrenheit_temperatures = list(map(celsius_to_fahrenheit, celsius_temperatures))
print(fahrenheit_temperatures) # Output: [32.0, 50.0, 68.0, 86.0, 104.0]
```
### Use Cases:
1. **Data Transformation**: When you need to apply a function to each item of a collection and obtain the transformed values, `map()` is very handy.
2. **Parallel Processing**: In some cases, `map()` can be utilized in parallel processing scenarios, especially when combined with `multiprocessing` or `concurrent.futures`.
3. **Cleaning and Formatting Data**: It's often used in data processing pipelines for tasks like converting data types, normalizing values, or applying formatting functions.
4. **Functional Programming**: In functional programming paradigms, `map()` is frequently used along with other functional constructs like `filter()` and `reduce()` for concise and expressive code.
5. **Generating Multiple Outputs**: You can use `map()` to generate multiple outputs simultaneously by passing multiple iterables. The function will be applied to corresponding items in the iterables.
6. **Lazy Evaluation**: In Python 3, `map()` returns an iterator rather than a list. This means it's memory efficient and can handle large datasets without loading everything into memory at once.
Remember, while `map()` is powerful, it's essential to balance its use with readability and clarity. Sometimes, a simple loop might be more understandable than a `map()` call.

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In Python object-oriented Programming (OOPs) is a programming paradigm
that uses objects and classes in programming. It aims to implement
real-world entities like inheritance, polymorphisms, encapsulation, etc.
in the programming. The main concept of object-oriented Programming
(OOPs) or oops concepts in Python is to bind the data and the functions
that work together as a single unit so that no other part of the code
can access this data.
**OOPs Concepts in Python**
1. Class in Python
2. Objects in Python
3. Polymorphism in Python
4. Encapsulation in Python
5. Inheritance in Python
6. Data Abstraction in Python
Python Class A class is a collection of objects. A class contains the
blueprints or the prototype from which the objects are being created. It
is a logical entity that contains some attributes and methods.
```python
#Simple Class in Python
class Dog:
pass
```
**Python Objects** In object oriented programming Python, The object is
an entity that has a state and behavior associated with it. It may be
any real-world object like a mouse, keyboard, chair, table, pen, etc.
Integers, strings, floating-point numbers, even arrays, and
dictionaries, are all objects.
```python
obj = Dog()
```
This creates an instance for class Dog
**The Python **init** Method**
The **init** method is similar to constructors in C++ and Java. It is
run as soon as an object of a class is instantiated. The method is
useful to do any initialization you want to do with your object.
```python
class Dog:
# class attribute
attr1 = "mammal"
# Instance attribute
def __init__(self, name):
self.name = name
# Object instantiation
Rodger = Dog("Rodger")
Tommy = Dog("Tommy")
# Accessing class attributes
print("Rodger is a {}".format(Rodger.__class__.attr1))
print("Tommy is also a {}".format(Tommy.__class__.attr1))
# Accessing instance attributes
print("My name is {}".format(Rodger.name))
print("My name is {}".format(Tommy.name))
```
In the above mentioned code, init method is used to initialize the name.
**Inheritance**
In Python object oriented Programming, Inheritance is the capability of
one class to derive or inherit the properties from another class. The
class that derives properties is called the derived class or child class
and the class from which the properties are being derived is called the
base class or parent class.
Types of Inheritances:
- Single Inheritance
- Multilevel Inheritance
- Multiple Inheritance
- Hierarchial Inheritance
```python
#Single Inheritance
# Parent class
class Animal:
def __init__(self, name, sound):
self.name = name
self.sound = sound
def make_sound(self):
print(f"{self.name} says {self.sound}")
# Child class inheriting from Animal
class Dog(Animal):
def __init__(self, name):
# Call the constructor of the parent class
super().__init__(name, "Woof")
# Child class inheriting from Animal
class Cat(Animal):
def __init__(self, name):
# Call the constructor of the parent class
super().__init__(name, "Meow")
# Creating objects of the derived classes
dog = Dog("Buddy")
cat = Cat("Whiskers")
# Accessing methods of the parent class
dog.make_sound()
cat.make_sound()
```
The above code depicts the Single Inheritance, in case of single inheritance there's only a single base class and a derived class. Here, Dog and Cat are the derived classes with Animal as the parent class. They can access the methods of the base class or derive their own methods.
```python
#Multilevel Inheritance
# Parent class
class Animal:
def __init__(self, name):
self.name = name
def speak(self):
print(f"{self.name} speaks")
# Child class inheriting from Animal
class Dog(Animal):
def bark(self):
print(f"{self.name} barks")
# Grandchild class inheriting from Dog
class GermanShepherd(Dog):
def guard(self):
print(f"{self.name} guards")
# Creating objects of the derived classes
german_shepherd = GermanShepherd("Rocky")
# Accessing methods from all levels of inheritance
german_shepherd.speak() # Accessing method from the Animal class
german_shepherd.bark() # Accessing method from the Dog class
german_shepherd.guard() # Accessing method from the GermanShepherd class
```
Multilevel inheritance is a concept in object-oriented programming where a class inherits properties and behaviors from another class, which itself may inherit from another class. In other words, it involves a chain of inheritance where a subclass inherits from a superclass, and that subclass can then become a superclass for another subclass.Its similar to GrandFather ,Father and Son .In the above code,Animal class is the superclass, Dog is derived from Animal and Dog is the parent of GermanShepherd. GermenShepherd is the child class of Dog. GermenShepherd can access methods of both Animal and Dog.
```python
#Hierarchial Inheritance
# Parent class
class Animal:
def __init__(self, name):
self.name = name
def speak(self):
print(f"{self.name} speaks")
# Child class 1 inheriting from Animal
class Dog(Animal):
def bark(self):
print(f"{self.name} barks")
# Child class 2 inheriting from Animal
class Cat(Animal):
def meow(self):
print(f"{self.name} meows")
# Creating objects of the derived classes
dog = Dog("Buddy")
cat = Cat("Whiskers")
# Accessing methods from the parent and child classes
dog.speak() # Accessing method from the Animal class
dog.bark() # Accessing method from the Dog class
cat.speak() # Accessing method from the Animal class
cat.meow() # Accessing method from the Cat class
```
Hierarchical inheritance is a type of inheritance in object-oriented programming where one class serves as a superclass for multiple subclasses. In this inheritance model, each subclass inherits properties and behaviors from the same superclass, creating a hierarchical tree-like structure.
```python
#Multiple Inheritance
# Parent class 1
class Herbivore:
def eat_plants(self):
print("Eating plants")
# Parent class 2
class Carnivore:
def eat_meat(self):
print("Eating meat")
# Child class inheriting from both Herbivore and Carnivore
class Omnivore(Herbivore, Carnivore):
def eat(self):
print("Eating everything")
# Creating an object of the Omnivore class
omnivore = Omnivore()
# Accessing methods from both parent classes
omnivore.eat_plants() # Accessing method from Herbivore
omnivore.eat_meat() # Accessing method from Carnivore
omnivore.eat() # Accessing method from Omnivore
```
Multiple inheritance is a concept in object-oriented programming where a class can inherit properties and behaviors from more than one parent class. This means that a subclass can have multiple immediate parent classes, allowing it to inherit features from each of them.
**Polymorphism** In object oriented Programming Python, Polymorphism
simply means having many forms
```python
class Bird:
def intro(self):
print("There are many types of birds.")
def flight(self):
print("Most of the birds can fly but some cannot.")
class sparrow(Bird):
def flight(self):
print("Sparrows can fly.")
class ostrich(Bird):
def flight(self):
print("Ostriches cannot fly.")
obj_bird = Bird()
obj_spr = sparrow()
obj_ost = ostrich()
obj_bird.intro()
obj_bird.flight()
obj_spr.intro()
obj_spr.flight()
obj_ost.intro()
obj_ost.flight()
```
Poly stands for 'many' and morphism for 'forms'. In the above code, method flight() has many forms.
**Python Encapsulation**
In Python object oriented programming, Encapsulation is one of the
fundamental concepts in object-oriented programming (OOP). It describes
the idea of wrapping data and the methods that work on data within one
unit. This puts restrictions on accessing variables and methods directly
and can prevent the accidental modification of data. To prevent
accidental change, an object's variable can only be changed by an
object's method. Those types of variables are known as private
variables.
```python
class Car:
def __init__(self, make, model, year):
self._make = make # Encapsulated attribute with single underscore
self._model = model # Encapsulated attribute with single underscore
self._year = year # Encapsulated attribute with single underscore
self._odometer_reading = 0 # Encapsulated attribute with single underscore
def get_make(self):
return self._make
def get_model(self):
return self._model
def get_year(self):
return self._year
def get_odometer_reading(self):
return self._odometer_reading
def update_odometer(self, mileage):
if mileage >= self._odometer_reading:
self._odometer_reading = mileage
else:
print("You can't roll back an odometer!")
def increment_odometer(self, miles):
self._odometer_reading += miles
# Creating an instance of the Car class
my_car = Car("Toyota", "Camry", 2021)
# Accessing encapsulated attributes through methods
print("Make:", my_car.get_make())
print("Model:", my_car.get_model())
print("Year:", my_car.get_year())
# Modifying encapsulated attribute through method
my_car.update_odometer(100)
print("Odometer Reading:", my_car.get_odometer_reading())
# Incrementing odometer reading
my_car.increment_odometer(50)
print("Odometer Reading after increment:", my_car.get_odometer_reading())
```
**Data Abstraction** It hides unnecessary code details from the user.
Also, when we do not want to give out sensitive parts of our code
implementation and this is where data abstraction came.
```python
from abc import ABC, abstractmethod
# Abstract class defining the interface for a Shape
class Shape(ABC):
def __init__(self, name):
self.name = name
@abstractmethod
def area(self):
pass
@abstractmethod
def perimeter(self):
pass
# Concrete class implementing the Shape interface for a Rectangle
class Rectangle(Shape):
def __init__(self, name, length, width):
super().__init__(name)
self.length = length
self.width = width
def area(self):
return self.length * self.width
def perimeter(self):
return 2 * (self.length + self.width)
# Concrete class implementing the Shape interface for a Circle
class Circle(Shape):
def __init__(self, name, radius):
super().__init__(name)
self.radius = radius
def area(self):
return 3.14 * self.radius * self.radius
def perimeter(self):
return 2 * 3.14 * self.radius
# Creating objects of the derived classes
rectangle = Rectangle("Rectangle", 5, 4)
circle = Circle("Circle", 3)
# Accessing methods defined by the Shape interface
print(f"{rectangle.name}: Area = {rectangle.area()}, Perimeter = {rectangle.perimeter()}")
print(f"{circle.name}: Area = {circle.area()}, Perimeter = {circle.perimeter()}")
```
To implement Data Abstraction , we have to import abc . ABC stands for Abstract Base Class . All those classes which want to implement data abstraction have to inherit from ABC.
@abstractmethod is a decorator provided by the abc module, which stands for "abstract method". It's used to define abstract methods within abstract base classes (ABCs). An abstract method is a method declared in a class, but it does not contain an implementation. Instead, it serves as a placeholder, and its concrete implementation must be provided by subclasses.
Abstract methods can be implemented by the derived classes.

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# Protocols in Python
Python can establish informal interfaces using protocols In order to improve code structure, reusability, and type checking. Protocols allow for progressive adoption and are more flexible than standard interfaces in other programming languages like JAVA, which are tight contracts that specify the methods and attributes a class must implement.
>Before going into depth of this topic let's understand another topic which is pre-requisite od this topic \#TypingModule
## Typing Module
This is a module in python which provides
1. Provides classes, functions, and type aliases.
2. Allows adding type annotations to our code.
3. Enhances code readability.
4. Helps in catching errors early.
### Type Hints in Python:
Type hints allow you to specify the expected data types of variables, function parameters, and return values. This can improve code readability and help with debugging.
Here is a simple function that adds two numbers:
```python
def add(a,b):
return a + b
add(10,20)
```
>Output: 30
While this works fine, adding type hints makes the code more understandable and serves as documentation:
```python
def add(a:int, b:int)->int:
return a + b
print(add(1,10))
```
>Output: 11
In this version, `a` and `b` are expected to be integers, and the function is expected to return an integer. This makes the function's purpose and usage clearer.
#### let's see another example
The function given below takes an iterable (it can be any off list, tuple, dict, set, frozeset, String... etc) and print it's content in a single line along with it's type.
```python
from typing import Iterable
# type alias
def print_all(l: Iterable)->None:
print(type(l),end=' ')
for i in l:
print(i,end=' ')
print()
l = [1,2,3,4,5] # type: List[int]
s = {1,2,3,4,5} # type: Set[int]
t = (1,2,3,4,5) # type: Tuple[int]
for iter_obj in [l,s,t]:
print_all(iter_obj)
```
Output:
> <class 'list'> 1 2 3 4 5
> <class 'set'> 1 2 3 4 5
> <class 'tuple'> 1 2 3 4 5
and now lets try calling the function `print_all` using a non-iterable object `int` as argument.
```python
a = 10
print_all(a) # This will raise an error
```
Output:
>TypeError: 'int' object is not iterable
This error occurs because `a` is an `integer`, and the `integer` class does not have any methods or attributes that make it work like an iterable. In other words, the integer class does not conform to the `Iterable` protocol.
**Benefits of Type Hints**
Using type hints helps in several ways:
1. **Error Detection**: Tools like mypy can catch type-related problems during development, decreasing runtime errors.
2. **Code Readability**: Type hints serve as documentation, making it easy to comprehend what data types are anticipated and returned.
3. **Improved Maintenance**: With unambiguous type expectations, maintaining and updating code becomes easier, especially in huge codebases.
Now that we have understood about type hints and typing module let's dive deep into protocols.
## Understanding Protocols
In Python, protocols define interfaces similar to Java interfaces. They let you specify methods and attributes that an object must implement without requiring inheritance from a base class. Protocols are part of the `typing` module and provide a way to enforce certain structures in your classes, enhancing type safety and code clarity.
### What is a Protocol?
A protocol specifies one or more method signatures that a class must implement to be considered as conforming to the protocol.
This concept is often referred to as "structural subtyping" or "duck typing," meaning that if an object implements the required methods and attributes, it can be treated as an instance of the protocol.
Let's write our own protocol:
```python
from typing import Protocol
# Define a Printable protocol
class Printable(Protocol):
def print(self) -> None:
"""Print the object"""
pass
# Book class implements the Printable protocol
class Book:
def __init__(self, title: str):
self.title = title
def print(self) -> None:
print(f"Book Title: {self.title}")
# print_object function takes a Printable object and calls its print method
def print_object(obj: Printable) -> None:
obj.print()
book = Book("Python Programming")
print_object(book)
```
Output:
> Book Title: Python Programming
In this example:
1. **Printable Protocol:** Defines an interface with a single method print.
2. **Book Class:** Implements the Printable protocol by providing a print method.
3. **print_object Function:** Accepts any object that conforms to the Printable protocol and calls its print method.
we got our output because the class `Book` confirms to the protocols `printable`.
similarly When you pass an object to `print_object` that does not conform to the Printable protocol, an error will occur. This is because the object does not implement the required `print` method.
Let's see an example:
```python
class Team:
def huddle(self) -> None:
print("Team Huddle")
c = Team()
print_object(c) # This will raise an error
```
Output:
>AttributeError: 'Team' object has no attribute 'print'
In this case:
- The `Team` class has a `huddle` method but does not have a `print` method.
- When `print_object` tries to call the `print` method on a `Team` instance, it raises an `AttributeError`.
> This is an important aspect of using protocols: they ensure that objects provide the necessary methods, leading to more predictable and reliable code.
**Ensuring Protocol Conformance**
To avoid such errors, you need to ensure that any object passed to `print_object` implements the `Printable` protocol. Here's how you can modify the `Team` class to conform to the protocol:
```python
class Team:
def __init__(self, name: str):
self.name = name
def huddle(self) -> None:
print("Team Huddle")
def print(self) -> None:
print(f"Team Name: {self.name}")
c = Team("Dream Team")
print_object(c)
```
Output:
>Team Name: Dream Team
The `Team` class now implements the `print` method, conforming to the `Printable` protocol. and hence, no longer raises an error.
### Protocols and Inheritance:
Protocols can also be used in combination with inheritance to create more complex interfaces.
we can do that by following these steps:
**Step 1 - Base protocol**: Define a base protocol that specifies a common set of methods and attributes.
**Step 2 - Derived Protocols**: Create derives protocols that extends the base protocol with addition requirements
**Step 3 - Polymorphism**: Objects can then conform to multiple protocols, allowing for Polymorphic behavior.
Let's see an example on this as well:
```python
from typing import Protocol
# Base Protocols
class Printable(Protocol):
def print(self) -> None:
"""Print the object"""
pass
# Base Protocols-2
class Serializable(Protocol):
def serialize(self) -> str:
pass
# Derived Protocol
class PrintableAndSerializable(Printable, Serializable):
pass
# class with implementation of both Printable and Serializable
class Book_serialize:
def __init__(self, title: str):
self.title = title
def print(self) -> None:
print(f"Book Title: {self.title}")
def serialize(self) -> None:
print(f"serialize: {self.title}")
# function accepts the object which implements PrintableAndSerializable
def test(obj: PrintableAndSerializable):
obj.print()
obj.serialize()
book = Book_serialize("lean-in")
test(book)
```
Output:
> Book Title: lean-in
serialize: lean-in
In this example:
**Printable Protocol:** Specifies a `print` method.
**Serializable Protocol:** Specifies a `serialize` method.
**PrintableAndSerializable Protocol:** Combines both `Printable` and `Serializable`.
**Book Class**: Implements both `print` and `serialize` methods, conforming to `PrintableAndSerializable`.
**test Function:** Accepts any object that implements the `PrintableAndSerializable` protocol.
If you try to pass an object that does not conform to the `PrintableAndSerializable` protocol to the test function, it will raise an `error`. Let's see an example:
```python
class Team:
def huddle(self) -> None:
print("Team Huddle")
c = Team()
test(c) # This will raise an error
```
output:
> AttributeError: 'Team' object has no attribute 'print'
In this case:
The `Team` class has a `huddle` method but does not implement `print` or `serialize` methods.
When test tries to call `print` and `serialize` on a `Team` instance, it raises an `AttributeError`.
**In Conclusion:**
>Python protocols offer a versatile and powerful means of defining interfaces, encouraging the decoupling of code, improving readability, and facilitating static type checking. They are particularly handy for scenarios involving file-like objects, bespoke containers, and any case where you wish to enforce certain behaviors without requiring inheritance from a specific base class. Ensuring that classes conform to protocols reduces runtime problems and makes your code more robust and maintainable.

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## Regular Expressions in Python
Regular expressions (regex) are a powerful tool for pattern matching and text manipulation.
Python's re module provides comprehensive support for regular expressions, enabling efficient text processing and validation.
## 1. Introduction to Regular Expressions
A regular expression is a sequence of characters defining a search pattern. Common use cases include validating input, searching within text, and extracting
specific patterns.
## 2. Basic Syntax
Literal Characters: Match exact characters (e.g., abc matches "abc").
Metacharacters: Special characters like ., *, ?, +, ^, $, [ ], and | used to build patterns.
**Common Metacharacters:**
* .: Any character except newline.
* ^: Start of the string.
* $: End of the string.
* *: 0 or more repetitions.
* +: 1 or more repetitions.
* ?: 0 or 1 repetition.
* []: Any one character inside brackets (e.g., [a-z]).
* |: Either the pattern before or after.
## 3. Using the re Module
**Key functions in the re module:**
* re.match(): Checks for a match at the beginning of the string.
* re.search(): Searches for a match anywhere in the string.
* re.findall(): Returns a list of all matches.
* re.sub(): Replaces matches with a specified string.
Examples:
```bash
import re
# Match at the beginning
print(re.match(r'\d+', '123abc').group()) # Output: 123
# Search anywhere
print(re.search(r'\d+', 'abc123').group()) # Output: 123
# Find all matches
print(re.findall(r'\d+', 'abc123def456')) # Output: ['123', '456']
# Substitute matches
print(re.sub(r'\d+', '#', 'abc123def456')) # Output: abc#def#
```
## 4. Compiling Regular Expressions
Compiling regular expressions improves performance for repeated use.
Example:
```bash
import re
pattern = re.compile(r'\d+')
print(pattern.match('123abc').group()) # Output: 123
print(pattern.search('abc123').group()) # Output: 123
print(pattern.findall('abc123def456')) # Output: ['123', '456']
```
## 5. Groups and Capturing
Parentheses () group and capture parts of the match.
Example:
```bash
import re
match = re.match(r'(\d{3})-(\d{2})-(\d{4})', '123-45-6789')
if match:
print(match.group()) # Output: 123-45-6789
print(match.group(1)) # Output: 123
print(match.group(2)) # Output: 45
print(match.group(3)) # Output: 6789
```
## 6. Special Sequences
Special sequences are shortcuts for common patterns:
* \d: Any digit.
* \D: Any non-digit.
* \w: Any alphanumeric character.
* \W: Any non-alphanumeric character.
* \s: Any whitespace character.
* \S: Any non-whitespace character.
Example:
```bash
import re
print(re.search(r'\w+@\w+\.\w+', 'Contact: support@example.com').group()) # Output: support@example.com
```
## Summary
Regular expressions are a versatile tool for text processing in Python. The re module offers powerful functions and metacharacters for pattern matching,
searching, and manipulation, making it an essential skill for handling complex text processing tasks.

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# Introduction to Type Hinting in Python
Type hinting is a feature in Python that allows you to specify the expected data types of variables, function arguments, and return values. It was introduced
in Python 3.5 via PEP 484 and has since become a standard practice to improve code readability and facilitate static analysis tools.
**Benefits of Type Hinting**
1. Improved Readability: Type hints make it clear what type of data is expected, making the code easier to understand for others and your future self.
2. Error Detection: Static analysis tools like MyPy can use type hints to detect type errors before runtime, reducing bugs and improving code quality.
3.Better Tooling Support: Modern IDEs and editors can leverage type hints to provide better autocompletion, refactoring, and error checking features.
4. Documentation: Type hints serve as a form of documentation, indicating the intended usage of functions and classes.
**Syntax of Type Hinting** <br>
Type hints can be added to variables, function arguments, and return values using annotations.
1. Variable Annotations:
```bash
age: int = 25
name: str = "Alice"
is_student: bool = True
```
2. Function Annotations:
```bash
def greet(name: str) -> str:
return f"Hello, {name}!"
```
3. Multiple Arguments and Return Types:
```bash
def add(a: int, b: int) -> int:
return a + b
```
4. Optional Types: Use the Optional type from the typing module for values that could be None.
```bash
from typing import Optional
def get_user_name(user_id: int) -> Optional[str]:
# Function logic here
return None # Example return value
```
5. Union Types: Use the Union type when a variable can be of multiple types.
```bash
from typing import Union
def get_value(key: str) -> Union[int, str]:
# Function logic here
return "value" # Example return value
```
6. List and Dictionary Types: Use the List and Dict types from the typing module for collections.
```bash
from typing import List, Dict
def process_data(data: List[int]) -> Dict[str, int]:
# Function logic here
return {"sum": sum(data)} # Example return value
```
7. Type Aliases: Create type aliases for complex types to make the code more readable.
```bash
from typing import List, Tuple
Coordinates = List[Tuple[int, int]]
def draw_shape(points: Coordinates) -> None:
# Function logic here
pass
```
**Example of Type Hinting in a Class** <br>
Here is a more comprehensive example using type hints in a class:
```bash
from typing import List
class Student:
def __init__(self, name: str, age: int, grades: List[int]) -> None:
self.name = name
self.age = age
self.grades = grades
def average_grade(self) -> float:
return sum(self.grades) / len(self.grades)
def add_grade(self, grade: int) -> None:
self.grades.append(grade)
# Example usage
student = Student("Alice", 20, [90, 85, 88])
print(student.average_grade()) # Output: 87.66666666666667
student.add_grade(92)
print(student.average_grade()) # Output: 88.75
```
### Conclusion
Type hinting in Python enhances code readability, facilitates error detection through static analysis, and improves tooling support. By adopting
type hinting, you can write clearer and more maintainable code, reducing the likelihood of bugs and making your codebase easier to navigate for yourself and others.

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# FastAPI
## Table of Contents
- [Introduction](#introduction)
- [Features](#features)
- [Installation](#installation)
- [Making First API](#making-first-api)
- [GET Method](#get-method)
- [Running Server and calling API](#running-server-and-calling-api)
- [Path Parameters](#pata-parameters)
- [Query Parameters](#query-parameters)
- [POST Method](#post-method)
- [PUT Method](#put-method)
- [Additional Content](#additional-content)
- [Swagger UI](#swagger-ui)
## Introduction
FastAPI is a modern, web-framework for building APIs with Python.
It uses python 3.7+
## Features
1. **Speed ⚡:** FastAPI is built on top of Starlette, a lightweight ASGI framework. It's designed for high performance and handles thousands of requests per second .
2. **Easy to use 😃:** FastAPI is designed to be intuitive and easy to use, especially for developers familiar with Python. It uses standard Python type hints for request and response validation, making it easy to understand and write code.
3. **Automatic Interactive API Documentation generation 🤩:** FastAPI automatically generates interactive API documentation (Swagger UI or ReDoc) based on your code and type annotations. Swagger UI also allows you to test API endpoints.
4. **Asynchronous Support 🔁:** FastAPI fully supports asynchronous programming, allowing you to write asynchronous code with async/await syntax. This enables handling high-concurrency scenarios and improves overall performance.
Now, lets get hands-on with FastAPI.
## Installation
Make sure that you have python version 3.7 or greater.
Then, simply open your command shell and give the following command.
```bash
pip install fastapi
```
After this, you need to install uvicorn. uvicorn is an ASGI server on which we will be running our API.
```bash
pip install uvicorn
```
## Making First API
After successful installation we will be moving towards making an API and seeing how to use it.
Firstly, the first thing in an API is its root/index page which is sent as response when API is called.
Follow the given steps to make your first FastAPI🫨
First, lets import FastAPI to get things started.
```python
from fastapi import FastAPI
app = FastAPI()
```
Now, we will write the ``GET`` method for the root of the API. As you have already seen, the GET method is ``HTTP request`` method used to fetch data from a source. In web development, it is primarily used to *retrieve data* from server.
The root of the app is ``"/"`` When the API will be called, response will be generated by on this url: ```localhost:8000```
### GET method
Following is the code to write GET method which will be calling API.
When the API is called, the ``read_root()`` function will be hit and the JSON response will be returned which will be shown on your web browser.
```python
@app.get("/")
def read_root():
return {"Hello": "World"}
```
Tadaaa! you have made your first FastAPI! Now lets run it!
### Running Server and calling API
Open your terminal and give following command:
```bash
uvicorn myapi:app --reload
```
Here, ``myapi`` is the name of your API which is name of your python file. ``app`` is the name you have given to your API in assignment ``app = FastAPI()``
After running this command, uvicorn server will be live and you can access your API.
As right now we have only written root ``GET`` method, only its corresponding response will be displayed.
On running this API, we get the response in JSON form:
```json
{
"Hello": "World"
}
```
## Path Parameters
Path parameters are a way to send variables to an API endpoint so that an operation may be perfomed on it.
This feature is particularly useful for defining routes that need to operate on resources identified by unique identifiers, such as user IDs, product IDs, or any other unique value.
### Example
Lets take an example to make it understandable.
Assume that we have some Students 🧑‍🎓 in our class and we have saved their data in form of dictionary in our API (in practical scenarios they will be saved in a database and API will query database).
So we have a student dictionary that looks something like this:
```python
students = {
1: {
"name": "John",
"age": 17,
"class": "year 12"
},
2: {
"name": "Jane",
"age": 16,
"class": "year 11"
},
3: {
"name": "Alice",
"age": 17,
"class": "year 12"
}
}
```
Here, keys are ``student_id``.
Let's say user wants the data of the student whose ID is 2. Here, we will take ID as **path parameter** from the user and return the data of that ID.
Lets see how it will be done!
```python
@app.get("/students/{student_id}")
def read_student(student_id: int):
return students[student_id]
```
Here is the explanatory breakdown of the method:
- ``/students`` is the URL of students endpoint in API.
- ``{student_id}`` is the path parameter, which is a dynamic variable the user will give to fetch the record of a particular student.
- ``def read_student(student_id: int)`` is the signature of function which takes the student_id we got from path parameter. Its type is defined as ``int`` as our ID will be an integer.
**Note that there will be automatic type checking of the parameter. If it is not same as type defined in method, an Error response ⛔ will be generated.**
- ``return students[student_id]`` will return the data of required student from dictionary.
When the user passes the URL ``http://127.0.0.1:8000/students/1`` the data of student with student_id=1 is fetched and displayed.
In this case following output will be displayed:
```json
{
"name": "John",
"age": 17,
"class": "year 12"
}
```
## Query Parameters
Query parameters in FastAPI allow you to pass data to your API endpoints via the URL's query string. This is useful for filtering, searching, and other operations that do not fit well with the path parameters.
Query parameters are specified after the ``?`` symbol in the URL and are typically used for optional parameters.
### Example
Lets continue the example of students to understand the query parameters.
Assume that we want to search students by name. In this case, we will be sending datat in query parameter which will be read by our method and respective result will be returned.
Lets see the method:
```python
@app.get("/get-by-name")
def read_student(name: str):
for student_id in students:
if students[student_id]["name"] == name:
return students[student_id]
return {"Error": "Student not found"}
```
Here is the explanatory breakdown of this process:
- ``/get-by-name`` is the URL of the endpoint. After this URL, client will enter the query parameter(s).
- ``http://127.0.0.1:8000/get-by-name?name=Jane`` In this URL, ``name=Jane`` is the query parameter. It means that user needs to search the student whose name is Jane. When you hit this URL, ``read_student(name:str)`` method is called and respective response is returned.
In this case, the output will be:
```json
{
"name": "Jane",
"age": 16,
"class": "year 11"
}
```
If we pass a name that doesn't exist in dictionary, Error response will be returned.
## POST Method
The ``POST`` method in FastAPI is used to **create resources** or submit data to an API endpoint. This method typically involves sending data in the request body, which the server processes to create or modify resources.
**⛔ In case of ``GET`` method, sent data is part of URL, but in case of ``POST`` metohod, sent data is part of request body.**
### Example
Again continuing with the example of student. Now, lets assume we need to add student. Following is the ``POST`` method to do this:
```python
@app.post("/create-student/{student_id}")
def create_student(student_id: int, student: dict):
if student_id in students:
return {"Error": "Student exists"}
students[student_id] = student
return students
```
Here is the explanation of process:
- ``/create-student/{student_id}`` shows that only student_id will be part of URL, rest of the data will be sent in request body.
- Data in the request body will be in JSON format and will be received in ``student: dict``
- Data sent in JSON format is given as:
```json
{
"name":"Seerat",
"age":22,
"class":"8 sem"
}
```
*Note:* I have used Swagger UI to send data in request body to test my ``POST`` method but you may use any other API tesing tool like Postman etc.
- This new student will be added in the dictionary, and if operation is successful, new dictionary will be returned as response.
Following is the output of this ``POST`` method call:
```json
{
"1": {
"name": "John",
"age": 17,
"class": "year 12"
},
"2": {
"name": "Jane",
"age": 16,
"class": "year 11"
},
"3": {
"name": "Alice",
"age": 17,
"class": "year 12"
},
"4": {
"name": "Seerat",
"age": 22,
"class": "8 sem"
}
}
```
## PUT Method
The ``PUT`` method in FastAPI is used to **update** existing resources or create resources if they do not already exist. It is one of the standard HTTP methods and is idempotent, meaning that multiple identical requests should have the same effect as a single request.
### Example
Let's update the record of a student.
```python
@app.put("/update-student/{student_id}")
def update_student(student_id: int, student: dict):
if student_id not in students:
return {"Error": "Student does not exist"}
students[student_id] = student
return students
```
``PUT`` method is nearly same as ``POST`` method but ``PUT`` is indempotent while ``POST`` is not.
The given method will update an existing student record and if student doesnt exist, it'll send error response.
## Additional Content
### Swagger UI
Swagger UI automatically generates UI for API tesing. Just write ``/docs`` with the URL and UI mode of Swagger UI will be launched.
Following Screenshot shows the Swagger UI
![App Screenshot](assets/image.png)
Here is how I tested ``POST`` method in UI:
![Screenshot](assets/image2.png)
That's all for FastAPI for now.... Happy Learning!

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# List of sections
- [API Methods](api-methods.md)
- [FastAPI](fast-api.md)

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# List of sections
- [Section title](filename.md)
- [Introduction to MySQL and Queries](intro_mysql_queries.md)
- [SQLAlchemy and Aggregation Functions](sqlalchemy-aggregation.md)

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# Introduction to MySQL Queries
MySQL is a widely-used open-source relational database management system (RDBMS) that utilizes SQL (Structured Query Language) for managing and querying data. In Python, the **mysql-connector-python** library allows you to connect to MySQL databases and execute SQL queries, providing a way to interact with the database from within a Python program.
## Prerequisites
* Python and MySQL Server must be installed and configured.
* The library: **mysql-connector-python** must be installed.
## Establishing connection with server
To establish a connection with the MySQL server, you need to import the **mysql.connector** module and create a connection object using the **connect()** function by providing the prompt server details as mentioned.
```python
import mysql.connector
con = mysql.connector.connect(
host ="localhost",
user ="root",
passwd ="12345"
)
print((con.is_connected()))
```
Having established a connection with the server, you get the following output :
```
True
```
## Creating a Database [CREATE]
To create a database, you need to execute the **CREATE DATABASE** query. The following code snippet demonstrates how to create a database named **GSSOC**.
```python
import mysql.connector
# Establish the connection
conn = mysql.connector.connect(
host="localhost",
user="root",
password="12345"
)
# Create a cursor object
cursor = conn.cursor()
# Execute the query to show databases
cursor.execute("SHOW DATABASES")
# Fetch and print the databases
databases = cursor.fetchall()
for database in databases:
print(database[0])
# Execute the query to create database GSSOC
cursor.execute("CREATE DATABASE GSSOC")
print("\nAfter creation of the database\n")
# Execute the query to show databases
cursor.execute("SHOW DATABASES")
# Fetch and print the databases
databases = cursor.fetchall()
for database in databases:
print(database[0])
cursor.close()
conn.close()
```
You can observe in the output below, after execution of the query a new database named **GSSOC** has been created.
#### Output:
```
information_schema
mysql
performance_schema
sakila
sys
world
After creation of the database
gssoc
information_schema
mysql
performance_schema
sakila
sys
world
```
## Creating a Table in the Database [CREATE]
Now, we will create a table in the database. We will create a table named **example_table** in the database **GSSOC**. We will execute **CREATE TABLE** query and provide the fields for the table as mentioned in the code below:
```python
import mysql.connector
# Establish the connection
conn = mysql.connector.connect(
host="localhost",
user="root",
password="12345"
)
# Create a cursor object
cursor = conn.cursor()
# Execute the query to show tables
cursor.execute("USE GSSOC")
cursor.execute("SHOW TABLES")
# Fetch and print the tables
tables = cursor.fetchall()
print("Before creation of table\n")
for table in tables:
print(table[0])
create_table_query = """
CREATE TABLE example_table (
name VARCHAR(255) NOT NULL,
age INT NOT NULL,
email VARCHAR(255)
)
"""
# Execute the query
cursor.execute(create_table_query)
# Commit the changes
conn.commit()
print("\nAfter creation of Table\n")
# Execute the query to show tables in GSSOC
cursor.execute("SHOW TABLES")
# Fetch and print the tables
tables = cursor.fetchall()
for table in tables:
print(table[0])
cursor.close()
conn.close()
```
#### Output:
```
Before creation of table
After creation of Table
example_table
```
## Inserting Data [INSERT]
To insert data in an existing table, the **INSERT INTO** query is used, followed by the name of the table in which the data needs to be inserted. The following code demonstrates the insertion of multiple records in the table by **executemany()**.
```python
import mysql.connector
# Establish the connection
conn = mysql.connector.connect(
host="localhost",
user="root",
password="12345"
)
# Create a cursor object
cursor = conn.cursor()
cursor.execute("USE GSSOC")
# SQL query to insert data
insert_data_query = """
INSERT INTO example_table (name, age, email)
VALUES (%s, %s, %s)
"""
# Data to be inserted
data_to_insert = [
("John Doe", 28, "john.doe@example.com"),
("Jane Smith", 34, "jane.smith@example.com"),
("Sam Brown", 22, "sam.brown@example.com")
]
# Execute the query for each data entry
cursor.executemany(insert_data_query, data_to_insert)
conn.commit()
cursor.close()
conn.close()
```
## Displaying Data [SELECT]
To display the data from a table, the **SELECT** query is used. The following code demonstrates the display of data from the table.
```python
import mysql.connector
# Establish the connection
conn = mysql.connector.connect(
host="localhost",
user="root",
password="12345"
)
# Create a cursor object
cursor = conn.cursor()
cursor.execute("USE GSSOC")
# SQL query to display data
display_data_query = "SELECT * FROM example_table"
# Execute the query for each data entry
cursor.execute(display_data_query)
# Fetch all the rows
rows = cursor.fetchall()
# Print the column names
column_names = [desc[0] for desc in cursor.description]
print(column_names)
# Print the rows
for row in rows:
print(row)
cursor.close()
conn.close()
```
#### Output :
```
['name', 'age', 'email']
('John Doe', 28, 'john.doe@example.com')
('Jane Smith', 34, 'jane.smith@example.com')
('Sam Brown', 22, 'sam.brown@example.com')
```
## Updating Data [UPDATE]
To update data in the table, **UPDATE** query is used. In the following code, we will be updating the email and age of the record where the name is John Doe.
```python
import mysql.connector
# Establish the connection
conn = mysql.connector.connect(
host="localhost",
user="root",
password="12345"
)
# Create a cursor object
cursor = conn.cursor()
cursor.execute("USE GSSOC")
# SQL query to display data
display_data_query = "SELECT * FROM example_table"
# SQL Query to update data of John Doe
update_data_query = """
UPDATE example_table
SET age = %s, email = %s
WHERE name = %s
"""
# Data to be updated
data_to_update = (30, "new.email@example.com", "John Doe")
# Execute the query
cursor.execute(update_data_query, data_to_update)
# Commit the changes
conn.commit()
# Execute the query for each data entry
cursor.execute(display_data_query)
# Fetch all the rows
rows = cursor.fetchall()
# Print the column names
column_names = [desc[0] for desc in cursor.description]
print(column_names)
# Print the rows
for row in rows:
print(row)
cursor.close()
conn.close()
```
#### Output:
```
['name', 'age', 'email']
('John Doe', 30, 'new.email@example.com')
('Jane Smith', 34, 'jane.smith@example.com')
('Sam Brown', 22, 'sam.brown@example.com')
```
## Deleting Data [DELETE]
In this segment, we will Delete the record named "John Doe" using the **DELETE** and **WHERE** statements in the query. The following code explains the same and the observe the change in output.
```python
import mysql.connector
# Establish the connection
conn = mysql.connector.connect(
host="localhost",
user="root",
password="12345"
)
# Create a cursor object
cursor = conn.cursor()
cursor.execute("USE GSSOC")
# SQL query to display data
display_data_query = "SELECT * FROM example_table"
# SQL query to delete data
delete_data_query = "DELETE FROM example_table WHERE name = %s"
# Data to be deleted
data_to_delete = ("John Doe",)
# Execute the query
cursor.execute(delete_data_query, data_to_delete)
# Commit the changes
conn.commit()
# Execute the query for each data entry
cursor.execute(display_data_query)
# Fetch all the rows
rows = cursor.fetchall()
# Print the column names
column_names = [desc[0] for desc in cursor.description]
print(column_names)
# Print the rows
for row in rows:
print(row)
cursor.close()
conn.close()
```
#### Output:
```
['name', 'age', 'email']
('Jane Smith', 34, 'jane.smith@example.com')
('Sam Brown', 22, 'sam.brown@example.com')
```
## Deleting the Table/Database [DROP]
For deleting a table, you can use the **DROP** query in the following manner:
```python
import mysql.connector
# Establish the connection
conn = mysql.connector.connect(
host="localhost",
user="root",
password="12345"
)
# Create a cursor object
cursor = conn.cursor()
cursor.execute("USE GSSOC")
# SQL query to delete the table
delete_table_query = "DROP TABLE IF EXISTS example_table"
# Execute the query
cursor.execute(delete_table_query)
# Verify the table deletion
cursor.execute("SHOW TABLES LIKE 'example_table'")
result = cursor.fetchone()
cursor.close()
conn.close()
if result:
print("Table deletion failed.")
else:
print("Table successfully deleted.")
```
#### Output:
```
Table successfully deleted.
```
Similarly, you can delete the database also by using the **DROP** and accordingly changing the query to be executed.

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# SQLAlchemy
SQLAlchemy is a powerful and flexible SQL toolkit and Object-Relational Mapping (ORM) library for Python. It is a versatile library that bridges the gap between Python applications and relational databases.
SQLAlchemy allows the user to write database-agnostic code that can work with a variety of relational databases such as SQLite, MySQL, PostgreSQL, Oracle, and Microsoft SQL Server. The ORM layer in SQLAlchemy allows developers to map Python classes to database tables. This means you can interact with your database using Python objects instead of writing raw SQL queries.
## Setting up the Environment
* Python and MySQL Server must be installed and configured.
* The library: **mysql-connector-python** and **sqlalchemy** must be installed.
```bash
pip install sqlalchemy mysql-connector-python
```
* If not installed, you can install them using the above command in terminal,
## Establishing Connection with Database
* Create a connection with the database using the following code snippet:
```python
from sqlalchemy import create_engine
from sqlalchemy.orm import declarative_base
from sqlalchemy.orm import sessionmaker
DATABASE_URL = 'mysql+mysqlconnector://root:12345@localhost/gssoc'
engine = create_engine(DATABASE_URL)
Session = sessionmaker(bind=engine)
session = Session()
Base = declarative_base()
```
* The connection string **DATABASE_URL** is passed as an argument to **create_engine** function which is used to create a connection to the database. This connection string contains the database credentials such as the database type, username, password, and database name.
* The **sessionmaker** function is used to create a session object which is used to interact with the database
* The **declarative_base** function is used to create a base class for all the database models. This base class is used to define the structure of the database tables.
## Creating Tables
* The following code snippet creates a table named **"products"** in the database:
```python
from sqlalchemy import Column, Integer, String, Float
class Product(Base):
__tablename__ = 'products'
id = Column(Integer, primary_key=True)
name = Column(String(50))
category = Column(String(50))
price = Column(Float)
quantity = Column(Integer)
Base.metadata.create_all(engine)
```
* The **Product class** inherits from **Base**, which is a base class for all the database models.
* The **Base.metadata.create_all(engine)** statement is used to create the table in the database. The engine object is a connection to the database that was created earlier.
## Inserting Data for Aggregation Functions
* The following code snippet inserts data into the **"products"** table:
```python
products = [
Product(name='Laptop', category='Electronics', price=1000, quantity=50),
Product(name='Smartphone', category='Electronics', price=700, quantity=150),
Product(name='Tablet', category='Electronics', price=400, quantity=100),
Product(name='Headphones', category='Accessories', price=100, quantity=200),
Product(name='Charger', category='Accessories', price=20, quantity=300),
]
session.add_all(products)
session.commit()
```
* A list of **Product** objects is created. Each Product object represents a row in the **products table** in the database.
* The **add_all** method of the session object is used to add all the Product objects to the session. This method takes a **list of objects as an argument** and adds them to the session.
* The **commit** method of the session object is used to commit the changes made to the database.
## Aggregation Functions
SQLAlchemy provides functions that correspond to SQL aggregation functions and are available in the **sqlalchemy.func module**.
### COUNT
The **COUNT** function returns the number of rows in a result set. It can be demonstrated using the following code snippet:
```python
from sqlalchemy import func
total_products = session.query(func.count(Product.id)).scalar()
print(f'Total products: {total_products}')
```
### SUM
The **SUM** function returns the sum of all values in a column. It can be demonstrated using the following code snippet:
```python
total_price = session.query(func.sum(Product.price)).scalar()
print(f'Total price of all products: {total_price}')
```
### AVG
The **AVG** function returns the average of all values in a column. It can be demonstrated by the following code snippet:
```python
average_price = session.query(func.avg(Product.price)).scalar()
print(f'Average price of products: {average_price}')
```
### MAX
The **MAX** function returns the maximum value in a column. It can be demonstrated using the following code snippet :
```python
max_price = session.query(func.max(Product.price)).scalar()
print(f'Maximum price of products: {max_price}')
```
### MIN
The **MIN** function returns the minimum value in a column. It can be demonstrated using the following code snippet:
```python
min_price = session.query(func.min(Product.price)).scalar()
print(f'Minimum price of products: {min_price}')
```
In general, the aggregation functions can be implemented by utilising the **session** object to execute the desired query on the table present in a database using the **query()** method. The **scalar()** method is called on the query object to execute the query and return a single value

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# Divide and Conquer Algorithms
Divide and Conquer is a paradigm for solving problems that involves breaking a problem into smaller sub-problems, solving the sub-problems recursively, and then combining their solutions to solve the original problem.
## Merge Sort
Merge Sort is a popular sorting algorithm that follows the divide and conquer strategy. It divides the input array into two halves, recursively sorts the halves, and then merges them.
**Algorithm Overview:**
- **Divide:** Divide the unsorted list into two sublists of about half the size.
- **Conquer:** Recursively sort each sublist.
- **Combine:** Merge the sorted sublists back into one sorted list.
```python
def merge_sort(arr):
if len(arr) > 1:
mid = len(arr) // 2
left_half = arr[:mid]
right_half = arr[mid:]
merge_sort(left_half)
merge_sort(right_half)
i = j = k = 0
while i < len(left_half) and j < len(right_half):
if left_half[i] < right_half[j]:
arr[k] = left_half[i]
i += 1
else:
arr[k] = right_half[j]
j += 1
k += 1
while i < len(left_half):
arr[k] = left_half[i]
i += 1
k += 1
while j < len(right_half):
arr[k] = right_half[j]
j += 1
k += 1
arr = [12, 11, 13, 5, 6, 7]
merge_sort(arr)
print("Sorted array:", arr)
```
## Complexity Analysis
- **Time Complexity:** O(n log n) in all cases
- **Space Complexity:** O(n) additional space for the merge operation
---

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# Dynamic Programming
Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems and solving each subproblem only once. It stores the solutions to subproblems to avoid redundant computations, making it particularly useful for optimization problems where the solution can be obtained by combining solutions to smaller subproblems.
## Real-Life Examples of Dynamic Programming
- **Fibonacci Sequence:** Computing the nth Fibonacci number efficiently.
- **Shortest Path:** Finding the shortest path in a graph from a source to a destination.
- **String Edit Distance:** Calculating the minimum number of operations required to transform one string into another.
- **Knapsack Problem:** Maximizing the value of items in a knapsack without exceeding its weight capacity.
# Some Common Dynamic Programming Techniques
# 1. Fibonacci Sequence
The Fibonacci sequence is a classic example used to illustrate dynamic programming. It is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1.
**Algorithm Overview:**
- **Base Cases:** The first two numbers in the Fibonacci sequence are defined as 0 and 1.
- **Memoization:** Store the results of previously computed Fibonacci numbers to avoid redundant computations.
- **Recurrence Relation:** Compute each Fibonacci number by adding the two preceding numbers.
## Fibonacci Sequence Code in Python (Top-Down Approach with Memoization)
```python
def fibonacci(n, memo={}):
if n in memo:
return memo[n]
if n <= 1:
return n
memo[n] = fibonacci(n-1, memo) + fibonacci(n-2, memo)
return memo[n]
n = 10
print(f"The {n}th Fibonacci number is: {fibonacci(n)}.")
```
## Fibonacci Sequence Code in Python (Bottom-Up Approach)
```python
def fibonacci(n):
fib = [0, 1]
for i in range(2, n + 1):
fib.append(fib[i - 1] + fib[i - 2])
return fib[n]
n = 10
print(f"The {n}th Fibonacci number is: {fibonacci(n)}.")
```
## Complexity Analysis
- **Time Complexity**: O(n) for both approaches
- **Space Complexity**: O(n) for the top-down approach (due to memoization), O(1) for the bottom-up approach
</br>
<hr>
</br>
# 2. Longest Common Subsequence
The longest common subsequence (LCS) problem is to find the longest subsequence common to two sequences. A subsequence is a sequence that appears in the same relative order but not necessarily contiguous.
**Algorithm Overview:**
- **Base Cases:** If one of the sequences is empty, the LCS is empty.
- **Memoization:** Store the results of previously computed LCS lengths to avoid redundant computations.
- **Recurrence Relation:** Compute the LCS length by comparing characters of the sequences and making decisions based on whether they match.
## Longest Common Subsequence Code in Python (Top-Down Approach with Memoization)
```python
def longest_common_subsequence(X, Y, m, n, memo={}):
if (m, n) in memo:
return memo[(m, n)]
if m == 0 or n == 0:
return 0
if X[m - 1] == Y[n - 1]:
memo[(m, n)] = 1 + longest_common_subsequence(X, Y, m - 1, n - 1, memo)
else:
memo[(m, n)] = max(longest_common_subsequence(X, Y, m, n - 1, memo),
longest_common_subsequence(X, Y, m - 1, n, memo))
return memo[(m, n)]
X = "AGGTAB"
Y = "GXTXAYB"
print("Length of Longest Common Subsequence:", longest_common_subsequence(X, Y, len(X), len(Y)))
```
## Complexity Analysis
- **Time Complexity**: O(m * n) for the top-down approach, where m and n are the lengths of the input sequences
- **Space Complexity**: O(m * n) for the memoization table
</br>
<hr>
</br>
# 3. 0-1 Knapsack Problem
The 0-1 knapsack problem is a classic optimization problem where the goal is to maximize the total value of items selected while keeping the total weight within a specified limit.
**Algorithm Overview:**
- **Base Cases:** If the capacity of the knapsack is 0 or there are no items to select, the total value is 0.
- **Memoization:** Store the results of previously computed subproblems to avoid redundant computations.
- **Recurrence Relation:** Compute the maximum value by considering whether to include the current item or not.
## 0-1 Knapsack Problem Code in Python (Top-Down Approach with Memoization)
```python
def knapsack(weights, values, capacity, n, memo={}):
if (capacity, n) in memo:
return memo[(capacity, n)]
if n == 0 or capacity == 0:
return 0
if weights[n - 1] > capacity:
memo[(capacity, n)] = knapsack(weights, values, capacity, n - 1, memo)
else:
memo[(capacity, n)] = max(values[n - 1] + knapsack(weights, values, capacity - weights[n - 1], n - 1, memo),
knapsack(weights, values, capacity, n - 1, memo))
return memo[(capacity, n)]
weights = [10, 20, 30]
values = [60, 100, 120]
capacity = 50
n = len(weights)
print("Maximum value that can be obtained:", knapsack(weights, values, capacity, n))
```
## Complexity Analysis
- **Time Complexity**: O(n * W) for the top-down approach, where n is the number of items and W is the capacity of the knapsack
- **Space Complexity**: O(n * W) for the memoization table
</br>
<hr>
</br>

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# Graph Data Stucture
Graph is a non-linear data structure consisting of vertices and edges. It is a powerful tool for representing and analyzing complex relationships between objects or entities.
## Components of a Graph
1. **Vertices:** Vertices are the fundamental units of the graph. Sometimes, vertices are also known as vertex or nodes. Every node/vertex can be labeled or unlabeled.
2. **Edges:** Edges are drawn or used to connect two nodes of the graph. It can be ordered pair of nodes in a directed graph. Edges can connect any two nodes in any possible way. There are no rules. very edge can be labelled/unlabelled.
## Basic Operations on Graphs
- Insertion of Nodes/Edges in the graph
- Deletion of Nodes/Edges in the graph
- Searching on Graphs
- Traversal of Graphs
## Types of Graph
**1. Undirected Graph:** In an undirected graph, edges have no direction, and they represent symmetric relationships between nodes. If there is an edge between node A and node B, you can travel from A to B and from B to A.
**2. Directed Graph (Digraph):** In a directed graph, edges have a direction, indicating a one-way relationship between nodes. If there is an edge from node A to node B, you can travel from A to B but not necessarily from B to A.
**3. Weighted Graph:** In a weighted graph, edges have associated weights or costs. These weights can represent various attributes such as distance, cost, or capacity. Weighted graphs are commonly used in applications like route planning or network optimization.
**4. Cyclic Graph:** A cyclic graph contains at least one cycle, which is a path that starts and ends at the same node. In other words, you can traverse the graph and return to a previously visited node by following the edges.
**5. Acyclic Graph:** An acyclic graph, as the name suggests, does not contain any cycles. This type of graph is often used in scenarios where a cycle would be nonsensical or undesirable, such as representing dependencies between tasks or events.
**6. Tree:** A tree is a special type of acyclic graph where each node has a unique parent except for the root node, which has no parent. Trees have a hierarchical structure and are frequently used in data structures like binary trees or decision trees.
## Representation of Graphs
There are two ways to store a graph:
1. **Adjacency Matrix:**
In this method, the graph is stored in the form of the 2D matrix where rows and columns denote vertices. Each entry in the matrix represents the weight of the edge between those vertices.
```python
def create_adjacency_matrix(graph):
num_vertices = len(graph)
adj_matrix = [[0] * num_vertices for _ in range(num_vertices)]
for i in range(num_vertices):
for j in range(num_vertices):
if graph[i][j] == 1:
adj_matrix[i][j] = 1
adj_matrix[j][i] = 1
return adj_matrix
graph = [
[0, 1, 0, 0],
[1, 0, 1, 0],
[0, 1, 0, 1],
[0, 0, 1, 0]
]
adj_matrix = create_adjacency_matrix(graph)
for row in adj_matrix:
print(' '.join(map(str, row)))
```
2. **Adjacency List:**
In this method, the graph is represented as a collection of linked lists. There is an array of pointer which points to the edges connected to that vertex.
```python
def create_adjacency_list(edges, num_vertices):
adj_list = [[] for _ in range(num_vertices)]
for u, v in edges:
adj_list[u].append(v)
adj_list[v].append(u)
return adj_list
if __name__ == "__main__":
num_vertices = 4
edges = [(0, 1), (0, 2), (1, 2), (2, 3), (3, 1)]
adj_list = create_adjacency_list(edges, num_vertices)
for i in range(num_vertices):
print(f"{i} -> {' '.join(map(str, adj_list[i]))}")
```
`Output`
`0 -> 1 2`
`1 -> 0 2 3`
`2 -> 0 1 3`
`3 -> 2 1 `
# Traversal Techniques
## Breadth First Search (BFS)
- It is a graph traversal algorithm that explores all the vertices in a graph at the current depth before moving on to the vertices at the next depth level.
- It starts at a specified vertex and visits all its neighbors before moving on to the next level of neighbors.
BFS is commonly used in algorithms for pathfinding, connected components, and shortest path problems in graphs.
**Steps of BFS algorithms**
- **Step 1:** Initially queue and visited arrays are empty.
- **Step 2:** Push node 0 into queue and mark it visited.
- **Step 3:** Remove node 0 from the front of queue and visit the unvisited neighbours and push them into queue.
- **Step 4:** Remove node 1 from the front of queue and visit the unvisited neighbours and push them into queue.
- **Step 5:** Remove node 2 from the front of queue and visit the unvisited neighbours and push them into queue.
- **Step 6:** Remove node 3 from the front of queue and visit the unvisited neighbours and push them into queue.
- **Step 7:** Remove node 4 from the front of queue and visit the unvisited neighbours and push them into queue.
```python
from collections import deque
def bfs(adjList, startNode, visited):
q = deque()
visited[startNode] = True
q.append(startNode)
while q:
currentNode = q.popleft()
print(currentNode, end=" ")
for neighbor in adjList[currentNode]:
if not visited[neighbor]:
visited[neighbor] = True
q.append(neighbor)
def addEdge(adjList, u, v):
adjList[u].append(v)
def main():
vertices = 5
adjList = [[] for _ in range(vertices)]
addEdge(adjList, 0, 1)
addEdge(adjList, 0, 2)
addEdge(adjList, 1, 3)
addEdge(adjList, 1, 4)
addEdge(adjList, 2, 4)
visited = [False] * vertices
print("Breadth First Traversal", end=" ")
bfs(adjList, 0, visited)
if __name__ == "__main__": #Output : Breadth First Traversal 0 1 2 3 4
main()
```
- **Time Complexity:** `O(V+E)`, where V is the number of nodes and E is the number of edges.
- **Auxiliary Space:** `O(V)`
## Depth-first search
Depth-first search is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
**Steps of DFS algorithms**
- **Step 1:** Initially stack and visited arrays are empty.
- **Step 2:** Visit 0 and put its adjacent nodes which are not visited yet into the stack.
- **Step 3:** Now, Node 1 at the top of the stack, so visit node 1 and pop it from the stack and put all of its adjacent nodes which are not visited in the stack.
- **Step 4:** Now, Node 2 at the top of the stack, so visit node 2 and pop it from the stack and put all of its adjacent nodes which are not visited (i.e, 3, 4) in the stack.
- **Step 5:** Now, Node 4 at the top of the stack, so visit node 4 and pop it from the stack and put all of its adjacent nodes which are not visited in the stack.
- **Step 6:** Now, Node 3 at the top of the stack, so visit node 3 and pop it from the stack and put all of its adjacent nodes which are not visited in the stack.
```python
from collections import defaultdict
class Graph:
def __init__(self):
self.graph = defaultdict(list)
def addEdge(self, u, v):
self.graph[u].append(v)
def DFSUtil(self, v, visited):
visited.add(v)
print(v, end=' ')
for neighbour in self.graph[v]:
if neighbour not in visited:
self.DFSUtil(neighbour, visited)
def DFS(self, v):
visited = set()
self.DFSUtil(v, visited)
if __name__ == "__main__":
g = Graph()
g.addEdge(0, 1)
g.addEdge(0, 2)
g.addEdge(1, 2)
g.addEdge(2, 0)
g.addEdge(2, 3)
g.addEdge(3, 3)
print("Depth First Traversal (starting from vertex 2): ",g.DFS(2))
```
`Output: Depth First Traversal (starting from vertex 2): 2 0 1 3 `
- **Time complexity:** `O(V + E)`, where V is the number of vertices and E is the number of edges in the graph.
- **Auxiliary Space:** `O(V + E)`, since an extra visited array of size V is required, And stack size for iterative call to DFS function.
</br>

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# Greedy Algorithms
Greedy algorithms are simple, intuitive algorithms that make a sequence of choices at each step with the hope of finding a global optimum. They are called "greedy" because at each step, they choose the most advantageous option without considering the future consequences. Despite their simplicity, greedy algorithms are powerful tools for solving optimization problems, especially when the problem exhibits the greedy-choice property.
## Real-Life Examples of Greedy Algorithms
- **Coin Change:** Finding the minimum number of coins to make a certain amount of change.
- **Job Scheduling:** Assigning tasks to machines to minimize completion time.
- **Huffman Coding:** Constructing an optimal prefix-free binary code for data compression.
- **Fractional Knapsack:** Selecting items to maximize the value within a weight limit.
# Some Common Greedy Algorithms
# 1. Coin Change Problem
The coin change problem is a classic example of a greedy algorithm. Given a set of coin denominations and a target amount, the objective is to find the minimum number of coins required to make up that amount.
**Algorithm Overview:**
- **Greedy Strategy:** At each step, the algorithm selects the largest denomination coin that is less than or equal to the remaining amount.
- **Repeat Until Amount is Zero:** The process continues until the remaining amount becomes zero.
## Coin Change Code in Python
```python
def coin_change(coins, amount):
coins.sort(reverse=True)
num_coins = 0
for coin in coins:
num_coins += amount // coin
amount %= coin
if amount == 0:
return num_coins
else:
return -1
coins = [1, 5, 10, 25]
amount = 63
result = coin_change(coins, amount)
if result != -1:
print(f"Minimum number of coins required: {result}.")
else:
print("It is not possible to make the amount with the given denominations.")
```
## Complexity Analysis
- **Time Complexity**: O(n log n) for sorting (if not pre-sorted), O(n) for iteration
- **Space Complexity**: O(1)
</br>
<hr>
</br>
# 2. Activity Selection Problem
The activity selection problem involves selecting the maximum number of mutually compatible activities that can be performed by a single person or machine, assuming that a person can only work on one activity at a time.
**Algorithm Overview:**
- **Greedy Strategy:** Sort the activities based on their finish times.
- **Selecting Activities:** Iterate through the sorted activities, selecting each activity if it doesn't conflict with the previously selected ones.
## Activity Selection Code in Python
```python
def activity_selection(start, finish):
n = len(start)
activities = []
i = 0
activities.append(i)
for j in range(1, n):
if start[j] >= finish[i]:
activities.append(j)
i = j
return activities
start = [1, 3, 0, 5, 8, 5]
finish = [2, 4, 6, 7, 9, 9]
selected_activities = activity_selection(start, finish)
print("Selected activities:", selected_activities)
```
## Complexity Analysis
- **Time Complexity**: O(n log n) for sorting (if not pre-sorted), O(n) for iteration
- **Space Complexity**: O(1)
</br>
<hr>
</br>
# 3. Huffman Coding
Huffman coding is a method of lossless data compression that efficiently represents characters or symbols in a file. It uses variable-length codes to represent characters, with shorter codes assigned to more frequent characters.
**Algorithm Overview:**
- **Frequency Analysis:** Determine the frequency of each character in the input data.
- **Building the Huffman Tree:** Construct a binary tree where each leaf node represents a character and the path to the leaf node determines its code.
- **Assigning Codes:** Traverse the Huffman tree to assign codes to each character, with shorter codes for more frequent characters.
## Huffman Coding Code in Python
```python
from heapq import heappush, heappop, heapify
from collections import defaultdict
def huffman_coding(data):
frequency = defaultdict(int)
for char in data:
frequency[char] += 1
heap = [[weight, [symbol, ""]] for symbol, weight in frequency.items()]
heapify(heap)
while len(heap) > 1:
lo = heappop(heap)
hi = heappop(heap)
for pair in lo[1:]:
pair[1] = '0' + pair[1]
for pair in hi[1:]:
pair[1] = '1' + pair[1]
heappush(heap, [lo[0] + hi[0]] + lo[1:] + hi[1:])
return sorted(heappop(heap)[1:], key=lambda p: (len(p[-1]), p))
data = "Huffman coding is a greedy algorithm"
encoded_data = huffman_coding(data)
print("Huffman Codes:")
for symbol, code in encoded_data:
print(f"{symbol}: {code}")
```
## Complexity Analysis
- **Time Complexity**: O(n log n) for heap operations, where n is the number of unique characters
- **Space Complexity**: O(n) for the heap
</br>
<hr>
</br>

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# Hashing with Linear Probing
In Data Structures and Algorithms, hashing is used to map data of arbitrary size to fixed-size values. A common approach to handle collisions in hashing is **linear probing**. In linear probing, if a collision occurs (i.e., the hash value points to an already occupied slot), we linearly probe through the table to find the next available slot. This method ensures that every element can be inserted or found in the hash table.
## Points to be Remembered
- **Hash Function**: A function that converts an input (or 'key') into an index in a hash table.
- **Collision**: When two keys hash to the same index.
- **Linear Probing**: A method to resolve collisions by checking the next slot (i.e., index + 1) until an empty slot is found.
## Real Life Examples of Hashing with Linear Probing
- **Student Record System**: Each student record is stored in a table where the student's ID number is hashed to an index. If two students have the same hash index, linear probing finds the next available slot.
- **Library System**: Books are indexed by their ISBN numbers. If two books hash to the same slot, linear probing helps find another spot for the book in the catalog.
## Applications of Hashing
Hashing is widely used in Computer Science:
- **Database Indexing**
- **Caches** (like CPU caches, web caches)
- **Associative Arrays** (or dictionaries in Python)
- **Sets** (unordered collections of unique elements)
Understanding these applications is essential for Software Development.
## Operations in Hash Table with Linear Probing
Key operations include:
- **INSERT**: Insert a new element into the hash table.
- **SEARCH**: Find the position of an element in the hash table.
- **DELETE**: Remove an element from the hash table.
## Implementing Hash Table with Linear Probing in Python
```python
class HashTable:
def __init__(self, size):
self.size = size
self.table = [None] * size
def hash_function(self, key):
return key % self.size
def insert(self, key, value):
hash_index = self.hash_function(key)
if self.table[hash_index] is None:
self.table[hash_index] = (key, value)
else:
while self.table[hash_index] is not None:
hash_index = (hash_index + 1) % self.size
self.table[hash_index] = (key, value)
def search(self, key):
hash_index = self.hash_function(key)
while self.table[hash_index] is not None:
if self.table[hash_index][0] == key:
return self.table[hash_index][1]
hash_index = (hash_index + 1) % self.size
return None
def delete(self, key):
hash_index = self.hash_function(key)
while self.table[hash_index] is not None:
if self.table[hash_index][0] == key:
self.table[hash_index] = None
return True
hash_index = (hash_index + 1) % self.size
return False
def display(self):
for index, item in enumerate(self.table):
print(f"Index {index}: {item}")
# Example usage
hash_table = HashTable(10)
hash_table.insert(1, 'A')
hash_table.insert(11, 'B')
hash_table.insert(21, 'C')
print("Hash Table after Insert operations:")
hash_table.display()
print("Search operation for key 11:", hash_table.search(11))
hash_table.delete(11)
print("Hash Table after Delete operation:")
hash_table.display()
```
## Output
```markdown
Hash Table after Insert operations:
Index 0: None
Index 1: (1, 'A')
Index 2: None
Index 3: None
Index 4: None
Index 5: None
Index 6: None
Index 7: None
Index 8: None
Index 9: None
Index 10: None
Index 11: (11, 'B')
Index 12: (21, 'C')
Search operation for key 11: B
Hash Table after Delete operation:
Index 0: None
Index 1: (1, 'A')
Index 2: None
Index 3: None
Index 4: None
Index 5: None
Index 6: None
Index 7: None
Index 8: None
Index 9: None
Index 10: None
Index 11: None
Index 12: (21, 'C')
```
## Complexity Analysis
- **Insertion**: Average case O(1), Worst case O(n) when many collisions occur.
- **Search**: Average case O(1), Worst case O(n) when many collisions occur.
- **Deletion**: Average case O(1), Worst case O(n) when many collisions occur.

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# List of sections
- [Section title](filename.md)
- [Time & Space Complexity](time-space-complexity.md)
- [Queues in Python](Queues.md)
- [Graphs](graph.md)
- [Sorting Algorithms](sorting-algorithms.md)
- [Recursion and Backtracking](recursion.md)
- [Divide and Conquer Algorithm](divide-and-conquer-algorithm.md)
- [Searching Algorithms](searching-algorithms.md)
- [Greedy Algorithms](greedy-algorithms.md)
- [Dynamic Programming](dynamic-programming.md)
- [Linked list](linked-list.md)
- [Stacks in Python](stacks.md)
- [Sliding Window Technique](sliding-window.md)
- [Trie](trie.md)
- [Hashing through Linear Probing](hashing-linear-probing.md)

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# Linked List Data Structure
Link list is a linear data Structure which can be defined as collection of objects called nodes that are randomly stored in the memory.
A node contains two types of metadata i.e. data stored at that particular address and the pointer which contains the address of the next node in the memory.
The last element in a linked list features a null pointer.
## Why use linked list over array?
From the beginning, we are using array data structure to organize the group of elements that are stored individually in the memory.
However, there are some advantage and disadvantage of array which should be known to decide which data structure will used throughout the program.
limitations
1. Before an array can be utilized in a program, its size must be established in advance.
2. Expanding an array's size is a lengthy process and is almost impossible to achieve during runtime.
3. Array elements must be stored in contiguous memory locations. To insert an element, all subsequent elements must be shifted
So we introduce a new data structure to overcome these limitations.
Linked list is used because,
1. Dynamic Memory Management: Linked lists allocate memory dynamically, meaning nodes can be located anywhere in memory and are connected through pointers, rather than being stored contiguously.
2. Adaptive Sizing: There is no need to predefine the size of a linked list. It can expand or contract during runtime, adapting to the program's requirements within the constraints of the available memory.
Let's code something
The smallest Unit: Node
```python
class Node:
def __init__(self, data):
self.data = data # Assigns the given data to the node
self.next = None # Initialize the next attribute to null
```
Now, we will see the types of linked list.
There are mainly four types of linked list,
1. Singly Link list
2. Doubly link list
3. Circular link list
4. Doubly circular link list
## 1. Singly linked list.
Simply think it is a chain of nodes in which each node remember(contains) the addresses of it next node.
### Creating a linked list class
```python
class LinkedList:
def __init__(self):
self.head = None # Initialize head as None
```
### Inserting a new node at the beginning of a linked list
```python
def insertAtBeginning(self, new_data):
new_node = Node(new_data) # Create a new node
new_node.next = self.head # Next for new node becomes the current head
self.head = new_node # Head now points to the new node
```
### Inserting a new node at the end of a linked list
```python
def insertAtEnd(self, new_data):
new_node = Node(new_data) # Create a new node
if self.head is None:
self.head = new_node # If the list is empty, make the new node the head
return
last = self.head
while last.next: # Otherwise, traverse the list to find the last node
last = last.next
last.next = new_node # Make the new node the next node of the last node
```
### Inserting a new node at the middle of a linked list
```python
def insertAtPosition(self, data, position):
new_node = Node(data)
if position <= 0: #check if position is valid or not
print("Position should be greater than 0")
return
if position == 1:
new_node.next = self.head
self.head = new_node
return
current_node = self.head
current_position = 1
while current_node and current_position < position - 1: #Iterating to behind of the postion.
current_node = current_node.next
current_position += 1
if not current_node: #Check if Position is out of bound or not
print("Position is out of bounds")
return
new_node.next = current_node.next #connect the intermediate node
current_node.next = new_node
```
### Printing the Linked list
```python
def printList(self):
temp = self.head # Start from the head of the list
while temp:
print(temp.data,end=' ') # Print the data in the current node
temp = temp.next # Move to the next node
print() # Ensures the output is followed by a new line
```
Lets complete the code and create a linked list.
Connect all the code.
```python
if __name__ == '__main__':
llist = LinkedList()
# Insert words at the beginning
llist.insertAtBeginning(4) # <4>
llist.insertAtBeginning(3) # <3> 4
llist.insertAtBeginning(2) # <2> 3 4
llist.insertAtBeginning(1) # <1> 2 3 4
# Insert a word at the end
llist.insertAtEnd(10) # 1 2 3 4 <10>
llist.insertAtEnd(7) # 1 2 3 4 10 <7>
#Insert at a random position
llist.insertAtPosition(9,4) ## 1 2 3 <9> 4 10 7
# Print the list
llist.printList()
```
## output:
1 2 3 9 4 10 7
### Deleting a node from the beginning of a linked list
check the list is empty otherwise shift the head to next node.
```python
def deleteFromBeginning(self):
if self.head is None:
return "The list is empty" # If the list is empty, return this string
self.head = self.head.next # Otherwise, remove the head by making the next node the new head
```
### Deleting a node from the end of a linked list
```python
def deleteFromEnd(self):
if self.head is None:
return "The list is empty"
if self.head.next is None:
self.head = None # If there's only one node, remove the head by making it None
return
temp = self.head
while temp.next.next: # Otherwise, go to the second-last node
temp = temp.next
temp.next = None # Remove the last node by setting the next pointer of the second-last node to None
```
### Search in a linked list
```python
def search(self, value):
current = self.head # Start with the head of the list
position = 0 # Counter to keep track of the position
while current: # Traverse the list
if current.data == value: # Compare the list's data to the search value
return f"Value '{value}' found at position {position}" # Print the value if a match is found
current = current.next
position += 1
return f"Value '{value}' not found in the list"
```
```python
if __name__ == '__main__':
llist = LinkedList()
# Insert words at the beginning
llist.insertAtBeginning(4) # <4>
llist.insertAtBeginning(3) # <3> 4
llist.insertAtBeginning(2) # <2> 3 4
llist.insertAtBeginning(1) # <1> 2 3 4
# Insert a word at the end
llist.insertAtEnd(10) # 1 2 3 4 <10>
llist.insertAtEnd(7) # 1 2 3 4 10 <7>
#Insert at a random position
llist.insertAtPosition(9,4) # 1 2 3 <9> 4 10 7
llist.insertAtPositon(56,4) # 1 2 3 <56> 9 4 10 7
#delete at the beginning
llist.deleteFromBeginning() # 2 3 56 9 4 10 7
#delete at the end
llist.deleteFromEnd() # 2 3 56 9 4 10
# Print the list
llist.printList()
```
## Output:
2 3 56 9 4 10
## Real Life uses of Linked List
Here are a few practical applications of linked lists in various fields:
1. **Music Player**: In a music player, songs are often linked to the previous and next tracks. This allows for seamless navigation between songs, enabling you to play tracks either from the beginning or the end of the playlist. This is akin to a doubly linked list where each song node points to both the previous and the next song, enhancing the flexibility of song selection.
2. **GPS Navigation Systems**: Linked lists can be highly effective for managing lists of locations and routes in GPS navigation systems. Each location or waypoint can be represented as a node, making it easy to add or remove destinations and to navigate smoothly from one location to another. This is similar to how you might plan a road trip, plotting stops along the way in a flexible, dynamic manner.
3. **Task Scheduling**: Operating systems utilize linked lists to manage task scheduling. Each process waiting to be executed is represented as a node in a linked list. This organization allows the system to efficiently keep track of which processes need to be run, enabling fair and systematic scheduling of tasks. Think of it like a to-do list where each task is a node, and the system executes tasks in a structured order.
4. **Speech Recognition**: Speech recognition software uses linked lists to represent possible phonetic pronunciations of words. Each potential pronunciation is a node, allowing the software to dynamically explore different pronunciation paths as it processes spoken input. This method helps in accurately recognizing and understanding speech by considering multiple possibilities in a flexible manner, much like evaluating various potential meanings in a conversation.
These examples illustrate how linked lists provide a flexible, dynamic data structure that can be adapted to a wide range of practical applications, making them a valuable tool in both software development and real-world problem-solving.

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# Queues in Python
A queue is a linear data structure where elements are added at the back (enqueue) and removed from the front (dequeue). Imagine a line at a coffee shop, the first in line (front) gets served first, and new customers join at the back. This FIFO approach ensures order and fairness in processing elements.
Queues offer efficient implementations for various scenarios. They are often used in:
- **Task Scheduling** - Operating systems utilize queues to manage processes waiting for CPU time.
- **Breadth-first search algorithms** - Traversing a tree or graph involves exploring neighbouring nodes level by level, often achieved using a queue.
- **Message passing** - Communication protocols leverage queues to buffer messages between applications for reliable delivery.
## Types of Queue
A queue can be classified into 4 types -
- **Simple Queue** - A simple queue is a queue, where we can only insert an element at the back and remove the element from the front of the queue, this type of queue follows the FIFO principle.
- **Double-Ended Queue (Dequeue)** - In this type of queue, insertions and deletions of elements can be performed from both ends of the queue.<br>
Double-ended queues can be classified into 2 types ->
- **Input-Restricted Queue**
- **Output-Restricted Queue**
- **Circular Queue** - It is a special type of queue where the back is connected to the front, where the operations follow the FIFO principle.
- **Priority Queue** - In this type of queue, elements are accessed based on their priority in the queue. <br>
Priority queues are of 2 types ->
- **Ascending Priority Queue**
- **Descending Priority Queue**
## Real Life Examples of Queues
- **Customer Service** - Consider how a customer service phone line works. Customers calling are put into a queue. The first customer to call is the first one to be served (FIFO). As more customers call, they are added to the end of the queue, and as customers are served, they are removed from the front. The entire process follows the queue data structure.
- **Printers** - Printers operate using a queue to manage print jobs. When a user sends a document to the printer, the job is added to the queue (enqueue). Once a job completes printing, it's removed from the queue (dequeue), and the next job in line starts. This sequential order of handling tasks perfectly exhibits the queue data structure.
- **Computer Memory** - Certain types of computer memory use a queue data structure to hold and process instructions. For example, in a computer's cache memory, the fetch-decode-execute cycle of an instruction follows a queue. The first instruction fetched is the first one to be decoded and executed, while new instructions fetched are added to the rear.
<hr>
# Important Terminologies in Queues
Understanding these terms is crucial for working with queues:
- **Enqueue** - Adding an element to the back of the queue.
- **Dequeue** - Removing the element at the front of the queue.
- **Front** - The first element in the queue, to be removed next.
- **Rear/Back** - The last element in the queue, where new elements are added.
- **Empty Queue** - A queue with no elements.
- **Overflow** - Attempting to enqueue an element when the queue is full.
- **Underflow** - Attempting to dequeue an element from an empty queue.
## Operations on a Queue
There are some key operations in a queue that include -
- **isFULL** - This operation checks if a queue is full.
- **isEMPTY** - This operation checks if a queue is empty.
- **Display** - This operation displays the queue elements.
- **Peek** - This operation is the process of getting the front value of a queue, without removing it. (i.e., Value at the front).
<hr>
# Implementation of Queue
```python
def isEmpty(Qu):
if Qu == []:
return True
else:
return False
def Enqueue(Qu, item) :
Qu.append(item)
if len(Qu) == 1:
front = rear = 0
else:
rear = len(Qu) - 1
print(item, "enqueued to queue")
def Dequeue(Qu):
if isEmpty(Qu):
print("Underflow")
else:
item = Qu.pop(0)
if len(Qu) == 0: #if it was single-element queue
front = rear = None
print(item, "dequeued from queue")
def Peek(Qu):
if isEmpty(Qu):
print("Underflow")
else:
front = 0
print("Frontmost item is :", Qu[front])
def Display(Qu):
if isEmpty(Qu):
print("Queue Empty!")
elif len(Qu) == 1:
print(Qu[0], "<== front, rear")
else:
front = 0
rear = len(Qu) - 1
print(Qu[front], "<-front")
for a in range(1, rear):
print(Qu[a])
print(Qu[rear], "<-rear")
queue = [] #initially queue is empty
front = None
# Example Usage
Enqueue(queue, 1)
Enqueue(queue, 2)
Enqueue(queue, 3)
Dequeue(queue)
Peek(queue)
Display(queue)
```
## Output
```
1 enqueued to queue
2 enqueued to queue
3 enqueued to queue
1 dequeued from queue
Frontmost item is : 2
2 <-front
3 <-rear
```
## Complexity Analysis
- **Worst case**: `O(n^2)` This occurs when the code performs lots of display operations.
- **Best case**: `O(n)` If the code mostly performs enqueue, dequeue and peek operations.
- **Average case**: `O(n^2)` It occurs when the number of operations in display are more than the operations in enqueue, dequeue and peek.

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# Introduction to Recursions
When a function calls itself to solve smaller instances of the same problem until a specified condition is fulfilled is called recursion. It is used for tasks that can be divided into smaller sub-tasks.
## How Recursion Works
To solve a problem using recursion we must define:
- Base condition :- The condition under which recursion ends.
- Recursive case :- The part of function which calls itself to solve a smaller instance of problem.
Steps of Recursion
When a recursive function is called, the following sequence of events occurs:
- Function Call: The function is invoked with a specific argument.
- Base Condition Check: The function checks if the argument satisfies the base case.
- Recursive Call: If the base case is not met, the function performs some operations and makes a recursive call with a modified argument.
- Stack Management: Each recursive call is placed on the call stack. The stack keeps track of each function call, its argument, and the point to return to once the call completes.
- Unwinding the Stack: When the base case is eventually met, the function returns a value, and the stack starts unwinding, returning values to previous function calls until the initial call is resolved.
## Python Code: Factorial using Recursion
```python
def fact(n):
if n == 0 or n == 1:
return 1
return n * fact(n - 1)
if __name__ == "__main__":
n = int(input("Enter a positive number: "))
print("Factorial of", n, "is", fact(n))
```
### Explanation
This Python script calculates the factorial of a given number using recursion.
- **Function `fact(n)`:**
- The function takes an integer `n` as input and calculates its factorial.
- It checks if `n` is 0 or 1. If so, it returns 1 (since the factorial of 0 and 1 is 1).
- Otherwise, it returns `n * fact(n - 1)`, which means it recursively calls itself with `n - 1` until it reaches either 0 or 1.
- **Main Section:**
- The main section prompts the user to enter a positive number.
- It then calls the `fact` function with the input number and prints the result.
#### Example : Let n = 4
The recursion unfolds as follows:
1. When `fact(4)` is called, it computes `4 * fact(3)`.
2. Inside `fact(3)`, it computes `3 * fact(2)`.
3. Inside `fact(2)`, it computes `2 * fact(1)`.
4. `fact(1)` returns 1 (`if` statement executes), which is received by `fact(2)`, resulting in `2 * 1` i.e. `2`.
5. Back to `fact(3)`, it receives the value from `fact(2)`, giving `3 * 2` i.e. `6`.
6. `fact(4)` receives the value from `fact(3)`, resulting in `4 * 6` i.e. `24`.
7. Finally, `fact(4)` returns 24 to the main function.
#### So, the result is 24.
#### What is Stack Overflow in Recursion?
Stack overflow is an error that occurs when the call stack memory limit is exceeded. During execution of recursion calls they are simultaneously stored in a recursion stack waiting for the recursive function to be completed. Without a base case, the function would call itself indefinitely, leading to a stack overflow.
## What is Backtracking
Backtracking is a recursive algorithmic technique used to solve problems by exploring all possible solutions and discarding those that do not meet the problem's constraints. It is particularly useful for problems involving combinations, permutations, and finding paths in a grid.
## How Backtracking Works
- Incremental Solution Building: Solutions are built one step at a time.
- Feasibility Check: At each step, a check is made to see if the current partial solution is valid.
- Backtracking: If a partial solution is found to be invalid, the algorithm backtracks by removing the last added part of the solution and trying the next possibility.
- Exploration of All Possibilities: The process continues recursively, exploring all possible paths, until a solution is found or all possibilities are exhausted.
## Example: Word Search
Given a 2D grid of characters and a word, determine if the word exists in the grid. The word can be constructed from letters of sequentially adjacent cells, where "adjacent" cells are horizontally or vertically neighboring. The same letter cell may not be used more than once.
Algorithm for Solving the Word Search Problem with Backtracking:
- Start at each cell: Attempt to find the word starting from each cell.
- Check all Directions: From each cell, try all four possible directions (up, down, left, right).
- Mark Visited Cells: Use a temporary marker to indicate cells that are part of the current path to avoid revisiting.
- Backtrack: If a path does not lead to a solution, backtrack by unmarking the visited cell and trying the next possibility.
```python
def exist(board, word):
rows, cols = len(board), len(board[0])
def backtrack(r, c, suffix):
if not suffix:
return True
if r < 0 or r >= rows or c < 0 or c >= cols or board[r][c] != suffix[0]:
return False
# Mark the cell as visited by replacing its character with a placeholder
ret = False
board[r][c], temp = '#', board[r][c]
# Explore the four possible directions
for row_offset, col_offset in [(0, 1), (1, 0), (0, -1), (-1, 0)]:
ret = backtrack(r + row_offset, c + col_offset, suffix[1:])
if ret:
break
# Restore the cell's original value
board[r][c] = temp
return ret
for row in range(rows):
for col in range(cols):
if backtrack(row, col, word):
return True
return False
# Test case
board = [
['A','B','C','E'],
['S','F','C','S'],
['A','D','E','E']
]
word = "ABCES"
print(exist(board, word)) # Output: True
```

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# Searching Algorithms
Searching algorithms are techniques used to locate specific items within a collection of data. These algorithms are fundamental in computer science and are employed in various applications, from databases to web search engines.
## Real Life Example of Searching
- Searching for a word in a dictionary
- Searching for a specific book in a library
- Searching for a contact in your phone's address book
- Searching for a file on your computer, etc.
# Some common searching techniques
# 1. Linear Search
Linear search, also known as sequential search, is a straightforward searching algorithm that checks each element in a collection until the target element is found or the entire collection has been traversed. It is simple to implement but becomes inefficient for large datasets.
**Algorithm Overview:**
- **Sequential Checking:** The algorithm iterates through each element in the collection, starting from the first element.
- **Comparing Elements:** At each iteration, it compares the current element with the target element.
- **Finding the Target:** If the current element matches the target, the search terminates, and the index of the element is returned.
- **Completing the Search:** If the entire collection is traversed without finding the target, the algorithm indicates that the element is not present.
## Linear Search Code in Python
```python
def linear_search(arr, target):
for i in range(len(arr)):
if arr[i] == target:
return i
return -1
arr = [5, 3, 8, 1, 2]
target = 8
result = linear_search(arr, target)
if result != -1:
print(f"Element {target} found at index {result}.")
else:
print(f"Element {target} not found.")
```
## Complexity Analysis
- **Time Complexity**: O(n)
- **Space Complexity**: O(1)
</br>
<hr>
</br>
# 2. Binary Search
Binary search is an efficient searching algorithm that works on sorted collections. It repeatedly divides the search interval in half until the target element is found or the interval is empty. Binary search is significantly faster than linear search but requires the collection to be sorted beforehand.
**Algorithm Overview:**
- **Initial State:** Binary search starts with the entire collection as the search interval.
- **Divide and Conquer:** At each step, it calculates the middle element of the current interval and compares it with the target.
- **Narrowing Down the Interval:** If the middle element is equal to the target, the search terminates successfully. Otherwise, it discards half of the search interval based on the comparison result.
- **Repeating the Process:** The algorithm repeats this process on the remaining half of the interval until the target is found or the interval is empty.
## Binary Search Code in Python (Iterative)
```python
def binary_search(arr, target):
low = 0
high = len(arr) - 1
while low <= high:
mid = (low + high) // 2
if arr[mid] == target:
return mid
elif arr[mid] < target:
low = mid + 1
else:
high = mid - 1
return -1
arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]
target = 13
result = binary_search(arr, target)
if result != -1:
print(f"Element {target} found at index {result}.")
else:
print(f"Element {target} not found.")
```
## Binary Search Code in Python (Recursive)
```python
def binary_search_recursive(arr, target, low, high):
if low <= high:
mid = (low + high) // 2
if arr[mid] == target:
return mid
elif arr[mid] < target:
return binary_search_recursive(arr, target, mid + 1, high)
else:
return binary_search_recursive(arr, target, low, mid - 1)
else:
return -1
arr = [1, 3, 5, 7, 9, 11, 13, 15, 17, 19]
target = 13
result = binary_search_recursive(arr, target, 0, len(arr) - 1)
if result != -1:
print(f"Element {target} found at index {result}.")
else:
print(f"Element {target} not found.")
```
## Complexity Analysis
- **Time Complexity**: O(log n)
- **Space Complexity**: O(1) (Iterative), O(log n) (Recursive)
</br>
<hr>
</br>
# 3. Interpolation Search
Interpolation search is an improved version of binary search, especially useful when the elements in the collection are uniformly distributed. Instead of always dividing the search interval in half, interpolation search estimates the position of the target element based on its value and the values of the endpoints of the search interval.
**Algorithm Overview:**
- **Estimating Position:** Interpolation search calculates an approximate position of the target element within the search interval based on its value and the values of the endpoints.
- **Refining the Estimate:** It adjusts the estimated position based on whether the target value is likely to be closer to the beginning or end of the search interval.
- **Updating the Interval:** Using the refined estimate, it narrows down the search interval iteratively until the target is found or the interval becomes empty.
## Interpolation Search Code in Python
```python
def interpolation_search(arr, target):
low = 0
high = len(arr) - 1
while low <= high and arr[low] <= target <= arr[high]:
if low == high:
if arr[low] == target:
return low
return -1
pos = low + ((target - arr[low]) * (high - low)) // (arr[high] - arr[low])
if arr[pos] == target:
return pos
elif arr[pos] < target:
low = pos + 1
else:
high = pos - 1
return -1
arr = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100]
target = 60
result = interpolation_search(arr, target)
if result != -1:
print(f"Element {target} found at index {result}.")
else:
print(f"Element {target} not found.")
```
## Complexity Analysis
- **Time Complexity**: O(log log n) (Average)
- **Space Complexity**: O(1)
</br>
<hr>
</br>

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contrib/ds-algorithms/sliding-window.md 100644
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# Sliding Window Technique
The sliding window technique is a fundamental approach used to solve problems involving arrays, lists, or sequences. It's particularly useful when you need to calculate something over a subarray or sublist of fixed size that slides over the entire array.
In easy words, It is the transformation of the nested loops into the single loop
## Concept
The sliding window technique involves creating a window (a subarray or sublist) that moves or "slides" across the entire array. This window can either be fixed in size or dynamically resized. By maintaining and updating this window as it moves, you can optimize certain computations, reducing time complexity.
## Types of Sliding Windows
1. **Fixed Size Window**: The window size remains constant as it slides from the start to the end of the array.
2. **Variable Size Window**: The window size can change based on certain conditions, such as the sum of elements within the window meeting a specified target.
## Steps to Implement a Sliding Window
1. **Initialize the Window**: Set the initial position of the window and any required variables (like sum, count, etc.).
2. **Expand the Window**: Add the next element to the window and update the relevant variables.
3. **Shrink the Window**: If needed, remove elements from the start of the window and update the variables.
4. **Slide the Window**: Move the window one position to the right by including the next element and possibly excluding the first element.
5. **Repeat**: Continue expanding, shrinking, and sliding the window until you reach the end of the array.
## Example Problems
### 1. Maximum Sum Subarray of Fixed Size K
Given an array of integers and an integer k, find the maximum sum of a subarray of size k.
**Steps:**
1. Initialize the sum of the first k elements.
2. Slide the window from the start of the array to the end, updating the sum by subtracting the element that is left behind and adding the new element.
3. Track the maximum sum encountered.
**Python Code:**
```python
def max_sum_subarray(arr, k):
n = len(arr)
if n < k:
return None
# Compute the sum of the first window
window_sum = sum(arr[:k])
max_sum = window_sum
# Slide the window from start to end
for i in range(n - k):
window_sum = window_sum - arr[i] + arr[i + k]
max_sum = max(max_sum, window_sum)
return max_sum
# Example usage:
arr = [1, 3, 2, 5, 1, 1, 6, 2, 8, 5]
k = 3
print(max_sum_subarray(arr, k)) # Output: 16
```
### 2. Longest Substring Without Repeating Characters
Given a string, find the length of the longest substring without repeating characters.
**Steps:**
1. Use two pointers to represent the current window.
2. Use a set to track characters in the current window.
3. Expand the window by moving the right pointer.
4. If a duplicate character is found, shrink the window by moving the left pointer until the duplicate is removed.
**Python Code:**
```python
def longest_unique_substring(s):
n = len(s)
char_set = set()
left = 0
max_length = 0
for right in range(n):
while s[right] in char_set:
char_set.remove(s[left])
left += 1
char_set.add(s[right])
max_length = max(max_length, right - left + 1)
return max_length
# Example usage:
s = "abcabcbb"
print(longest_unique_substring(s)) # Output: 3
```
## 3. Minimum Size Subarray Sum
Given an array of positive integers and a positive integer `s`, find the minimal length of a contiguous subarray of which the sum is at least `s`. If there isn't one, return 0 instead.
### Steps:
1. Use two pointers, `left` and `right`, to define the current window.
2. Expand the window by moving `right` and adding `arr[right]` to `current_sum`.
3. If `current_sum` is greater than or equal to `s`, update `min_length` and shrink the window from the left by moving `left` and subtracting `arr[left]` from `current_sum`.
4. Repeat until `right` has traversed the array.
### Python Code:
```python
def min_subarray_len(s, arr):
n = len(arr)
left = 0
current_sum = 0
min_length = float('inf')
for right in range(n):
current_sum += arr[right]
while current_sum >= s:
min_length = min(min_length, right - left + 1)
current_sum -= arr[left]
left += 1
return min_length if min_length != float('inf') else 0
# Example usage:
arr = [2, 3, 1, 2, 4, 3]
s = 7
print(min_subarray_len(s, arr)) # Output: 2 (subarray [4, 3])
```
## 4. Longest Substring with At Most K Distinct Characters
Given a string `s` and an integer `k`, find the length of the longest substring that contains at most `k` distinct characters.
### Steps:
1. Use two pointers, `left` and `right`, to define the current window.
2. Use a dictionary `char_count` to count characters in the window.
3. Expand the window by moving `right` and updating `char_count`.
4. If `char_count` has more than `k` distinct characters, shrink the window from the left by moving `left` and updating `char_count`.
5. Keep track of the maximum length of the window with at most `k` distinct characters.
### Python Code:
```python
def longest_substring_k_distinct(s, k):
n = len(s)
char_count = {}
left = 0
max_length = 0
for right in range(n):
char_count[s[right]] = char_count.get(s[right], 0) + 1
while len(char_count) > k:
char_count[s[left]] -= 1
if char_count[s[left]] == 0:
del char_count[s[left]]
left += 1
max_length = max(max_length, right - left + 1)
return max_length
# Example usage:
s = "eceba"
k = 2
print(longest_substring_k_distinct(s, k)) # Output: 3 (substring "ece")
```
## 5. Maximum Number of Vowels in a Substring of Given Length
Given a string `s` and an integer `k`, return the maximum number of vowel letters in any substring of `s` with length `k`.
### Steps:
1. Use a sliding window of size `k`.
2. Keep track of the number of vowels in the current window.
3. Expand the window by adding the next character and update the count if it's a vowel.
4. If the window size exceeds `k`, remove the leftmost character and update the count if it's a vowel.
5. Track the maximum number of vowels found in any window of size `k`.
### Python Code:
```python
def max_vowels(s, k):
vowels = set('aeiou')
max_vowel_count = 0
current_vowel_count = 0
for i in range(len(s)):
if s[i] in vowels:
current_vowel_count += 1
if i >= k:
if s[i - k] in vowels:
current_vowel_count -= 1
max_vowel_count = max(max_vowel_count, current_vowel_count)
return max_vowel_count
# Example usage:
s = "abciiidef"
k = 3
print(max_vowels(s, k)) # Output: 3 (substring "iii")
```
## 6. Subarray Product Less Than K
Given an array of positive integers `nums` and an integer `k`, return the number of contiguous subarrays where the product of all the elements in the subarray is less than `k`.
### Steps:
1. Use two pointers, `left` and `right`, to define the current window.
2. Expand the window by moving `right` and multiplying `product` by `nums[right]`.
3. If `product` is greater than or equal to `k`, shrink the window from the left by moving `left` and dividing `product` by `nums[left]`.
4. For each position of `right`, the number of valid subarray ending at `right` is `right - left + 1`.
5. Sum these counts to get the total number of subarray with product less than `k`.
### Python Code:
```python
def num_subarray_product_less_than_k(nums, k):
if k <= 1:
return 0
product = 1
left = 0
count = 0
for right in range(len(nums)):
product *= nums[right]
while product >= k:
product /= nums[left]
left += 1
count += right - left + 1
return count
# Example usage:
nums = [10, 5, 2, 6]
k = 100
print(num_subarray_product_less_than_k(nums, k)) # Output: 8
```
## Advantages
- **Efficiency**: Reduces the time complexity from O(n^2) to O(n) for many problems.
- **Simplicity**: Provides a straightforward way to manage subarrays/substrings with overlapping elements.
## Applications
- Finding the maximum or minimum sum of subarrays of fixed size.
- Detecting unique elements in a sequence.
- Solving problems related to dynamic programming with fixed constraints.
- Efficiently managing and processing streaming data or real-time analytics.
By using the sliding window technique, you can tackle a wide range of problems in a more efficient manner.

216
contrib/ds-algorithms/sorting-algorithms.md
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@ -2,14 +2,15 @@
In computer science, a sorting algorithm takes a collection of items and arranges them in a specific order. This order is usually determined by comparing the items using a defined rule.
## Real Life Example of Sorting
Real Life Example of Sorting
- Sorting a deck of cards
- Sorting names in alphabetical order
- Sorting a list of items, etc.
# Some common sorting techniques
Some common sorting techniques:
# 1. Bubble Sort
## 1. Bubble Sort
Bubble sort is a basic sorting technique that iteratively steps through a list, comparing neighboring elements. If elements are out of order, it swaps them. While easy to understand, bubble sort becomes inefficient for large datasets due to its slow execution time.
@ -21,7 +22,7 @@ Bubble sort is a basic sorting technique that iteratively steps through a list,
- **Repeating Until Sorted:** The algorithm continues making passes through the list until no more swaps are needed. This indicates the entire list is sorted.
## Bubble Sort Code in Python
### Bubble Sort Code in Python
```python
def bubble_sort(arr):
@ -35,7 +36,8 @@ arr = [5, 3, 8, 1, 2]
bubble_sort(arr)
print("Sorted array:", arr) # Output: [1, 2, 3, 5, 8]
```
## Example with Visualization
### Example with Visualization
Let's sort the list `[5, 3, 8, 1, 2]` using bubble sort.
@ -53,17 +55,13 @@ Let's sort the list `[5, 3, 8, 1, 2]` using bubble sort.
- Comparing neighbors: `[1, 2, 3, 5, 8]`
- No swapping needed, the list is already sorted.
## Complexity Analysis
### Complexity Analysis
- **Worst Case:** `O(n^2)` comparisons and swaps. This happens when the list is in reverse order, and we need to make maximum swaps.
- **Best Case:** `O(n)` comparisons. This occurs when the list is already sorted, but we still need O(n^2) swaps because of the nested loops.
- **Average Case:** `O(n^2)` comparisons and swaps. This is the expected number of comparisons and swaps over all possible input sequences.
</br>
<hr>
</br>
# 2. Selection Sort
## 2. Selection Sort
Selection sort is a simple sorting algorithm that divides the input list into two parts: a sorted sublist and an unsorted sublist. The algorithm repeatedly finds the smallest (or largest, depending on sorting order) element from the unsorted sublist and moves it to the sorted sublist. It's not efficient for large datasets but performs better than bubble sort due to fewer swaps.
@ -73,7 +71,7 @@ Selection sort is a simple sorting algorithm that divides the input list into tw
- **Expanding the Sorted Sublist:** As elements are moved to the sorted sublist, it expands until all elements are sorted.
- **Repeating Until Sorted:** The process continues until the entire list is sorted.
## Example with Visualization
### Example with Visualization
Let's sort the list `[5, 3, 8, 1, 2]` using selection sort.
@ -97,7 +95,7 @@ Let's sort the list `[5, 3, 8, 1, 2]` using selection sort.
- Find the minimum: `5`
- No swapping needed, the list is already sorted.
## Selection Sort Code in Python
### Selection Sort Code in Python
```python
def selection_sort(arr):
@ -114,15 +112,13 @@ selection_sort(arr)
print("Sorted array:", arr) # Output: [1, 2, 3, 5, 8]
```
## Complexity Analysis
### Complexity Analysis
- **Worst Case**: `O(n^2)` comparisons and O(n) swaps. This occurs when the list is in reverse order, and we need to make maximum comparisons and swaps.
- **Best Case**: `O(n^2)` comparisons and O(n) swaps. This happens when the list is in sorted order, but the algorithm still needs to iterate through all elements for comparisons.
- **Average Case**: `O(n^2)` comparisons and O(n) swaps. This is the expected number of comparisons and swaps over all possible input sequences.
</br>
<hr>
</br>
# 3. Quick Sort
## 3. Quick Sort
Quick sort is a popular divide-and-conquer sorting algorithm known for its efficiency on average. It works by selecting a 'pivot' element from the array and partitioning the other elements into two sub-arrays according to whether they are less than or greater than the pivot. The sub-arrays are then recursively sorted.
**Algorithm Overview:**
@ -131,29 +127,24 @@ Quick sort is a popular divide-and-conquer sorting algorithm known for its effic
- **Recursion:** Apply the above steps recursively to the sub-arrays formed by partitioning until the base case is reached. The base case is usually when the size of the sub-array becomes 0 or 1, indicating it is already sorted.
- **Base Case:** If the sub-array size becomes 0 or 1, it is already sorted.
## Example with Visualization
### Example with Visualization
Let's sort the list `[5, 3, 8, 1, 2]` using quick sort.
1. **Initial Array:** `[5, 3, 8, 1, 2]`
2. **Choose Pivot:** Let's choose the last element, `2`, as the pivot.
3. **Partitioning:**
- We'll partition the array around the pivot `2`. All elements less than `2` will be placed to its left, and all elements greater than `2` will be placed to its right.
- After partitioning, the array becomes `[1, 2, 5, 3, 8]`. The pivot element, `2`, is now in its correct sorted position.
4. **Recursion:**
- Now, we recursively sort the sub-arrays `[1]` and `[5, 3, 8]`.
- For the sub-array `[5, 3, 8]`, we choose `8` as the pivot and partition it.
- After partitioning, the sub-array becomes `[3, 5, 8]`. The pivot element, `8`, is now in its correct sorted position.
5. **Concatenation:**
- Concatenating the sorted sub-arrays `[1]`, `[2]`, `[3, 5, 8]`, we get the final sorted array `[1, 2, 3, 5, 8]`.
## Quick Sort Code in Python (Iterative)
### Quick Sort Code in Python (Iterative)
```python
def partition(arr, low, high):
pivot = arr[high]
@ -180,7 +171,8 @@ quick_sort_iterative(arr)
print("Sorted array:", arr) # Output: [3, 9, 10, 27, 38, 43, 82]
```
## Quick Sort Code in Python (Recursive)
### Quick Sort Code in Python (Recursive)
```python
def quick_sort(arr):
@ -196,17 +188,15 @@ arr = [5, 3, 8, 1, 2]
sorted_arr = quick_sort(arr)
print("Sorted array:", sorted_arr) # Output: [1, 2, 3, 5, 8]
```
## Complexity Analysis
### Complexity Analysis
- **Worst Case**: The worst-case time complexity of quick sort is `O(n^2)`. This occurs when the pivot selection consistently results in unbalanced partitioning, such as choosing the smallest or largest element as the pivot.
-**Best Case**: The best-case time complexity is `O(n log n)`. This happens when the pivot selection leads to well-balanced partitioning, halving the array size in each recursive call.
- **Average Case**: The average-case time complexity is `O(n log n)`. This is the expected time complexity when the pivot selection results in reasonably balanced partitioning across recursive calls.
- **Space Complexity**: Quick sort has an `O(log n)` space complexity for the recursion stack, as it recursively sorts sub-arrays.
</br>
<hr>
</br>
# 4. Merge Sort
## 4. Merge Sort
Merge sort is a divide-and-conquer algorithm that recursively divides the input list into smaller sublists until each sublist contains only one element. Then, it repeatedly merges adjacent sublists while maintaining the sorted order until there is only one sublist remaining, which represents the sorted list.
@ -214,7 +204,7 @@ Merge sort is a divide-and-conquer algorithm that recursively divides the input
- **Divide:** Split the input list into smaller sublists recursively until each sublist contains only one element.
- **Merge:** Repeatedly merge adjacent sublists while maintaining the sorted order until there is only one sublist remaining, which represents the sorted list.
## Example with Visualization
### Example with Visualization
Let's sort the list `[38, 27, 43, 3, 9, 82, 10]` using merge sort.
@ -233,7 +223,7 @@ Let's sort the list `[38, 27, 43, 3, 9, 82, 10]` using merge sort.
3. **Final Sorted List:**
- `[3, 9, 10, 27, 38, 43, 82]`
## Merge Sort Code in Python (Iterative)
### Merge Sort Code in Python (Iterative)
```python
def merge_sort_iterative(arr):
@ -280,7 +270,9 @@ arr = [38, 27, 43, 3, 9, 82, 10]
merge_sort_iterative(arr)
print("Sorted array:", arr) # Output: [3, 9, 10, 27, 38, 43, 82]
```
## Merge Sort Code in Python (Recursive)
### Merge Sort Code in Python (Recursive)
```python
def merge_sort(arr):
if len(arr) > 1:
@ -320,10 +312,156 @@ arr = [38, 27, 43, 3, 9, 82, 10]
merge_sort(arr)
print("Sorted array:", arr) # Output: [3, 9, 10, 27, 38, 43, 82]
```
## Complexity Analysis
### Complexity Analysis
- **Time Complexity**: `O(n log n)` for all cases. Merge sort always divides the list into halves until each sublist contains only one element, and then merges them back together, resulting in O(n log n) time complexity.
- **Space Complexity**: `O(n)` auxiliary space. In the iterative version, merge sort uses additional space for creating temporary sublists during merging operations.
</br>
<hr>
</br>
## 5. Insertion Sort
Insertion sort is a straightforward and efficient sorting algorithm for small datasets. It builds the final sorted array one element at a time. It is much like sorting playing cards in your hands: you take one card at a time and insert it into its correct position among the already sorted cards.
**Algorithm Overview:**
- **Start from the Second Element:** Begin with the second element, assuming the first element is already sorted.
- **Compare with Sorted Subarray:** Take the current element and compare it with elements in the sorted subarray (the part of the array before the current element).
- **Insert in Correct Position:** Shift all elements in the sorted subarray that are greater than the current element to one position ahead. Insert the current element into its correct position.
- **Repeat Until End:** Repeat this process for all elements in the array.
### Example with Visualization
Let's sort the list `[5, 3, 8, 1, 2]` using insertion sort.
**Step-by-Step Visualization:**
**Initial List:** `[5, 3, 8, 1, 2]`
1. **Pass 1:**
- Current element: 3
- Compare 3 with 5, move 5 to the right: `[5, 5, 8, 1, 2]`
- Insert 3 in its correct position: `[3, 5, 8, 1, 2]`
2. **Pass 2:**
- Current element: 8
- 8 is already in the correct position: `[3, 5, 8, 1, 2]`
3. **Pass 3:**
- Current element: 1
- Compare 1 with 8, move 8 to the right: `[3, 5, 8, 8, 2]`
- Compare 1 with 5, move 5 to the right: `[3, 5, 5, 8, 2]`
- Compare 1 with 3, move 3 to the right: `[3, 3, 5, 8, 2]`
- Insert 1 in its correct position: `[1, 3, 5, 8, 2]`
4. **Pass 4:**
- Current element: 2
- Compare 2 with 8, move 8 to the right: `[1, 3, 5, 8, 8]`
- Compare 2 with 5, move 5 to the right: `[1, 3, 5, 5, 8]`
- Compare 2 with 3, move 3 to the right: `[1, 3, 3, 5, 8]`
- Insert 2 in its correct position: `[1, 2, 3, 5, 8]`
### Insertion Sort Code in Python
```python
def insertion_sort(arr):
# Traverse from 1 to len(arr)
for i in range(1, len(arr)):
key = arr[i]
# Move elements of arr[0..i-1], that are greater than key,
# to one position ahead of their current position
j = i - 1
while j >= 0 and key < arr[j]:
arr[j + 1] = arr[j]
j -= 1
arr[j + 1] = key
# Example usage
arr = [5, 3, 8, 1, 2]
insertion_sort(arr)
print("Sorted array:", arr) # Output: [1, 2, 3, 5, 8]
```
### Complexity Analysis
- **Worst Case:** `𝑂(𝑛^2)` comparisons and swaps. This occurs when the array is in reverse order.
- **Best Case:** `𝑂(𝑛)` comparisons and `𝑂(1)` swaps. This happens when the array is already sorted.
- **Average Case:** `𝑂(𝑛^2)` comparisons and swaps. This is the expected number of comparisons and swaps over all possible input sequences.
## 6. Heap Sort
Heap Sort is an efficient comparison-based sorting algorithm that uses a binary heap data structure. It divides its input into a sorted and an unsorted region and iteratively shrinks the unsorted region by extracting the largest (or smallest) element and moving it to the sorted region.
**Algorithm Overview:**
- **Build a Max Heap:** Convert the array into a max heap, a complete binary tree where the value of each node is greater than or equal to the values of its children.
- **Heapify:** Ensure that the subtree rooted at each node satisfies the max heap property. This process is called heapify.
- **Extract Maximum:** Swap the root (the maximum element) with the last element of the heap and reduce the heap size by one. Restore the max heap property by heapifying the root.
- **Repeat:** Continue extracting the maximum element and heapifying until the entire array is sorted.
### Example with Visualization
Let's sort the list `[5, 3, 8, 1, 2]` using heap sort.
1. **Build Max Heap:**
- Initial array: `[5, 3, 8, 1, 2]`
- Start heapifying from the last non-leaf node.
- Heapify at index 1: `[5, 3, 8, 1, 2]` (no change, children are already less than the parent)
- Heapify at index 0: `[8, 3, 5, 1, 2]` (swap 5 and 8 to make 8 the root)
2. **Heapify Process:**
- Heapify at index 0: `[8, 3, 5, 1, 2]` (no change needed, already a max heap)
3. **Extract Maximum:**
- Swap root with the last element: `[2, 3, 5, 1, 8]`
- Heapify at index 0: `[5, 3, 2, 1, 8]` (swap 2 and 5)
4. **Repeat Extraction:**
- Swap root with the second last element: `[1, 3, 2, 5, 8]`
- Heapify at index 0: `[3, 1, 2, 5, 8]` (swap 1 and 3)
- Swap root with the third last element: `[2, 1, 3, 5, 8]`
- Heapify at index 0: `[2, 1, 3, 5, 8]` (no change needed)
- Swap root with the fourth last element: `[1, 2, 3, 5, 8]`
After all extractions, the array is sorted: `[1, 2, 3, 5, 8]`.
### Heap Sort Code in Python
```python
def heapify(arr, n, i):
largest = i # Initialize largest as root
left = 2 * i + 1 # left child index
right = 2 * i + 2 # right child index
# See if left child of root exists and is greater than root
if left < n and arr[largest] < arr[left]:
largest = left
# See if right child of root exists and is greater than root
if right < n and arr[largest] < arr[right]:
largest = right
# Change root, if needed
if largest != i:
arr[i], arr[largest] = arr[largest], arr[i] # swap
# Heapify the root.
heapify(arr, n, largest)
def heap_sort(arr):
n = len(arr)
# Build a maxheap.
for i in range(n // 2 - 1, -1, -1):
heapify(arr, n, i)
# One by one extract elements
for i in range(n - 1, 0, -1):
arr[i], arr[0] = arr[0], arr[i] # swap
heapify(arr, i, 0)
# Example usage
arr = [5, 3, 8, 1, 2]
heap_sort(arr)
print("Sorted array:", arr) # Output: [1, 2, 3, 5, 8]
```
### Complexity Analysis
- **Worst Case:** `𝑂(𝑛log𝑛)`. Building the heap takes `𝑂(𝑛)` time, and each of the 𝑛 element extractions takes `𝑂(log𝑛)` time.
- **Best Case:** `𝑂(𝑛log𝑛)`. Even if the array is already sorted, heap sort will still build the heap and perform the extractions.
- **Average Case:** `𝑂(𝑛log𝑛)`. Similar to the worst-case, the overall complexity remains `𝑂(𝑛log𝑛)` because each insertion and deletion in a heap takes `𝑂(log𝑛)` time, and these operations are performed 𝑛 times.

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# Stacks in Python
In Data Structures and Algorithms, a stack is a linear data structure that complies with the Last In, First Out (LIFO) rule. It works by use of two fundamental techniques: **PUSH** which inserts an element on top of the stack and **POP** which takes out the topmost element.This concept is similar to a stack of plates in a cafeteria. Stacks are usually used for handling function calls, expression evaluation, and parsing in programming. Indeed, they are efficient in managing memory as well as tracking program state.
## Points to be Remebered
- A stack is a collection of data items that can be accessed at only one end, called **TOP**.
- Items can be inserted and deleted in a stack only at the TOP.
- The last item inserted in a stack is the first one to be deleted.
- Therefore, a stack is called a **Last-In-First-Out (LIFO)** data structure.
## Real Life Examples of Stacks
- **PILE OF BOOKS** - Suppose a set of books are placed one over the other in a pile. When you remove books from the pile, the topmost book will be removed first. Similarly, when you have to add a book to the pile, the book will be placed at the top of the file.
- **PILE OF PLATES** - The first plate begins the pile. The second plate is placed on the top of the first plate and the third plate is placed on the top of the second plate, and so on. In general, if you want to add a plate to the pile, you can keep it on the top of the pile. Similarly, if you want to remove a plate, you can remove the plate from the top of the pile.
- **BANGLES IN A HAND** - When a person wears bangles, the last bangle worn is the first one to be removed.
## Applications of Stacks
Stacks are widely used in Computer Science:
- Function call management
- Maintaining the UNDO list for the application
- Web browser *history management*
- Evaluating expressions
- Checking the nesting of parentheses in an expression
- Backtracking algorithms (Recursion)
Understanding these applications is essential for Software Development.
## Operations on a Stack
Key operations on a stack include:
- **PUSH** - It is the process of inserting a new element on the top of a stack.
- **OVERFLOW** - A situation when we are pushing an item in a stack that is full.
- **POP** - It is the process of deleting an element from the top of a stack.
- **UNDERFLOW** - A situation when we are popping item from an empty stack.
- **PEEK** - It is the process of getting the most recent value of stack *(i.e. the value at the top of the stack)*
- **isEMPTY** - It is the function which return true if stack is empty else false.
- **SHOW** -Displaying stack items.
## Implementing Stacks in Python
```python
def isEmpty(S):
if len(S) == 0:
return True
else:
return False
def Push(S, item):
S.append(item)
def Pop(S):
if isEmpty(S):
return "Underflow"
else:
val = S.pop()
return val
def Peek(S):
if isEmpty(S):
return "Underflow"
else:
top = len(S) - 1
return S[top]
def Show(S):
if isEmpty(S):
print("Sorry, No items in Stack")
else:
print("(Top)", end=' ')
t = len(S) - 1
while t >= 0:
print(S[t], "<", end=' ')
t -= 1
print()
stack = [] # initially stack is empty
Push(stack, 5)
Push(stack, 10)
Push(stack, 15)
print("Stack after Push operations:")
Show(stack)
print("Peek operation:", Peek(stack))
print("Pop operation:", Pop(stack))
print("Stack after Pop operation:")
Show(stack)
```
## Output
```markdown
Stack after Push operations:
(Top) 15 < 10 < 5 <
Peek operation: 15
Pop operation: 15
Stack after Pop operation:
(Top) 10 < 5 <
```
## Complexity Analysis
- **Worst case**: `O(n)` This occurs when the stack is full, it is dominated by the usage of Show operation.
- **Best case**: `O(1)` When the operations like isEmpty, Push, Pop and Peek are used, they have a constant time complexity of O(1).
- **Average case**: `O(n)` The average complexity is likely to be lower than O(n), as the stack is not always full.

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# Time and Space Complexity
We can solve a problem using one or more algorithms. It's essential to learn how to compare the performance of different algorithms and select the best one for a specific task.
Therefore, it is highly required to use a method to compare the solutions in order to judge which one is more optimal.
The method must be:
- Regardless of the system or its settings on which the algorithm is executing.
- Demonstrate a direct relationship with the quantity of inputs.
- Able to discriminate between two methods with clarity and precision.
Two such methods use to analyze algorithms are `time complexity` and `space complexity`.
## What is Time Complexity?
The _number of operations an algorithm performs in proportion to the quantity of the input_ is measured by time complexity. It facilitates our investigation of how the performance of the algorithm scales with increasing input size. But in real life, **_time complexity does not refer to the time taken by the machine to execute a particular code_**.
## Order of Growth and Asymptotic Notations
The Order of Growth explains how an algorithm's space or running time expands as the amount of the input does. This increase is described via asymptotic language, such Big O notation, which concentrates on the dominating term as the input size approaches infinity and is independent of lower-order terms and machine-specific constants.
### Common Asymptotic Notation
1. `Big Oh (O)`: Provides the worst-case scenario for describing the upper bound of an algorithm's execution time.
2. `Big Omega (Ω)`: Provides the best-case scenario and describes the lower bound.
3. `Big Theta (Θ)`: Gives a tight constraint on the running time by describing both the upper and lower bounds.
### 1. Big Oh (O) Notation
Big O notation describes how an algorithm behaves as the input size gets closer to infinity and provides an upper bound on the time or space complexity of the method. It helps developers and computer scientists to evaluate the effectiveness of various algorithms without regard to the software or hardware environment.
To denote asymptotic upper bound, we use O-notation. For a given function `g(n)`, we denote by `O(g(n))` (pronounced "big-oh of g of n") the set of functions:
$$
O(g(n)) = \{ f(n) : \exists \text{ positive constants } c \text{ and } n_0 \text{ such that } 0 \leq f(n) \leq c \cdot g(n) \text{ for all } n \geq n_0 \}
$$
Graphical representation of Big Oh:
![BigOh Notation Graph](images/Time-And-Space-Complexity-BigOh.png)
### 2. Big Omega (Ω) Notation
Big Omega (Ω) notation is used to describe the lower bound of an algorithm's running time. It provides a way to express the minimum time complexity that an algorithm will take to complete. In other words, Big Omega gives us a guarantee that the algorithm will take at least a certain amount of time to run, regardless of other factors.
To denote asymptotic lower bound, we use Omega-notation. For a given function `g(n)`, we denote by `Ω(g(n))` (pronounced "big-omega of g of n") the set of functions:
$$
\Omega(g(n)) = \{ f(n) : \exists \text{ positive constants } c \text{ and } n_0 \text{ such that } 0 \leq c \cdot g(n) \leq f(n) \text{ for all } n \geq n_0 \}
$$
Graphical representation of Big Omega:
![BigOmega Notation Graph](images/Time-And-Space-Complexity-BigOmega.png)
### 3. Big Theta (Θ) Notation
Big Theta (Θ) notation provides a way to describe the asymptotic tight bound of an algorithm's running time. It offers a precise measure of the time complexity by establishing both an upper and lower bound, indicating that the running time of an algorithm grows at the same rate as a given function, up to constant factors.
To denote asymptotic tight bound, we use Theta-notation. For a given function `g(n)`, we denote by `Θ(g(n))` (pronounced "big-theta of g of n") the set of functions:
$$
\Theta(g(n)) = \{ f(n) : \exists \text{ positive constants } c_1, c_2, \text{ and } n_0 \text{ such that } 0 \leq c_1 \cdot g(n) \leq f(n) \leq c_2 \cdot g(n) \text{ for all } n \geq n_0 \}
$$
Graphical representation of Big Theta:
![Big Theta Notation Graph](images/Time-And-Space-Complexity-BigTheta.png)
## Best Case, Worst Case and Average Case
### 1. Best-Case Scenario:
The best-case scenario refers to the situation where an algorithm performs optimally, achieving the lowest possible time or space complexity. It represents the most favorable conditions under which an algorithm operates.
#### Characteristics:
- Represents the minimum time or space required by an algorithm to solve a problem.
- Occurs when the input data is structured in such a way that the algorithm can exploit its strengths fully.
- Often used to analyze the lower bound of an algorithm's performance.
#### Example:
Consider the `linear search algorithm` where we're searching for a `target element` in an array. The best-case scenario occurs when the target element is found `at the very beginning of the array`. In this case, the algorithm would only need to make one comparison, resulting in a time complexity of `O(1)`.
### 2. Worst-Case Scenario:
The worst-case scenario refers to the situation where an algorithm performs at its poorest, achieving the highest possible time or space complexity. It represents the most unfavorable conditions under which an algorithm operates.
#### Characteristics:
- Represents the maximum time or space required by an algorithm to solve a problem.
- Occurs when the input data is structured in such a way that the algorithm encounters the most challenging conditions.
- Often used to analyze the upper bound of an algorithm's performance.
#### Example:
Continuing with the `linear search algorithm`, the worst-case scenario occurs when the `target element` is either not present in the array or located `at the very end`. In this case, the algorithm would need to iterate through the entire array, resulting in a time complexity of `O(n)`, where `n` is the size of the array.
### 3. Average-Case Scenario:
The average-case scenario refers to the expected performance of an algorithm over all possible inputs, typically calculated as the arithmetic mean of the time or space complexity.
#### Characteristics:
- Represents the typical performance of an algorithm across a range of input data.
- Takes into account the distribution of inputs and their likelihood of occurrence.
- Provides a more realistic measure of an algorithm's performance compared to the best-case or worst-case scenarios.
#### Example:
For the `linear search algorithm`, the average-case scenario considers the probability distribution of the target element's position within the array. If the `target element is equally likely to be found at any position in the array`, the average-case time complexity would be `O(n/2)`, as the algorithm would, on average, need to search halfway through the array.
## Space Complexity
The memory space that a code utilizes as it is being run is often referred to as space complexity. Additionally, space complexity depends on the machine, therefore rather than using the typical memory units like MB, GB, etc., we will express space complexity using the Big O notation.
#### Examples of Space Complexity
1. `Constant Space Complexity (O(1))`: Algorithms that operate on a fixed-size array or use a constant number of variables have O(1) space complexity.
2. `Linear Space Complexity (O(n))`: Algorithms that store each element of the input array in a separate variable or data structure have O(n) space complexity.
3. `Quadratic Space Complexity (O(n^2))`: Algorithms that create a two-dimensional array or matrix with dimensions based on the input size have O(n^2) space complexity.
#### Analyzing Space Complexity
To analyze space complexity:
- Identify the variables, data structures, and recursive calls used by the algorithm.
- Determine how the space requirements scale with the input size.
- Express the space complexity using Big O notation, considering the dominant terms that contribute most to the overall space usage.
## Examples to calculate time and space complexity
#### 1. Print all elements of given array
Consider each line takes one unit of time to run. So, to simply iterate over an array to print all elements it will take `O(n)` time, where n is the size of array.
Code:
```python
arr = [1,2,3,4] #1
for x in arr: #2
print(x) #3
```
Here, the 1st statement executes only once. So, it takes one unit of time to run. The for loop consisting of 2nd and 3rd statements executes 4 times.
Also, as the code dosen't take any additional space except the input arr its Space Complexity is O(1) constant.
#### 2. Linear Search
Linear search is a simple algorithm for finding an element in an array by sequentially checking each element until a match is found or the end of the array is reached. Here's an example of calculating the time and space complexity of linear search:
```python
def linear_search(arr, target):
for x in arr: # n iterations in worst case
if x == target: # 1
return True # 1
return False # If element not found
# Example usage
arr = [1, 3, 5, 7, 9]
target = 5
print(linear_search(arr, target))
```
**Time Complexity Analysis**
The for loop iterates through the entire array, which takes O(n) time in the worst case, where n is the size of the array.
Inside the loop, each operation takes constant time (O(1)).
Therefore, the time complexity of linear search is `O(n)`.
**Space Complexity Analysis**
The space complexity of linear search is `O(1)` since it only uses a constant amount of additional space for variables regardless of the input size.
#### 3. Binary Search
Binary search is an efficient algorithm for finding an element in a sorted array by repeatedly dividing the search interval in half. Here's an example of calculating the time and space complexity of binary search:
```python
def binary_search(arr, target):
left = 0 # 1
right = len(arr) - 1 # 1
while left <= right: # log(n) iterations in worst case
mid = (left + right) // 2 # log(n)
if arr[mid] == target: # 1
return mid # 1
elif arr[mid] < target: # 1
left = mid + 1 # 1
else:
right = mid - 1 # 1
return -1 # If element not found
# Example usage
arr = [1, 3, 5, 7, 9]
target = 5
print(binary_search(arr, target))
```
**Time Complexity Analysis**
The initialization of left and right takes constant time (O(1)).
The while loop runs for log(n) iterations in the worst case, where n is the size of the array.
Inside the loop, each operation takes constant time (O(1)).
Therefore, the time complexity of binary search is `O(log n)`.
**Space Complexity Analysis**
The space complexity of binary search is `O(1)` since it only uses a constant amount of additional space for variables regardless of the input size.
#### 4. Fibbonaci Sequence
Let's consider an example of a function that generates Fibonacci numbers up to a given index and stores them in a list. In this case, the space complexity will not be constant because the size of the list grows with the Fibonacci sequence.
```python
def fibonacci_sequence(n):
fib_list = [0, 1] # Initial Fibonacci sequence with first two numbers
while len(fib_list) < n: # O(n) iterations in worst case
next_fib = fib_list[-1] + fib_list[-2] # Calculating next Fibonacci number
fib_list.append(next_fib) # Appending next Fibonacci number to list
return fib_list
# Example usage
n = 10
fib_sequence = fibonacci_sequence(n)
print(fib_sequence)
```
**Time Complexity Analysis**
The while loop iterates until the length of the Fibonacci sequence list reaches n, so it takes `O(n)` iterations in the `worst case`.Inside the loop, each operation takes constant time (O(1)).
**Space Complexity Analysis**
The space complexity of this function is not constant because it creates and stores a list of Fibonacci numbers.
As n grows, the size of the list also grows, so the space complexity is O(n), where n is the index of the last Fibonacci number generated.

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# Trie
A Trie is a tree-like data structure used for storing a dynamic set of strings where the keys are usually strings. It is also known as prefix tree or digital tree.
>Trie is a type of search tree, where each node represents a single character of a string.
>Nodes are linked in such a way that they form a tree, where each path from the root to a leaf node represents a unique string stored in the Trie.
## Characteristics of Trie
- **Prefix Matching**: Tries are particularly useful for prefix matching operations. Any node in the Trie represents a common prefix of all strings below it.
- **Space Efficiency**: Tries can be more space-efficient than other data structures like hash tables for storing large sets of strings with common prefixes.
- **Time Complexity**: Insertion, deletion, and search operations in a Trie have a time complexity of
𝑂(𝑚), where m is the length of the string. This makes Tries very efficient for these operations.
## Structure of Trie
Trie mainly consists of three parts:
- **Root**: The root of a Trie is an empty node that does not contain any character.
- **Edges**: Each edge in the Trie represents a character in the alphabet of the stored strings.
- **Nodes**: Each node contains a character and possibly additional information, such as a boolean flag indicating if the node represents the end of a valid string.
To implement the nodes of trie. We use Classes in Python. Each node is an object of the Node Class.
Node Class have mainly two components
- *Array of size 26*: It is used to represent the 26 alphabets. Initially all are None. While inserting the words, then array will be filled with object of child nodes.
- *End of word*: It is used to represent the end of word while inserting.
Code Block of Node Class :
```python
class Node:
def __init__(self):
self.alphabets = [None] * 26
self.end_of_word = 0
```
Now we need to implement Trie. We create another class named Trie with some methods like Insertion, Searching and Deletion.
**Initialization:** In this, we initializes the Trie with a `root` node.
Code Implementation of Initialization:
```python
class Trie:
def __init__(self):
self.root = Node()
```
## Operations on Trie
1. **Insertion**: Inserts the word into the Trie. This method takes `word` as parameter. For each character in the word, it checks if there is a corresponding child node. If not, it creates a new `Node`. After processing all the characters in word, it increments the `end_of_word` value of the last node.
Code Implementation of Insertion:
```python
def insert(self, word):
node = self.root
for char in word:
index = ord(char) - ord('a')
if not node.alphabets[index]:
node.alphabets[index] = Node()
node = node.alphabets[index]
node.end_of_word += 1
```
2. **Searching**: Search the `word` in trie. Searching process starts from the `root` node. Each character of the `word` is processed. After traversing the whole word in trie, it return the count of words.
There are two cases in Searching:
- *Word Not found*: It happens when the word we search not present in the trie. This case will occur, if the value of `alphabets` array at that character is `None` or if the value of `end_of_word` of the node, reached after traversing the whole word is `0`.
- *Word found*: It happens when the search word is present in the Trie. This case will occur, when the `end_of_word` value is greater than `0` of the node after traversing the whole word.
Code Implementation of Searching:
```python
def Search(self, word):
node = self.root
for char in word:
index = ord(char) - ord('a')
if not node.alphabets[index]:
return 0
node = node.alphabets[index]
return node.end_of_word
```
3. **Deletion**: To delete a string, follow the path of the string. If the end node is reached and `end_of_word` is greater than `0` then decrement the value.
Code Implementation of Deletion:
```python
def delete(self, word):
node = self.root
for char in word:
index = ord(char) - ord('a')
node = node.alphabets[index]
if node.end_of_word:
node.end_of_word-=1
```
Python Code to implement Trie:
```python
class Node:
def __init__(self):
self.alphabets = [None] * 26
self.end_of_word = 0
class Trie:
def __init__(self):
self.root = Node()
def insert(self, word):
node = self.root
for char in word:
index = ord(char) - ord('a')
if not node.alphabets[index]:
node.alphabets[index] = Node()
node = node.alphabets[index]
node.end_of_word += 1
def Search(self, word):
node = self.root
for char in word:
index = ord(char) - ord('a')
if not node.alphabets[index]:
return 0
node = node.alphabets[index]
return node.end_of_word
def delete(self, word):
node = self.root
for char in word:
index = ord(char) - ord('a')
node = node.alphabets[index]
if node.end_of_word:
node.end_of_word-=1
if __name__ == "__main__":
trie = Trie()
word1 = "apple"
word2 = "app"
word3 = "bat"
trie.insert(word1)
trie.insert(word2)
trie.insert(word3)
print(trie.Search(word1))
print(trie.Search(word2))
print(trie.Search(word3))
trie.delete(word2)
print(trie.Search(word2))
```

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# Understanding the Neural Network
## Table of Contents
<details>
<summary>Click to expand</summary>
- [Introduciton](#introduction)
- [Neuron to Perceptron](#neuron-to-perceptron)
- [Key concepts](#key-concepts)
- [Layers](#layers)
- [Weights and Biases](#weights-and-biases)
- [Activation Function](#activation-functions)
- [Forward and Backward Pass](#forward-and-backward-propagation)
- [Implementation](#building-from-scratch)
</details>
## Introduction
This guide will walk you through a fundamental neural network implementation in Python. We'll build a `Neural Network` from scratch, allowing you to grasp the core concepts of how neural networks learn and make predictions.
### Let's start by Understanding the Basic Architecture of Neural Nets
## Neuron to Perceptron
| `Neuron` cells forming the humand nervous system | `Perceptron` inspired from human brain |
| :----------------------------------------------- | -------------------------------------: |
| Neurons are nerve cells that send messages all over your body to allow you to do everything from breathing to talking, eating, walking, and thinking. | The perceptron is a mathematical model of a biological neuron. Performing heavy computations to think like humans. |
| Neuron collects signals from dendrites. | The first layer is knownn as Input Layer, acting like dendritres to receive the input signal. |
| Synapses are the connections between neurons where signals are transmitted. | Weights represent synapses. |
The axon terminal releases neurotransmitters to transmit the signal to other neurons. | The output is the final result – between 1 & 0, representing classification or prediction. |
---
> Human brain has a Network of Neurons, about 86 billion neurons and more than a 100 trillion synapses connections!
## **Key Concepts**
Artificial neurons are the fundamental processing units in an ANN. They receive inputs, multiply them by weights (representing the strength of connections), sum those weighted inputs, and then apply an activation function to produce an output.
### Layers
Neurons in ANNs are organized into layers:
* **Input Layer:** Receives the raw data.
* **(n) Hidden Layers:** (Optional) Intermediate layers where complex transformations occur. They learn to detect patterns and features in the data.
* **Output Layer:** Produces the final result (prediction or classification).
### Weights and Biases
- For each input $(x_i)$, a weight $(w_i)$ is associated with it. Weights, multiplied with input units $(w_i \cdot x_i)$, determine the influence of one neuron's output on another.
- A bias $(b_i)$ is added to help influence the end product, giving the equation as $(w_i \cdot x_i + b_i)$.
- During training, the network adjusts these weights and biases to minimize errors and improve its predictions.
### Activation Functions
- An activation function is applied to the result to introduce non-linearity in the model, allowing ANNs to learn more complex relationships from the data.
- The resulting equation: $y = f(g(x))$, determines whether the neuron will "fire" or not, i.e., if its output will be used as input for the next neuron.
- Common activation functions include the sigmoid function, tanh (hyperbolic tangent), and ReLU (Rectified Linear Unit).
### Forward and Backward Propagation
- **Flow of Information:** All the above steps are part of Forward Propagation. It gives the output equation as $y = f\left(\sum_{i=1}^n w_i x_i + b_i\right)$
- **Error Correction:** Backpropagation is the algorithm used to train ANNs by calculating the gradient of error at the output layer and then propagating this error backward through the network. This allows the network to adjust its weights and biases in the direction that reduces the error.
- The chain rule of calculus is the foundational concept to compute the gradient of the error:
$
\delta_{ij}(E) = \frac{\partial E}{\partial w_{ij}} = \frac{\partial E}{\partial \hat{y}_j} \cdot \frac{\partial \hat{y}_j}{\partial \theta_j} \cdot \frac{\partial \theta_j}{\partial w_{ij}}
$
where $E$ is the error, $\hat{y}_j$ is the predicted output, $\theta_j$ is the input to the activation function of the $j^{th}$ neuron, and $w_{ij}$ is the weight from neuron $i$ to neuron $j$.
## Building From Scratch
```python
# Import required libraries
import numpy as np
import matplotlib.pyplot as plt
class SimpleNeuralNetwork:
def __init__(self, input_size, hidden_size, output_size):
self.input_size = input_size
self.hidden_size = hidden_size
self.output_size = output_size
# Initialize weights and biases
self.weights_input_hidden = np.random.randn(input_size, hidden_size)
self.bias_hidden = np.random.randn(hidden_size)
self.weights_hidden_output = np.random.randn(hidden_size, output_size)
self.bias_output = np.random.randn(output_size)
def sigmoid(self, x):
return 1 / (1 + np.exp(-x))
def sigmoid_derivative(self, x):
return x * (1 - x)
def forward(self, X):
self.hidden_layer_input = np.dot(X, self.weights_input_hidden) + self.bias_hidden
self.hidden_layer_output = self.sigmoid(self.hidden_layer_input)
self.output_layer_input = np.dot(self.hidden_layer_output, self.weights_hidden_output) + self.bias_output
self.output = self.sigmoid(self.output_layer_input)
return self.output
def backward(self, X, y, learning_rate):
output_error = y - self.output
output_delta = output_error * self.sigmoid_derivative(self.output)
hidden_error = output_delta.dot(self.weights_hidden_output.T)
hidden_delta = hidden_error * self.sigmoid_derivative(self.hidden_layer_output)
self.weights_hidden_output += self.hidden_layer_output.T.dot(output_delta) * learning_rate
self.bias_output += np.sum(output_delta, axis=0) * learning_rate
self.weights_input_hidden += X.T.dot(hidden_delta) * learning_rate
self.bias_hidden += np.sum(hidden_delta, axis=0) * learning_rate
def train(self, X, y, epochs, learning_rate):
self.losses = []
for epoch in range(epochs):
self.forward(X)
self.backward(X, y, learning_rate)
loss = np.mean(np.square(y - self.output))
self.losses.append(loss)
if epoch % 1000 == 0:
print(f"Epoch {epoch}, Loss: {loss}")
def plot_loss(self):
plt.plot(self.losses)
plt.xlabel('Epochs')
plt.ylabel('Loss')
plt.title('Training Loss Over Epochs')
plt.show()
```
### Creating the Input & Output Array
Let's create a dummy input and outpu dataset. Here, the first two columns will be useful, while the rest might be noise.
```python
X = np.array([[0,0], [0,1], [1,0], [1,1]])
y = np.array([[0], [1], [1], [1]])
```
### Defining the Neural Network
With our input and output data ready, we'll define a simple neural network with one hidden layer containing three neurons.
```python
# neural network architecture
input_size = 2
hidden_layers = 1
hidden_neurons = [2]
output_size = 1
```
### Visualizing the Training Loss
To understand how well our model is learning, let's visualize the training loss over epochs.
```python
model = NeuralNetwork(input_size, hidden_layers, hidden_neurons, output_size)
model.train(X, y, 100)
```

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# Binomial Distribution
## Introduction
The binomial distribution is a discrete probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. It is commonly used in statistics and probability theory.
### Key Characteristics
- **Number of trials (n):** The number of independent experiments or trials.
- **Probability of success (p):** The probability of success on an individual trial.
- **Number of successes (k):** The number of successful outcomes in n trials.
The binomial distribution is defined by the probability mass function (PMF):
P(X = k) = (n choose k) p^k (1 - p)^(n - k)
where:
- (n choose k) is the binomial coefficient, calculated as n! / (k!(n-k)!).
## Properties of Binomial Distribution
- **Mean:** μ = np
- **Variance:** σ² = np(1 - p)
- **Standard Deviation:** σ = √(np(1 - p))
## Python Implementation
Let's implement the binomial distribution using Python. We'll use the `scipy.stats` library to compute the binomial PMF and CDF, and `matplotlib` to visualize it.
### Step-by-Step Implementation
1. **Import necessary libraries:**
```python
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import binom
```
2. **Define parameters:**
```python
# Number of trials
n = 10
# Probability of success
p = 0.5
# Number of successes
k = np.arange(0, n + 1)
```
3. **Compute the PMF:**
```python
pmf = binom.pmf(k, n, p)
```
4. **Plot the PMF:**
```python
plt.bar(k, pmf, color='blue')
plt.xlabel('Number of Successes')
plt.ylabel('Probability')
plt.title('Binomial Distribution PMF')
plt.show()
```
5. **Compute the CDF:**
```python
cdf = binom.cdf(k, n, p)
```
6. **Plot the CDF:**
```python
plt.plot(k, cdf, marker='o', linestyle='--', color='blue')
plt.xlabel('Number of Successes')
plt.ylabel('Cumulative Probability')
plt.title('Binomial Distribution CDF')
plt.grid(True)
plt.show()
```
### Complete Code
Here is the complete code for the binomial distribution implementation:
```python
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import binom
# Parameters
n = 10 # Number of trials
p = 0.5 # Probability of success
# Number of successes
k = np.arange(0, n + 1)
# Compute PMF
pmf = binom.pmf(k, n, p)
# Plot PMF
plt.figure(figsize=(12, 6))
plt.subplot(1, 2, 1)
plt.bar(k, pmf, color='blue')
plt.xlabel('Number of Successes')
plt.ylabel('Probability')
plt.title('Binomial Distribution PMF')
# Compute CDF
cdf = binom.cdf(k, n, p)
# Plot CDF
plt.subplot(1, 2, 2)
plt.plot(k, cdf, marker='o', linestyle='--', color='blue')
plt.xlabel('Number of Successes')
plt.ylabel('Cumulative Probability')
plt.title('Binomial Distribution CDF')
plt.grid(True)
plt.tight_layout()
plt.show()

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# Clustering
Clustering is an unsupervised machine learning technique that groups a set of objects in such a way that objects in the same group (called a cluster) are more similar to each other than to those in other groups (clusters). This README provides an overview of clustering, including its fundamental concepts, types, algorithms, and how to implement it using Python.
## Introduction
Clustering is a technique used to find inherent groupings within data without pre-labeled targets. It is widely used in exploratory data analysis, pattern recognition, image analysis, information retrieval, and bioinformatics.
## Concepts
### Centroid
A centroid is the center of a cluster. In the k-means clustering algorithm, for example, each cluster is represented by its centroid, which is the mean of all the data points in the cluster.
### Distance Measure
Distance measures are used to quantify the similarity or dissimilarity between data points. Common distance measures include Euclidean distance, Manhattan distance, and cosine similarity.
### Inertia
Inertia is a metric used to assess the quality of the clusters formed. It is the sum of squared distances of samples to their nearest cluster center.
## Types of Clustering
1. **Hard Clustering**: Each data point either belongs to a cluster completely or not at all.
2. **Soft Clustering (Fuzzy Clustering)**: Each data point can belong to multiple clusters with varying degrees of membership.
## Clustering Algorithms
### K-Means Clustering
K-Means is a popular clustering algorithm that partitions the data into k clusters, where each data point belongs to the cluster with the nearest mean. The algorithm follows these steps:
1. Initialize k centroids randomly.
2. Assign each data point to the nearest centroid.
3. Recalculate the centroids as the mean of all data points assigned to each cluster.
4. Repeat steps 2 and 3 until convergence.
### Hierarchical Clustering
Hierarchical clustering builds a tree of clusters. There are two types:
- **Agglomerative (bottom-up)**: Starts with each data point as a separate cluster and merges the closest pairs of clusters iteratively.
- **Divisive (top-down)**: Starts with all data points in one cluster and splits the cluster iteratively into smaller clusters.
### DBSCAN (Density-Based Spatial Clustering of Applications with Noise)
DBSCAN groups together points that are close to each other based on a distance measurement and a minimum number of points. It can find arbitrarily shaped clusters and is robust to noise.
## Implementation
### Using Scikit-learn
Scikit-learn is a popular machine learning library in Python that provides tools for clustering.
### Code Example
```python
import numpy as np
import pandas as pd
from sklearn.cluster import KMeans
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import silhouette_score
# Load dataset
data = pd.read_csv('path/to/your/dataset.csv')
# Preprocess the data
scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)
# Initialize and fit KMeans model
kmeans = KMeans(n_clusters=3, random_state=42)
kmeans.fit(data_scaled)
# Get cluster labels
labels = kmeans.labels_
# Calculate silhouette score
silhouette_avg = silhouette_score(data_scaled, labels)
print("Silhouette Score:", silhouette_avg)
# Add cluster labels to the original data
data['Cluster'] = labels
print(data.head())
```
## Evaluation Metrics
- **Silhouette Score**: Measures how similar a data point is to its own cluster compared to other clusters.
- **Inertia (Within-cluster Sum of Squares)**: Measures the compactness of the clusters.
- **Davies-Bouldin Index**: Measures the average similarity ratio of each cluster with the cluster that is most similar to it.
- **Dunn Index**: Ratio of the minimum inter-cluster distance to the maximum intra-cluster distance.
## Conclusion
Clustering is a powerful technique for discovering structure in data. Understanding different clustering algorithms and their evaluation metrics is crucial for selecting the appropriate method for a given problem.

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## Confusion Matrix
A confusion matrix is a fundamental performance evaluation tool used in machine learning to assess the accuracy of a classification model. It is an N x N matrix, where N represents the number of target classes.
For binary classification, it results in a 2 x 2 matrix that outlines four key parameters:
1. True Positive (TP) - The predicted value matches the actual value, or the predicted class matches the actual class.
For example - the actual value was positive, and the model predicted a positive value.
2. True Negative (TN) - The predicted value matches the actual value, or the predicted class matches the actual class.
For example - the actual value was negative, and the model predicted a negative value.
3. False Positive (FP)/Type I Error - The predicted value was falsely predicted.
For example - the actual value was negative, but the model predicted a positive value.
4. False Negative (FN)/Type II Error - The predicted value was falsely predicted.
For example - the actual value was positive, but the model predicted a negative value.
The confusion matrix enables the calculation of various metrics like accuracy, precision, recall, F1-Score and specificity.
1. Accuracy - It represents the proportion of correctly classified instances out of the total number of instances in the dataset.
2. Precision - It quantifies the accuracy of positive predictions made by the model.
3. Recall - It quantifies the ability of a model to correctly identify all positive instances in the dataset and is also known as sensitivity or true positive rate.
4. F1-Score - It is a single measure that combines precision and recall, offering a balanced evaluation of a classification model's effectiveness.
To implement the confusion matrix in Python, we can use the confusion_matrix() function from the sklearn.metrics module of the scikit-learn library.
The function returns a 2D array that represents the confusion matrix.
We can also visualize the confusion matrix using a heatmap.
```python
# Import necessary libraries
import numpy as np
from sklearn.metrics import confusion_matrix, classification_report
import seaborn as sns
import matplotlib.pyplot as plt
# Create the NumPy array for actual and predicted labels
actual = np.array(['Apple', 'Apple', 'Apple', 'Not Apple', 'Apple',
'Not Apple', 'Apple', 'Apple', 'Not Apple', 'Not Apple'])
predicted = np.array(['Apple', 'Not Apple', 'Apple', 'Not Apple', 'Apple',
'Apple', 'Apple', 'Apple', 'Not Apple', 'Not Apple'])
# Compute the confusion matrix
cm = confusion_matrix(actual,predicted)
# Plot the confusion matrix with the help of the seaborn heatmap
sns.heatmap(cm,
annot=True,
fmt='g',
xticklabels=['Apple', 'Not Apple'],
yticklabels=['Apple', 'Not Apple'])
plt.xlabel('Prediction', fontsize=13)
plt.ylabel('Actual', fontsize=13)
plt.title('Confusion Matrix', fontsize=17)
plt.show()
# Classifications Report based on Confusion Metrics
print(classification_report(actual, predicted))
```
### Results
```
1. Confusion Matrix:
[[5 1]
[1 3]]
2. Classification Report:
precision recall f1-score support
Apple 0.83 0.83 0.83 6
Not Apple 0.75 0.75 0.75 4
accuracy 0.80 10
macro avg 0.79 0.79 0.79 10
weighted avg 0.80 0.80 0.80 10
```

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# Cost Functions in Machine Learning
Cost functions, also known as loss functions, play a crucial role in training machine learning models. They measure how well the model performs on the training data by quantifying the difference between predicted and actual values. Different types of cost functions are used depending on the problem domain and the nature of the data.
## Types of Cost Functions
### 1. Mean Squared Error (MSE)
**Explanation:**
MSE is one of the most commonly used cost functions, particularly in regression problems. It calculates the average squared difference between the predicted and actual values.
**Mathematical Formulation:**
The MSE is defined as:
$$MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2$$
Where:
- `n` is the number of samples.
- $y_i$ is the actual value.
- $\hat{y}_i$ is the predicted value.
**Advantages:**
- Sensitive to large errors due to squaring.
- Differentiable and convex, facilitating optimization.
**Disadvantages:**
- Sensitive to outliers, as the squared term amplifies their impact.
**Python Implementation:**
```python
import numpy as np
def mean_squared_error(y_true, y_pred):
n = len(y_true)
return np.mean((y_true - y_pred) ** 2)
```
### 2. Mean Absolute Error (MAE)
**Explanation:**
MAE is another commonly used cost function for regression tasks. It measures the average absolute difference between predicted and actual values.
**Mathematical Formulation:**
The MAE is defined as:
$$MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i|$$
Where:
- `n` is the number of samples.
- $y_i$ is the actual value.
- $\hat{y}_i$ is the predicted value.
**Advantages:**
- Less sensitive to outliers compared to MSE.
- Provides a linear error term, which can be easier to interpret.
**Disadvantages:**
- Not differentiable at zero, which can complicate optimization.
**Python Implementation:**
```python
import numpy as np
def mean_absolute_error(y_true, y_pred):
n = len(y_true)
return np.mean(np.abs(y_true - y_pred))
```
### 3. Cross-Entropy Loss (Binary)
**Explanation:**
Cross-entropy loss is commonly used in binary classification problems. It measures the dissimilarity between the true and predicted probability distributions.
**Mathematical Formulation:**
For binary classification, the cross-entropy loss is defined as:
$$\text{Cross-Entropy} = -\frac{1}{n} \sum_{i=1}^{n} [y_i \log(\hat{y}_i) + (1 - y_i) \log(1 - \hat{y}_i)]$$
Where:
- `n` is the number of samples.
- $y_i$ is the actual class label (0 or 1).
- $\hat{y}_i$ is the predicted probability of the positive class.
**Advantages:**
- Penalizes confident wrong predictions heavily.
- Suitable for probabilistic outputs.
**Disadvantages:**
- Sensitive to class imbalance.
**Python Implementation:**
```python
import numpy as np
def binary_cross_entropy(y_true, y_pred):
n = len(y_true)
return -np.mean(y_true * np.log(y_pred) + (1 - y_true) * np.log(1 - y_pred))
```
### 4. Cross-Entropy Loss (Multiclass)
**Explanation:**
For multiclass classification problems, the cross-entropy loss is adapted to handle multiple classes.
**Mathematical Formulation:**
The multiclass cross-entropy loss is defined as:
$$\text{Cross-Entropy} = -\frac{1}{n} \sum_{i=1}^{n} \sum_{c=1}^{C} y_{i,c} \log(\hat{y}_{i,c})$$
Where:
- `n` is the number of samples.
- `C` is the number of classes.
- $y_{i,c}$ is the indicator function for the true class of sample `i`.
- $\hat{y}_{i,c}$ is the predicted probability of sample `i` belonging to class `c`.
**Advantages:**
- Handles multiple classes effectively.
- Encourages the model to assign high probabilities to the correct classes.
**Disadvantages:**
- Requires one-hot encoding for class labels, which can increase computational complexity.
**Python Implementation:**
```python
import numpy as np
def categorical_cross_entropy(y_true, y_pred):
n = len(y_true)
return -np.mean(np.sum(y_true * np.log(y_pred), axis=1))
```
### 5. Hinge Loss (SVM)
**Explanation:**
Hinge loss is commonly used in support vector machines (SVMs) for binary classification tasks. It penalizes misclassifications by a linear margin.
**Mathematical Formulation:**
For binary classification, the hinge loss is defined as:
$$\text{Hinge Loss} = \frac{1}{n} \sum_{i=1}^{n} \max(0, 1 - y_i \cdot \hat{y}_i)$$
Where:
- `n` is the number of samples.
- $y_i$ is the actual class label (-1 or 1).
- $\hat{y}_i$ is the predicted score for sample \( i \).
**Advantages:**
- Encourages margin maximization in SVMs.
- Robust to outliers due to the linear penalty.
**Disadvantages:**
- Not differentiable at the margin, which can complicate optimization.
**Python Implementation:**
```python
import numpy as np
def hinge_loss(y_true, y_pred):
n = len(y_true)
loss = np.maximum(0, 1 - y_true * y_pred)
return np.mean(loss)
```
### 6. Huber Loss
**Explanation:**
Huber loss is a combination of MSE and MAE, providing a compromise between the two. It is less sensitive to outliers than MSE and provides a smooth transition to MAE for large errors.
**Mathematical Formulation:**
The Huber loss is defined as:
$$\text{Huber Loss} = \frac{1}{n} \sum_{i=1}^{n} \left\{
\begin{array}{ll}
\frac{1}{2} (y_i - \hat{y}_i)^2 & \text{if } |y_i - \hat{y}_i| \leq \delta \\
\delta(|y_i - \hat{y}_i| - \frac{1}{2} \delta) & \text{otherwise}
\end{array}
\right.$$
Where:
- `n` is the number of samples.
- $\delta$ is a threshold parameter.
**Advantages:**
- Provides a smooth loss function.
- Less sensitive to outliers than MSE.
**Disadvantages:**
- Requires tuning of the threshold parameter.
**Python Implementation:**
```python
import numpy as np
def huber_loss(y_true, y_pred, delta):
error = y_true - y_pred
loss = np.where(np.abs(error) <= delta, 0.5 * error ** 2, delta * (np.abs(error) - 0.5 * delta))
return np.mean(loss)
```
### 7. Log-Cosh Loss
**Explanation:**
Log-Cosh loss is a smooth approximation of the MAE and is less sensitive to outliers than MSE. It provides a smooth transition from quadratic for small errors to linear for large errors.
**Mathematical Formulation:**
The Log-Cosh loss is defined as:
$$\text{Log-Cosh Loss} = \frac{1}{n} \sum_{i=1}^{n} \log(\cosh(y_i - \hat{y}_i))$$
Where:
- `n` is the number of samples.
**Advantages:**
- Smooth and differentiable everywhere.
- Less sensitive to outliers.
**Disadvantages:**
- Computationally more expensive than simple losses like MSE.
**Python Implementation:**
```python
import numpy as np
def logcosh_loss(y_true, y_pred):
error = y_true - y_pred
loss = np.log(np.cosh(error))
return np.mean(loss)
```
These implementations provide various options for cost functions suitable for different machine learning tasks. Each function has its advantages and disadvantages, making them suitable for different scenarios and problem domains.

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# Decision Trees
Decision trees are a type of supervised machine learning algorithm that is mostly used in classification problems. They work for both categorical and continuous input and output variables.
It is also interpreted as acyclic graph that can be utilized for decision-making is called a decision tree. Every branching node in the graph looks at a particular feature (j) of the feature vector. The left branch is taken when the feature's value is less than a certain threshold; the right branch is taken when it is higher. The class to which the example belongs is decided upon as soon as the leaf node is reached.
## Key Components of a Decision Tree
**Root Node:** This is the decision tree's first node, and it symbolizes the whole population or sample.
**Internal Nodes:** These are the nodes that make decisions and they stand in for the characteristics or features.
**Leaf Nodes:** These are the nodes that make decisions and they stand in for the characteristics or features.
**Branches:** These are the lines that connect the nodes, and they show how the choice was made depending on the feature value.
### Example: Predicting Loan Approval
In this example, we will use a decision tree to forecast the approval or denial of a loan application based on a number of features, including job status, credit score, and income.
```
Root Node
(All Applications)
/ \
Internal Node Internal Node
(Credit Score) (Employment Status)
/ \ / \
Leaf Node Leaf Node Leaf Node Leaf Node
(Approve Loan) (Deny Loan) (Approve Loan) (Deny Loan)
```
> There are various formulations of the decision tree learning algorithm. Here, we consider just one, called ID3.
## Appropriate Problems For Decision Tree Learning
In general, decision tree learning works best on issues that have the following characteristics:
1. ***Instances*** are represented by ***key-value pairs***
2. The ***output values of the target function are discrete***. Each sample is given a Boolean categorization (yes or no) by the decision tree. Learning functions with multiple possible output values can be effortlessly integrated into decision tree approaches.
3. ***Disjunctive descriptions may be required***
4. The ***training data may contain errors*** – ***Decision tree learning methods are robust to errors,*** both errors in classifications of the training examples and errors in the attribute
values that describe these examples.
5. ***Missing attribute values could be present in the training data.*** Using decision tree approaches is possible even in cases where some training examples have missing values.
# Decision Tree Algorithm
The decision tree method classifies the data according to a tree structure. The root node, that holds the complete dataset, is where it all begins. The algorithm then determines which feature, according to a certain criterion like information gain or Gini impurity, is appropriate for splitting the dataset. Subsets of the dataset are then created according to the values of the chosen feature. Until a halting condition is satisfied—for example, obtaining a minimal number of samples per leaf node or a maximum tree depth—this procedure is repeated recursively for every subset.
### Which Attribute Is the Best Classifier?
- The ID3 algorithm's primary idea is choose which characteristic to test at each tree node.
- Information gain, a statistical feature that quantifies how well a certain attribute divides the training samples into groups based on the target classification.
- When building the tree, ID3 chooses a candidate attribute  using the information gain metric.
## Entropy & Information
**Entropy** is a metric that quantifies the level of impurity or uncertainty present in a given dataset. When it comes to decision trees, entropy measures how similar the target variable is within a specific node or subset of the data. It is utilized for assessing the quality of potential splits during the tree construction process.
The entropy of a node is calculated as:
__Entropy = -Σ(p<sub>i</sub> * log<sub>2</sub>(p<sub>i</sub>))__
where `p`<sub>`i`</sub> is the proportion of instances belonging to class `i` in the current node. The entropy is at its maximum when all classes are equally represented in the node, indicating maximum impurity or uncertainty.
**Information Gain** is a measure used to estimate the possible reduction in entropy achieved by separating the data according to a certain attribute. It quantifies the projected decrease in impurity or uncertainty after the separation.
The information gain for a feature `A` is calculated as:
__Information Gain = Entropy(parent) - Σ(weight(child) * Entropy(child))__
### Example of a Decision Tree
Let us look at a basic decision tree example that predicts a person's likelihood of playing tennis based on climate conditions
**Data Set:**
---
| Day | Outlook | Temperature | Humidity | Wind | PlayTennis |
|-----|---------|-------------|----------|------|------------|
| D1 | Sunny | Hot | High | Weak | No |
| D2 | Sunny | Hot | High | Strong | No |
| D3 | Overcast| Hot | High | Weak | Yes |
| D4 | Rain | Mild | High | Weak | Yes |
| D5 | Rain | Cool | Normal | Weak | Yes |
| D6 | Rain | Cool | Normal | Strong | No |
| D7 | Overcast| Cool | Normal | Strong | Yes |
| D8 | Sunny | Mild | High | Weak | No |
| D9 | Sunny | Cool | Normal | Weak | Yes |
| D10 | Rain | Mild | Normal | Weak | Yes |
| D11 | Sunny | Mild | Normal | Strong | Yes |
| D12 | Overcast| Mild | High | Strong | Yes |
| D13 | Overcast| Hot | Normal | Weak | Yes |
| D14 | Rain | Mild | High | Strong | No |
---
1. Calculate the entropy of the entire dataset.
2. For each feature, calculate the information gain by splitting the data based on that feature.
3. Select the feature with the highest information gain to create the root node.
4. Repeat steps 1-3 for each child node until a stopping criterion is met (e.g., all instances in a node belong to the same class, or the maximum depth is reached).
Let's start with calculating the entropy of the entire dataset:
Total instances: 14
No instances: 5
Yes instances: 9
**Entropy** = -((5/14) * log2(5/14) + (9/14) * log2(9/14)) = 0.940
Now, we'll calculate the information gain for each feature:
**Outlook**:
- Sunny: 2 No, 3 Yes (Entropy = 0.971)
- Overcast: 0 No, 4 Yes (Entropy = 0)
- Rain: 3 No, 2 Yes (Entropy = 0.971)
Information Gain = 0.940 - ((5/14) * 0.971 + (4/14) * 0 + (5/14) * 0.971) = 0.246
**Temperature**:
- Hot: 2 No, 2 Yes (Entropy = 1)
- Mild: 2 No, 4 Yes (Entropy = 0.811)
- Cool: 1 No, 3 Yes (Entropy = 0.918)
Information Gain = 0.940 - ((4/14) * 1 + (6/14) * 0.811 + (4/14) * 0.918) = 0.029
**Humidity**:
- High: 3 No, 4 Yes (Entropy = 0.985)
- Normal: 2 No, 5 Yes (Entropy = 0.971)
Information Gain = 0.940 - ((7/14) * 0.985 + (7/14) * 0.971) = 0.012
**Wind**:
- Weak: 2 No, 6 Yes (Entropy = 0.811)
- Strong: 3 No, 3 Yes (Entropy = 1)
Information Gain = 0.940 - ((8/14) * 0.811 + (6/14) * 1) = 0.048
The feature with the highest information gain is Outlook, so we'll create the root node based on that.
**Step 1: Root Node (Outlook)**
```
Root Node (Outlook)
/ | \
Sunny Overcast Rain
Entropy: 0.971 Entropy: 0 Entropy: 0.971
5 instances 4 instances 5 instances
```
Now, we'll continue building the tree by recursively splitting the child nodes based on the feature with the highest information gain within each subset.
**Step 2: Splitting Sunny and Rain Nodes**
For the Sunny node:
- Temperature:
- Hot: 2 No, 0 Yes (Entropy = 0)
- Mild: 0 No, 3 Yes (Entropy = 0)
- Cool: 0 No, 0 Yes (Entropy = 0)
Information Gain = 0.971
- Humidity:
- High: 1 No, 2 Yes (Entropy = 0.918)
- Normal: 1 No, 1 Yes (Entropy = 1)
Information Gain = 0.153
- Wind:
- Weak: 1 No, 2 Yes (Entropy = 0.918)
- Strong: 1 No, 1 Yes (Entropy = 1)
Information Gain = 0.153
The highest information gain is achieved by splitting on Temperature, so we'll create child nodes for Sunny based on Temperature.
For the Rain node:
- Wind:
- Weak: 1 No, 3 Yes (Entropy = 0.918)
- Strong: 2 No, 0 Yes (Entropy = 0)
Information Gain = 0.153
Since there is only one feature left (Wind), we'll create child nodes for Rain based on Wind.
**Step 3: Updated Decision Tree**
```
Root Node (Outlook)
/ | \
Sunny Overcast Rain
/ | \ Entropy: 0 / \
Hot Mild Cool 4 instances Weak Strong
Entropy: 0 Entropy: 0 Entropy: 0.918 Entropy: 0
2 instances 3 instances 4 instances 1 instance
```
At this point, all leaf nodes are either pure (entropy = 0) or have instances belonging to a single class. Therefore, we can stop the tree construction process.
**Step 4: Pruning the Decision Tree**
The decision tree we constructed in the previous steps is a complete tree that perfectly classifies the training data. However, this can lead to overfitting, meaning the tree may perform poorly on new, unseen data due to its complexity and memorization of noise in the training set.
To address this, we can prune the tree by removing some of the leaf nodes or branches that contribute little to the overall classification accuracy. Pruning helps to generalize the tree and improve its performance on unseen data.
There are various pruning techniques, such as:
1. **Pre-pruning**: Stopping the tree growth based on a pre-defined criterion (e.g., maximum depth, minimum instances in a node, etc.).
2. **Post-pruning**: Growing the tree to its full depth and then removing subtrees or branches based on a pruning criterion.
>We can observe that the "Cool" node under the "Sunny" branch has no instances in the training data. Removing this node will not affect the classification accuracy on the training set, and it may help generalize the tree better.
**Step 5: Pruned Decision Tree**
```
Root Node (Outlook)
/ | \
/ | \
Sunny Overcast Rain
/ \ Entropy: 0 / \
Hot Mild 4 instances Weak Strong
Entropy: 0 Entropy: 0.918 Entropy: 0 Entropy: 0
2 instances 4 instances 3 instances 2 instances
```
**Step 6: Visualizing the Decision Tree**
Decision trees can be visualized graphically to provide a clear representation of the hierarchical structure and the decision rules. This visualization can aid in understanding the tree's logic and interpreting the results.
There are various tools and libraries available for visualizing decision trees. One popular library in Python is `graphviz`, which can create tree-like diagrams and visualizations.
Here's an example of how to visualize our pruned decision tree using `graphviz` in Python:
```python
import graphviz
from sklearn import tree
# Create a decision tree classifier
decision_tree_classifier = tree.DecisionTreeClassifier()
# Train the classifier on the dataset X and labels y
decision_tree_classifier.fit(X, y)
# Visualize the decision tree
tree_dot_data = tree.export_graphviz(decision_tree_classifier, out_file=None,
feature_names=['Outlook', 'Temperature', 'Humidity', 'Wind'],
class_names=['No', 'Yes'], filled=True, rounded=True, special_characters=True)
# Create a graph from the DOT data
graph = graphviz.Source(tree_dot_data)
# Render and save the decision tree as an image file
graph.render("decision_tree")
```
```
Outlook
/ | \
Sunny Overcast Rain
/ | / \
Humidity Yes Wind Wind
/ \ / \
High Normal Weak Strong
No Yes Yes No
```
The final decision tree classifies instances based on the following rules:
- If Outlook is Overcast, PlayTennis is Yes
- If Outlook is Sunny and Temperature is Hot, PlayTennis is No
- If Outlook is Sunny and Temperature is Mild, PlayTennis is Yes
- If Outlook is Sunny and Temperature is Cool, PlayTennis is Yes (no instances in the dataset)
- If Outlook is Rain and Wind is Weak, PlayTennis is Yes
- If Outlook is Rain and Wind is Strong, PlayTennis is No
> Note that the calculated entropies and information gains may vary slightly depending on the specific implementation and rounding methods used.

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# Ensemble Learning
Ensemble Learning is a powerful machine learning paradigm that combines multiple models to achieve better performance than any individual model. The idea is to leverage the strengths of different models to improve overall accuracy, robustness, and generalization.
## Introduction
Ensemble Learning is a technique that combines the predictions from multiple machine learning models to make more accurate and robust predictions than a single model. It leverages the diversity of different models to reduce errors and improve performance.
## Types of Ensemble Learning
### Bagging
Bagging, or Bootstrap Aggregating, involves training multiple versions of the same model on different subsets of the training data and averaging their predictions. The most common example of bagging is the `RandomForest` algorithm.
### Boosting
Boosting focuses on training models sequentially, where each new model corrects the errors made by the previous ones. This way, the ensemble learns from its mistakes, leading to improved performance. `AdaBoost` and `Gradient Boosting` are popular examples of boosting algorithms.
### Stacking
Stacking involves training multiple models (the base learners) and a meta-model that combines their predictions. The base learners are trained on the original dataset, while the meta-model is trained on the outputs of the base learners. This approach allows leveraging the strengths of different models.
## Advantages and Disadvantages
### Advantages
- **Improved Accuracy**: Combines the strengths of multiple models.
- **Robustness**: Reduces the risk of overfitting and model bias.
- **Versatility**: Can be applied to various machine learning tasks, including classification and regression.
### Disadvantages
- **Complexity**: More complex than individual models, making interpretation harder.
- **Computational Cost**: Requires more computational resources and training time.
- **Implementation**: Can be challenging to implement and tune effectively.
## Key Concepts
- **Diversity**: The models in the ensemble should be diverse to benefit from their different strengths.
- **Voting/Averaging**: For classification, majority voting is used to combine predictions. For regression, averaging is used.
- **Weighting**: In some ensembles, models are weighted based on their accuracy or other metrics.
## Code Examples
### Bagging with Random Forest
Below is an example of using Random Forest for classification on the Iris dataset.
```python
import numpy as np
import pandas as pd
from sklearn.datasets import load_iris
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, classification_report
# Load dataset
iris = load_iris()
X, y = iris.data, iris.target
# Split dataset
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
# Initialize Random Forest model
clf = RandomForestClassifier(n_estimators=100, random_state=42)
# Train the model
clf.fit(X_train, y_train)
# Make predictions
y_pred = clf.predict(X_test)
# Evaluate the model
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy * 100:.2f}%")
print("Classification Report:\n", classification_report(y_test, y_pred))
```
### Boosting with AdaBoost
Below is an example of using AdaBoost for classification on the Iris dataset.
```
from sklearn.ensemble import AdaBoostClassifier
from sklearn.tree import DecisionTreeClassifier
# Initialize base model
base_model = DecisionTreeClassifier(max_depth=1)
# Initialize AdaBoost model
ada_clf = AdaBoostClassifier(base_estimator=base_model, n_estimators=50, random_state=42)
# Train the model
ada_clf.fit(X_train, y_train)
# Make predictions
y_pred = ada_clf.predict(X_test)
# Evaluate the model
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy * 100:.2f}%")
print("Classification Report:\n", classification_report(y_test, y_pred))
```
### Stacking with Multiple Models
Below is an example of using stacking with multiple models for classification on the Iris dataset.
```
from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import KNeighborsClassifier
from sklearn.svm import SVC
from sklearn.ensemble import StackingClassifier
# Define base models
base_models = [
('knn', KNeighborsClassifier(n_neighbors=5)),
('svc', SVC(kernel='linear', probability=True))
]
# Define meta-model
meta_model = LogisticRegression()
# Initialize Stacking model
stacking_clf = StackingClassifier(estimators=base_models, final_estimator=meta_model, cv=5)
# Train the model
stacking_clf.fit(X_train, y_train)
# Make predictions
y_pred = stacking_clf.predict(X_test)
# Evaluate the model
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy * 100:.2f}%")
print("Classification Report:\n", classification_report(y_test, y_pred))
```
## Conclusion
Ensemble Learning is a powerful technique that combines multiple models to improve overall performance. By leveraging the strengths of different models, it provides better accuracy, robustness, and generalization. However, it comes with increased complexity and computational cost. Understanding and implementing ensemble methods can significantly enhance machine learning solutions.

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# Grid Search
Grid Search is a hyperparameter tuning technique in Machine Learning that helps to find the best combination of hyperparameters for a given model. It works by defining a grid of hyperparameters and then training the model with all the possible combinations of hyperparameters to find the best performing set.
The Grid Search Method considers some hyperparameter combinations and selects the one returning a lower error score. This method is specifically useful when there are only some hyperparameters in order to optimize. However, it is outperformed by other weighted-random search methods when the Machine Learning model grows in complexity.
## Implementation
Before applying Grid Searching on any algorithm, data is divided into training and validation set, a validation set is used to validate the models. A model with all possible combinations of hyperparameters is tested on the validation set to choose the best combination.
Grid Searching can be applied to any hyperparameters algorithm whose performance can be improved by tuning hyperparameter. For example, we can apply grid searching on K-Nearest Neighbors by validating its performance on a set of values of K in it. Same thing we can do with Logistic Regression by using a set of values of learning rate to find the best learning rate at which Logistic Regression achieves the best accuracy.
Let us consider that the model accepts the below three parameters in the form of input:
1. Number of hidden layers `[2, 4]`
2. Number of neurons in every layer `[5, 10]`
3. Number of epochs `[10, 50]`
If we want to try out two options for every parameter input (as specified in square brackets above), it estimates different combinations. For instance, one possible combination can be `[2, 5, 10]`. Finding such combinations manually would be a headache.
Now, suppose that we had ten different parameters as input, and we would like to try out five possible values for each and every parameter. It would need manual input from the programmer's end every time we like to alter the value of a parameter, re-execute the code, and keep a record of the outputs for every combination of the parameters.
Grid Search automates that process, as it accepts the possible value for every parameter and executes the code in order to try out each and every possible combination outputs the result for the combinations and outputs the combination having the best accuracy.
Higher values of C tell the model, the training data resembles real world information, place a greater weight on the training data. While lower values of C do the opposite.
## Explaination of the Code
The code provided performs hyperparameter tuning for a Logistic Regression model using a manual grid search approach. It evaluates the model's performance for different values of the regularization strength hyperparameter C on the Iris dataset.
1. datasets from sklearn is imported to load the Iris dataset.
2. LogisticRegression from sklearn.linear_model is imported to create and fit the logistic regression model.
3. The Iris dataset is loaded, with X containing the features and y containing the target labels.
4. A LogisticRegression model is instantiated with max_iter=10000 to ensure convergence during the fitting process, as the default maximum iterations (100) might not be sufficient.
5. A list of different values for the regularization strength C is defined. The hyperparameter C controls the regularization strength, with smaller values specifying stronger regularization.
6. An empty list scores is initialized to store the model's performance scores for different values of C.
7. A for loop iterates over each value in the C list:
8. logit.set_params(C=choice) sets the C parameter of the logistic regression model to the current value in the loop.
9. logit.fit(X, y) fits the logistic regression model to the entire Iris dataset (this is typically done on training data in a real scenario, not the entire dataset).
10. logit.score(X, y) calculates the accuracy of the fitted model on the dataset and appends this score to the scores list.
11. After the loop, the scores list is printed, showing the accuracy for each value of C.
### Python Code
```python
from sklearn import datasets
from sklearn.linear_model import LogisticRegression
iris = datasets.load_iris()
X = iris['data']
y = iris['target']
logit = LogisticRegression(max_iter = 10000)
C = [0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2]
scores = []
for choice in C:
logit.set_params(C=choice)
logit.fit(X, y)
scores.append(logit.score(X, y))
print(scores)
```
#### Results
```
[0.9666666666666667, 0.9666666666666667, 0.9733333333333334, 0.9733333333333334, 0.98, 0.98, 0.9866666666666667, 0.9866666666666667]
```
We can see that the lower values of `C` performed worse than the base parameter of `1`. However, as we increased the value of `C` to `1.75` the model experienced increased accuracy.
It seems that increasing `C` beyond this amount does not help increase model accuracy.

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# Hierarchical Clustering
Hierarchical Clustering is a method of cluster analysis that seeks to build a hierarchy of clusters. This README provides an overview of the hierarchical clustering algorithm, including its fundamental concepts, types, steps, and how to implement it using Python.
## Introduction
Hierarchical Clustering is an unsupervised learning method used to group similar objects into clusters. Unlike other clustering techniques, hierarchical clustering does not require the number of clusters to be specified beforehand. It produces a tree-like structure called a dendrogram, which displays the arrangement of the clusters and their sub-clusters.
## Concepts
### Dendrogram
A dendrogram is a tree-like diagram that records the sequences of merges or splits. It is a useful tool for visualizing the process of hierarchical clustering.
### Distance Measure
Distance measures are used to quantify the similarity or dissimilarity between data points. Common distance measures include Euclidean distance, Manhattan distance, and cosine similarity.
### Linkage Criteria
Linkage criteria determine how the distance between clusters is calculated. Different linkage criteria include single linkage, complete linkage, average linkage, and Ward's linkage.
## Types of Hierarchical Clustering
1. **Agglomerative Clustering (Bottom-Up Approach)**:
- Starts with each data point as a separate cluster.
- Repeatedly merges the closest pairs of clusters until only one cluster remains or a stopping criterion is met.
2. **Divisive Clustering (Top-Down Approach)**:
- Starts with all data points in a single cluster.
- Repeatedly splits clusters into smaller clusters until each data point is its own cluster or a stopping criterion is met.
## Steps in Hierarchical Clustering
1. **Calculate Distance Matrix**: Compute the distance between each pair of data points.
2. **Create Clusters**: Treat each data point as a single cluster.
3. **Merge Closest Clusters**: Find the two clusters that are closest to each other and merge them into a single cluster.
4. **Update Distance Matrix**: Update the distance matrix to reflect the distance between the new cluster and the remaining clusters.
5. **Repeat**: Repeat steps 3 and 4 until all data points are merged into a single cluster or the desired number of clusters is achieved.
## Linkage Criteria
1. **Single Linkage (Minimum Linkage)**: The distance between two clusters is defined as the minimum distance between any single data point in the first cluster and any single data point in the second cluster.
2. **Complete Linkage (Maximum Linkage)**: The distance between two clusters is defined as the maximum distance between any single data point in the first cluster and any single data point in the second cluster.
3. **Average Linkage**: The distance between two clusters is defined as the average distance between all pairs of data points, one from each cluster.
4. **Ward's Linkage**: The distance between two clusters is defined as the increase in the sum of squared deviations from the mean when the two clusters are merged.
## Implementation
### Using Scikit-learn
Scikit-learn is a popular machine learning library in Python that provides tools for hierarchical clustering.
### Code Example
```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.cluster.hierarchy import dendrogram, linkage
from sklearn.cluster import AgglomerativeClustering
from sklearn.preprocessing import StandardScaler
# Load dataset
data = pd.read_csv('path/to/your/dataset.csv')
# Preprocess the data
scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)
# Perform hierarchical clustering
Z = linkage(data_scaled, method='ward')
# Plot the dendrogram
plt.figure(figsize=(10, 7))
dendrogram(Z)
plt.title('Dendrogram')
plt.xlabel('Data Points')
plt.ylabel('Distance')
plt.show()
# Perform Agglomerative Clustering
agg_clustering = AgglomerativeClustering(n_clusters=3, affinity='euclidean', linkage='ward')
labels = agg_clustering.fit_predict(data_scaled)
# Add cluster labels to the original data
data['Cluster'] = labels
print(data.head())
```
## Evaluation Metrics
- **Silhouette Score**: Measures how similar a data point is to its own cluster compared to other clusters.
- **Cophenetic Correlation Coefficient**: Measures how faithfully a dendrogram preserves the pairwise distances between the original data points.
- **Dunn Index**: Ratio of the minimum inter-cluster distance to the maximum intra-cluster distance.
## Conclusion
Hierarchical clustering is a versatile and intuitive method for clustering data. It is particularly useful when the number of clusters is not known beforehand. By understanding the different linkage criteria and evaluation metrics, one can effectively apply hierarchical clustering to various types of data.

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# List of sections
- [Section title](filename.md)
- [Introduction to scikit-learn](sklearn-introduction.md)
- [Binomial Distribution](binomial-distribution.md)
- [Regression in Machine Learning](regression.md)
- [Confusion Matrix](confusion-matrix.md)
- [Decision Tree Learning](decision-tree.md)
- [Random Forest](random-forest.md)
- [Support Vector Machine Algorithm](support-vector-machine.md)
- [Artificial Neural Network from the Ground Up](ann.md)
- [Introduction To Convolutional Neural Networks (CNNs)](intro-to-cnn.md)
- [TensorFlow.md](tensorflow.md)
- [PyTorch.md](pytorch.md)
- [Ensemble Learning](ensemble-learning.md)
- [Types of optimizers](types-of-optimizers.md)
- [Logistic Regression](logistic-regression.md)
- [Types_of_Cost_Functions](cost-functions.md)
- [Clustering](clustering.md)
- [Hierarchical Clustering](hierarchical-clustering.md)
- [Grid Search](grid-search.md)
- [Transformers](transformers.md)
- [K-nearest neighbor (KNN)](knn.md)

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# Understanding Convolutional Neural Networks (CNN)
## Introduction
Convolutional Neural Networks (CNNs) are a specialized type of artificial neural network designed primarily for processing structured grid data like images. CNNs are particularly powerful for tasks involving image recognition, classification, and computer vision. They have revolutionized these fields, outperforming traditional neural networks by leveraging their unique architecture to capture spatial hierarchies in images.
### Why CNNs are Superior to Traditional Neural Networks
1. **Localized Receptive Fields**: CNNs use convolutional layers that apply filters to local regions of the input image. This localized connectivity ensures that the network learns spatial hierarchies and patterns, such as edges and textures, which are essential for image recognition tasks.
2. **Parameter Sharing**: In CNNs, the same filter (set of weights) is used across different parts of the input, significantly reducing the number of parameters compared to fully connected layers in traditional neural networks. This not only lowers the computational cost but also mitigates the risk of overfitting.
3. **Translation Invariance**: Due to the shared weights and pooling operations, CNNs are inherently invariant to translations of the input image. This means that they can recognize objects even when they appear in different locations within the image.
4. **Hierarchical Feature Learning**: CNNs automatically learn a hierarchy of features from low-level features like edges to high-level features like shapes and objects. Traditional neural networks, on the other hand, require manual feature extraction which is less effective and more time-consuming.
### Use Cases of CNNs
- **Image Classification**: Identifying objects within an image (e.g., classifying a picture as containing a cat or a dog).
- **Object Detection**: Detecting and locating objects within an image (e.g., finding faces in a photo).
- **Image Segmentation**: Partitioning an image into segments or regions (e.g., dividing an image into different objects and background).
- **Medical Imaging**: Analyzing medical scans like MRI, CT, and X-rays for diagnosis.
> This guide will walk you through the fundamentals of CNNs and their implementation in Python. We'll build a simple CNN from scratch, explaining each component to help you understand how CNNs process images and extract features.
### Let's start by understanding the basic architecture of CNNs.
## CNN Architecture
Convolution layers, pooling layers, and fully connected layers are just a few of the many building blocks that CNNs use to automatically and adaptively learn spatial hierarchies of information through backpropagation.
### Convolutional Layer
The convolutional layer is the core building block of a CNN. The layer's parameters consist of a set of learnable filters (or kernels), which have a small receptive field but extend through the full depth of the input volume.
#### Input Shape
The dimensions of the input image, including the number of channels (e.g., 3 for RGB images & 1 for Grayscale images).
![image](assets/cnn-input_shape.png)
- The input matrix is a binary image of handwritten digits,
where '1' marks the pixels containing the digit (ink/grayscale area) and '0' marks the background pixels (empty space).
- The first matrix shows the represnetation of 1 and 0, which can be depicted as a vertical line and a closed loop.
- The second matrix represents 9, combining the loop and line.
#### Strides
The step size with which the filter moves across the input image.
![image](assets/cnn-strides.png)
- This visualization will help you understand how the filter (kernel) moves acroos the input matrix with stride values of (3,3) and (2,2).
- A stride of 1 means the filter moves one step at a time, ensuring it covers the entire input matrix.
- However, with larger strides (like 3 or 2 in this example), the filter may not cover all elements, potentially missing some information.
- While this might seem like a drawback, higher strides are often used to reduce computational cost and decrease the output size, which can be beneficial in speeding up the training process and preventing overfitting.
#### Padding
Determines whether the output size is the same as the input size ('same') or reduced ('valid').
![image](assets/cnn-padding.png)
- `Same` padding is preferred in earlier layers to preserve spatial and edge information, as it can help the network learn more detailed features.
- Choose `valid` padding when focusing on the central input region or requiring specific output dimensions.
- Padding value can be determined by $ ( f - 1 ) \over 2 $, where f isfilter size
#### Filters
Small matrices that slide over the input data to extract features.
![image](assets/cnn-filters.png)
- The first filter aims to detect closed loops within the input image, being highly relevant for recognizing digits with circular or oval shapes, such as '0', '6', '8', or '9'.
- The next filter helps in detecting vertical lines, crucial for identifying digits like '1', '4', '7', and parts of other digits that contain vertical strokes.
- The last filter shows how to detect diagonal lines in the input image, useful for identifying the slashes present in digits like '1', '7', or parts of '4' and '9'.
#### Output
A set of feature maps that represent the presence of different features in the input.
![image](assets/cnn-ouputs.png)
- With no padding and a stride of 1, the 3x3 filter moves one step at a time across the 7x5 input matrix. The filter can only move within the original boundaries of the input, resulting in a smaller 5x3 output matrix. This configuration is useful when you want to reduce the spatial dimensions of the feature map while preserving the exact spatial relationships between features.
- By adding zero padding to the input matrix, it is expanded to 9x7, allowing the 3x3 filter to "fit" fully on the edges and corners. With a stride of 1, the filter still moves one step at a time, but now the output matrix is the same size (7x5) as the original input. Same padding is often preferred in early layers of a CNN to preserve spatial information and avoid rapid feature map shrinkage.
- Without padding, the 3x3 filter operates within the original input matrix boundaries, but now it moves two steps at a time (stride 2). This significantly reduces the output matrix size to 3x2. Larger strides are employed to decrease computational cost and the output size, which can be beneficial in speeding up the training process and preventing overfitting. However, they might miss some finer details due to the larger jumps.
- The output dimension of a CNN model is given by, $$ n_{out} = { n_{in} + (2 \cdot p) - k \over s } $$
where,
n<sub>in</sub> = number of input features
p = padding
k = kernel size
s = stride
- Also, the number of trainable parameters for each layer is given by, $ (n_c \cdot [k \cdot k] \cdot f) + f $
where,
n<sub>c</sub> = number of input channels
k x k = kernel size
f = number of filters
an additional f is added for bias
### Pooling Layer
Pooling layers reduce the dimensionality of each feature map while retaining the most critical information. The most common form of pooling is max pooling.
- **Input Shape:** The dimensions of the feature map from the convolutional layer.
- **Pooling Size:** The size of the pooling window (e.g., 2x2).
- **Strides:** The step size for the pooling operation.
- **Output:** A reduced feature map highlighting the most important features.
<div align='center'>
<img src='assets/cnn-pooling.png' width='800'></img>
</div>
- The high values (8) indicate that the "closed loop" filter found a strong match in those regions.
- First matrix of size 6x4 represents a downsampled version of the input.
- While the second matrix with 3x2, resulting in more aggressive downsampling.
### Flatten Layer
The flatten layer converts the 2D matrix data to a 1D vector, which can be fed into a fully connected (dense) layer.
- **Input Shape:** The 2D feature maps from the previous layer.
- **Output:** A 1D vector that represents the same data in a flattened format.
![image](assets/cnn-flattened.png)
### Dropout Layer
Dropout is a regularization technique to prevent overfitting in neural networks by randomly setting a fraction of input units to zero at each update during training time.
- **Input Shape:** The data from the previous layer.
- **Dropout Rate:** The fraction of units to drop (e.g., 0.5 for 50% dropout).
- **Output:** The same shape as the input, with some units set to zero.
![image](assets/cnn-dropout.png)
- The updated 0 values represents the dropped units.
## Implementation
Below is the implementation of a simple CNN in Python. Each function within the `CNN` class corresponds to a layer in the network.
```python
import numpy as np
class CNN:
def __init__(self):
pass
def convLayer(self, input_shape, channels, strides, padding, filter_size):
height, width = input_shape
input_shape_with_channels = (height, width, channels)
print("Input Shape (with channels):", input_shape_with_channels)
# Generate random input and filter matrices
input_matrix = np.random.randint(0, 10, size=input_shape_with_channels)
filter_matrix = np.random.randint(0, 5, size=(filter_size[0], filter_size[1], channels))
print("\nInput Matrix:\n", input_matrix[:, :, 0])
print("\nFilter Matrix:\n", filter_matrix[:, :, 0])
padding = padding.lower()
if padding == 'same':
# Calculate padding needed for each dimension
pad_height = filter_size[0] // 2
pad_width = filter_size[1] // 2
# Apply padding to the input matrix
input_matrix = np.pad(input_matrix, ((pad_height, pad_height), (pad_width, pad_width), (0, 0)), mode='constant')
# Adjust height and width to consider the padding
height += 2 * pad_height
width += 2 * pad_width
elif padding == 'valid':
pass
else:
return "Invalid Padding!!"
# Output dimensions
conv_height = (height - filter_size[0]) // strides[0] + 1
conv_width = (width - filter_size[1]) // strides[1] + 1
output_matrix = np.zeros((conv_height, conv_width, channels))
# Convolution Operation
for i in range(0, height - filter_size[0] + 1, strides[0]):
for j in range(0, width - filter_size[1] + 1, strides[1]):
receptive_field = input_matrix[i:i + filter_size[0], j:j + filter_size[1], :]
output_matrix[i // strides[0], j // strides[1], :] = np.sum(receptive_field * filter_matrix, axis=(0, 1, 2))
return output_matrix
def maxPooling(self, input_matrix, pool_size=(2, 2), strides_pooling=(2, 2)):
input_height, input_width, input_channels = input_matrix.shape
pool_height, pool_width = pool_size
stride_height, stride_width = strides_pooling
# Calculate output dimensions
pooled_height = (input_height - pool_height) // stride_height + 1
pooled_width = (input_width - pool_width) // stride_width + 1
# Initialize output
pooled_matrix = np.zeros((pooled_height, pooled_width, input_channels))
# Perform max pooling
for c in range(input_channels):
for i in range(0, input_height - pool_height + 1, stride_height):
for j in range(0, input_width - pool_width + 1, stride_width):
patch = input_matrix[i:i + pool_height, j:j + pool_width, c]
pooled_matrix[i // stride_height, j // stride_width, c] = np.max(patch)
return pooled_matrix
def flatten(self, input_matrix):
return input_matrix.flatten()
def dropout(self, input_matrix, dropout_rate=0.5):
assert 0 <= dropout_rate < 1, "Dropout rate must be in [0, 1)."
dropout_mask = np.random.binomial(1, 1 - dropout_rate, size=input_matrix.shape)
return input_matrix * dropout_mask
```
Run the below command to generate output with random input and filter matrices, depending on the given size.
```python
input_shape = (5, 5)
channels = 1
strides = (1, 1)
padding = 'valid'
filter_size = (3, 3)
cnn_model = CNN()
conv_output = cnn_model.convLayer(input_shape, channels, strides, padding, filter_size)
print("\nConvolution Output:\n", conv_output[:, :, 0])
pool_size = (2, 2)
strides_pooling = (1, 1)
maxPool_output = cnn_model.maxPooling(conv_output, pool_size, strides_pooling)
print("\nMax Pooling Output:\n", maxPool_output[:, :, 0])
flattened_output = cnn_model.flatten(maxPool_output)
print("\nFlattened Output:\n", flattened_output)
dropout_output = cnn_model.dropout(flattened_output, dropout_rate=0.3)
print("\nDropout Output:\n", dropout_output)
```
Feel free to play around with the parameters!

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# K-Nearest Neighbors (KNN) Machine Learning Algorithm in Python
## Introduction
K-Nearest Neighbors (KNN) is a simple, yet powerful, supervised machine learning algorithm used for both classification and regression tasks. It assumes that similar things exist in close proximity. In other words, similar data points are near to each other.
## How KNN Works
KNN works by finding the distances between a query and all the examples in the data, selecting the specified number of examples (K) closest to the query, then voting for the most frequent label (in classification) or averaging the labels (in regression).
### Steps:
1. **Choose the number K of neighbors**
2. **Calculate the distance** between the query-instance and all the training samples
3. **Sort the distances** and determine the nearest neighbors based on the K-th minimum distance
4. **Gather the labels** of the nearest neighbors
5. **Vote for the most frequent label** (in case of classification) or **average the labels** (in case of regression)
## When to Use KNN
### Advantages:
- **Simple and easy to understand:** KNN is intuitive and easy to implement.
- **No training phase:** KNN is a lazy learner, meaning there is no explicit training phase.
- **Effective with a small dataset:** KNN performs well with a small number of input variables.
### Disadvantages:
- **Computationally expensive:** The algorithm becomes significantly slower as the number of examples and/or predictors/independent variables increase.
- **Sensitive to irrelevant features:** All features contribute to the distance equally.
- **Memory-intensive:** Storing all the training data can be costly.
### Use Cases:
- **Recommender Systems:** Suggest items based on similarity to user preferences.
- **Image Recognition:** Classify images by comparing new images to the training set.
- **Finance:** Predict credit risk or fraud detection based on historical data.
## KNN in Python
### Required Libraries
To implement KNN, we need the following Python libraries:
- `numpy`
- `pandas`
- `scikit-learn`
- `matplotlib` (for visualization)
### Installation
```bash
pip install numpy pandas scikit-learn matplotlib
```
### Example Code
Let's implement a simple KNN classifier using the Iris dataset.
#### Step 1: Import Libraries
```python
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.neighbors import KNeighborsClassifier
from sklearn.metrics import accuracy_score
import matplotlib.pyplot as plt
```
#### Step 2: Load Dataset
```python
from sklearn.datasets import load_iris
iris = load_iris()
X = iris.data
y = iris.target
```
#### Step 3: Split Dataset
```python
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
```
#### Step 4: Train KNN Model
```python
knn = KNeighborsClassifier(n_neighbors=3)
knn.fit(X_train, y_train)
```
#### Step 5: Make Predictions
```python
y_pred = knn.predict(X_test)
```
#### Step 6: Evaluate the Model
```python
accuracy = accuracy_score(y_test, y_pred)
print(f'Accuracy: {accuracy}')
```
### Visualization (Optional)
```python
# Plotting the decision boundary for visualization (for 2D data)
h = .02 # step size in the mesh
# Create color maps
cmap_light = plt.cm.RdYlBu
cmap_bold = plt.cm.RdYlBu
# For simplicity, we take only the first two features of the dataset
X_plot = X[:, :2]
x_min, x_max = X_plot[:, 0].min() - 1, X_plot[:, 0].max() + 1
y_min, y_max = X_plot[:, 1].min() - 1, y_plot[:, 1].max() + 1
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = knn.predict(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
plt.figure()
plt.pcolormesh(xx, yy, Z, cmap=cmap_light)
# Plot also the training points
plt.scatter(X_plot[:, 0], X_plot[:, 1], c=y, edgecolor='k', cmap=cmap_bold)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("3-Class classification (k = 3)")
plt.show()
```
## Generalization and Considerations
- **Choosing K:** The choice of K is critical. Smaller values of K can lead to noisy models, while larger values make the algorithm computationally expensive and might oversimplify the model.
- **Feature Scaling:** Since KNN relies on distance calculations, features should be scaled (standardized or normalized) to ensure that all features contribute equally to the distance computation.
- **Distance Metrics:** The choice of distance metric (Euclidean, Manhattan, etc.) can affect the performance of the algorithm.
In conclusion, KNN is a versatile and easy-to-implement algorithm suitable for various classification and regression tasks, particularly when working with small datasets and well-defined features. However, careful consideration should be given to the choice of K, feature scaling, and distance metrics to optimize its performance.

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# Logistic Regression
Logistic Regression is a statistical method used for binary classification problems. It is a type of regression analysis where the dependent variable is categorical. This README provides an overview of logistic regression, including its fundamental concepts, assumptions, and how to implement it using Python.
## Table of Contents
1. [Introduction](#introduction)
2. [Concepts](#concepts)
3. [Assumptions](#assumptions)
4. [Implementation](#implementation)
- [Using Scikit-learn](#using-scikit-learn)
- [Code Example](#code-example)
5. [Evaluation Metrics](#evaluation-metrics)
6. [Conclusion](#conclusion)
7. [References](#references)
## Introduction
Logistic Regression is used to model the probability of a binary outcome based on one or more predictor variables (features). It is widely used in various fields such as medical research, social sciences, and machine learning for tasks such as spam detection, fraud detection, and predicting user behavior.
## Concepts
### Sigmoid Function
The logistic regression model uses the sigmoid function to map predicted values to probabilities. The sigmoid function is defined as:
$$
\sigma(z) = \frac{1}{1 + e^{-z}}
$$
Where \( z \) is a linear combination of the input features.
### Odds and Log-Odds
- **Odds**: The odds represent the ratio of the probability of an event occurring to the probability of it not occurring.
$$\text{Odds} = \frac{P(Y=1)}{P(Y=0)}$$
- **Log-Odds**: The log-odds is the natural logarithm of the odds.
$$\text{Log-Odds} = \log \left( \frac{P(Y=1)}{P(Y=0)} \right)$$
Logistic regression models the log-odds as a linear combination of the input features.
### Model Equation
The logistic regression model equation is:
$$
\log \left( \frac{P(Y=1)}{P(Y=0)} \right) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \cdots + \beta_n X_n
$$
Where:
- &beta;₀ is the intercept.
- &beta;<sub>i</sub> are the coefficients for the predictor variables X<sub>i</sub>.
## Assumptions
1. **Linearity**: The log-odds of the response variable are a linear combination of the predictor variables.
2. **Independence**: Observations should be independent of each other.
3. **No Multicollinearity**: Predictor variables should not be highly correlated with each other.
4. **Large Sample Size**: Logistic regression requires a large sample size to provide reliable results.
## Implementation
### Using Scikit-learn
Scikit-learn is a popular machine learning library in Python that provides tools for logistic regression.
### Code Example
```python
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import accuracy_score, confusion_matrix, classification_report
# Load dataset
data = pd.read_csv('path/to/your/dataset.csv')
# Define features and target variable
X = data[['feature1', 'feature2', 'feature3']]
y = data['target']
# Split data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
# Initialize and train logistic regression model
model = LogisticRegression()
model.fit(X_train, y_train)
# Make predictions
y_pred = model.predict(X_test)
# Evaluate the model
accuracy = accuracy_score(y_test, y_pred)
conf_matrix = confusion_matrix(y_test, y_pred)
class_report = classification_report(y_test, y_pred)
print("Accuracy:", accuracy)
print("Confusion Matrix:\n", conf_matrix)
print("Classification Report:\n", class_report)
```
## Evaluation Metrics
- **Accuracy**: The proportion of correctly classified instances among all instances.
- **Confusion Matrix**: A table showing the number of true positives, true negatives, false positives, and false negatives.
- **Precision, Recall, and F1-Score**: Metrics to evaluate the performance of the classification model.
## Conclusion
Logistic regression is a fundamental classification technique that is easy to implement and interpret. It is a powerful tool for binary classification problems and provides a probabilistic framework for predicting binary outcomes.

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# PyTorch: A Comprehensive Overview
## Introduction
PyTorch is an open-source deep learning framework developed by Facebook's AI Research lab. It provides a flexible and efficient platform for building and deploying machine learning models. PyTorch is known for its dynamic computational graph, ease of use, and strong support for GPU acceleration.
## Key Features
- **Dynamic Computational Graphs**: PyTorch's dynamic computation graph (or define-by-run) allows you to change the network architecture during runtime. This feature makes debugging and experimenting with different model architectures easier.
- **GPU Acceleration**: PyTorch supports CUDA, enabling efficient computation on GPUs.
- **Extensive Libraries and Tools**: PyTorch has a rich ecosystem of libraries and tools such as torchvision for computer vision, torchtext for natural language processing, and more.
- **Community Support**: PyTorch has a large and active community, providing extensive resources, tutorials, and forums for support.
## Installation
To install PyTorch, you can use pip:
```sh
pip install torch torchvision
```
For detailed installation instructions, including GPU support, visit the [official PyTorch installation guide](https://pytorch.org/get-started/locally/).
## Basic Usage
### Tensors
Tensors are the fundamental building blocks in PyTorch. They are similar to NumPy arrays but can run on GPUs.
```python
import torch
# Creating a tensor
x = torch.tensor([1.0, 2.0, 3.0])
print(x)
# Performing basic operations
y = torch.tensor([4.0, 5.0, 6.0])
z = x + y
print(z)
```
### Autograd
Autograd is PyTorch's automatic differentiation engine that powers neural network training. It tracks operations on tensors to automatically compute gradients.
```python
# Requires gradient
x = torch.tensor([1.0, 2.0, 3.0], requires_grad=True)
# Perform operations
y = x ** 2
z = y.sum()
# Compute gradients
z.backward()
print(x.grad)
```
### Building Neural Networks
PyTorch provides the `torch.nn` module to build neural networks.
```python
import torch
import torch.nn as nn
import torch.optim as optim
# Define a simple neural network
class SimpleNN(nn.Module):
def __init__(self):
super(SimpleNN, self).__init__()
self.fc1 = nn.Linear(3, 1)
def forward(self, x):
x = self.fc1(x)
return x
# Create the network, define the criterion and optimizer
model = SimpleNN()
criterion = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=0.01)
# Dummy input and target
inputs = torch.tensor([[1.0, 2.0, 3.0]])
targets = torch.tensor([[0.5]])
# Forward pass
outputs = model(inputs)
loss = criterion(outputs, targets)
# Backward pass and optimization
loss.backward()
optimizer.step()
print(f'Loss: {loss.item()}')
```
## When to Use PyTorch
### Use PyTorch When:
1. **Research and Development**: PyTorch's dynamic computation graph makes it ideal for experimentation and prototyping.
2. **Computer Vision and NLP**: With extensive libraries like torchvision and torchtext, PyTorch is well-suited for these domains.
3. **Custom Operations**: If your work involves custom layers or operations, PyTorch provides the flexibility to implement and integrate them easily.
4. **Community and Ecosystem**: If you prefer a strong community support and extensive third-party resources, PyTorch is a good choice.
### Consider Alternatives When:
1. **Production Deployment**: While PyTorch has made strides in deployment (e.g., TorchServe), TensorFlow's TensorFlow Serving is more mature for large-scale deployment.
2. **Static Graphs**: If your model architecture doesn't change frequently and you prefer static computation graphs, TensorFlow might be more suitable.
3. **Multi-Language Support**: If you need integration with languages other than Python (e.g., Java, JavaScript), TensorFlow offers better support.
## Conclusion
PyTorch is a powerful and flexible deep learning framework that caters to both researchers and practitioners. Its ease of use, dynamic computation graph, and strong community support make it an excellent choice for many machine learning tasks. However, for certain production scenarios or specific requirements, alternatives like TensorFlow may be more appropriate.
## Additional Resources
- [PyTorch Official Documentation](https://pytorch.org/docs/stable/index.html)
- [PyTorch Tutorials](https://pytorch.org/tutorials/)
- [PyTorch Forum](https://discuss.pytorch.org/)
Feel free to explore and experiment with PyTorch to harness the full potential of this versatile framework!

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# Random Forest
Random Forest is a versatile machine learning algorithm capable of performing both regression and classification tasks. It is an ensemble method that operates by constructing a multitude of decision trees during training and outputting the average prediction of the individual trees (for regression) or the mode of the classes (for classification).
## Introduction
Random Forest is an ensemble learning method used for classification and regression tasks. It is built from multiple decision trees and combines their outputs to improve the model's accuracy and control over-fitting.
## How Random Forest Works
### 1. Bootstrap Sampling:
* Random subsets of the training dataset are created with replacement. Each subset is used to train an individual tree.
### 2. Decision Trees:
* Multiple decision trees are trained on these subsets.
### 3. Feature Selection:
* At each split in the decision tree, a random selection of features is chosen. This randomness helps create diverse trees.
### 4. Voting/Averaging:
For classification, the mode of the classes predicted by individual trees is taken (majority vote).
For regression, the average of the outputs of the individual trees is taken.
### Detailed Working Mechanism
#### Step 1: Bootstrap Sampling:
Each tree is trained on a random sample of the original data, drawn with replacement (bootstrap sample). This means some data points may appear multiple times in a sample while others may not appear at all.
#### Step 2: Tree Construction:
Each node in the tree is split using the best split among a random subset of the features. This process adds an additional layer of randomness, contributing to the robustness of the model.
#### Step 3: Aggregation:
For classification tasks, the final prediction is based on the majority vote from all the trees. For regression tasks, the final prediction is the average of all the tree predictions.
### Advantages and Disadvantages
#### Advantages
* Robustness: Reduces overfitting and generalizes well due to the law of large numbers.
* Accuracy: Often provides high accuracy because of the ensemble method.
* Versatility: Can be used for both classification and regression tasks.
* Handles Missing Values: Can handle missing data better than many other algorithms.
* Feature Importance: Provides estimates of feature importance, which can be valuable for understanding the model.
#### Disadvantages
* Complexity: More complex than individual decision trees, making interpretation difficult.
* Computational Cost: Requires more computational resources due to multiple trees.
* Training Time: Can be slow to train compared to simpler models, especially with large datasets.
### Hyperparameters
#### Key Hyperparameters
* n_estimators: The number of trees in the forest.
* max_features: The number of features to consider when looking for the best split.
* max_depth: The maximum depth of the tree.
* min_samples_split: The minimum number of samples required to split an internal node.
* min_samples_leaf: The minimum number of samples required to be at a leaf node.
* bootstrap: Whether bootstrap samples are used when building trees. If False, the whole dataset is used to build each tree.
##### Tuning Hyperparameters
Hyperparameter tuning can significantly improve the performance of a Random Forest model. Common techniques include Grid Search and Random Search.
### Code Examples
#### Classification Example
Below is a simple example of using Random Forest for a classification task with the Iris dataset.
```python
import numpy as np
import pandas as pd
from sklearn.datasets import load_iris
from sklearn.ensemble import RandomForestClassifier
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score, classification_report
# Load dataset
iris = load_iris()
X, y = iris.data, iris.target
# Split dataset
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
# Initialize Random Forest model
clf = RandomForestClassifier(n_estimators=100, random_state=42)
# Train the model
clf.fit(X_train, y_train)
# Make predictions
y_pred = clf.predict(X_test)
# Evaluate the model
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy * 100:.2f}%")
print("Classification Report:\n", classification_report(y_test, y_pred))
```
#### Feature Importance
Random Forest provides a way to measure the importance of each feature in making predictions.
```python
import matplotlib.pyplot as plt
# Get feature importances
importances = clf.feature_importances_
indices = np.argsort(importances)[::-1]
# Print feature ranking
print("Feature ranking:")
for f in range(X.shape[1]):
print(f"{f + 1}. Feature {indices[f]} ({importances[indices[f]]})")
# Plot the feature importances
plt.figure()
plt.title("Feature importances")
plt.bar(range(X.shape[1]), importances[indices], align='center')
plt.xticks(range(X.shape[1]), indices)
plt.xlim([-1, X.shape[1]])
plt.show()
```
#### Hyperparameter Tuning
Using Grid Search for hyperparameter tuning.
```python
from sklearn.model_selection import GridSearchCV
# Define the parameter grid
param_grid = {
'n_estimators': [100, 200, 300],
'max_features': ['auto', 'sqrt', 'log2'],
'max_depth': [4, 6, 8, 10, 12],
'criterion': ['gini', 'entropy']
}
# Initialize the Grid Search model
grid_search = GridSearchCV(estimator=clf, param_grid=param_grid, cv=3, n_jobs=-1, verbose=2)
# Fit the model
grid_search.fit(X_train, y_train)
# Print the best parameters
print("Best parameters found: ", grid_search.best_params_)
```
#### Regression Example
Below is a simple example of using Random Forest for a regression task with the Boston housing dataset.
```python
import numpy as np
import pandas as pd
from sklearn.datasets import load_boston
from sklearn.ensemble import RandomForestRegressor
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error, r2_score
# Load dataset
boston = load_boston()
X, y = boston.data, boston.target
# Split dataset
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
# Initialize Random Forest model
regr = RandomForestRegressor(n_estimators=100, random_state=42)
# Train the model
regr.fit(X_train, y_train)
# Make predictions
y_pred = regr.predict(X_test)
# Evaluate the model
mse = mean_squared_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)
print(f"Mean Squared Error: {mse:.2f}")
print(f"R^2 Score: {r2:.2f}")
```
## Conclusion
Random Forest is a powerful and flexible machine learning algorithm that can handle both classification and regression tasks. Its ability to create an ensemble of decision trees leads to robust and accurate models. However, it is important to be mindful of the computational cost associated with training multiple trees.
## References
Scikit-learn Random Forest Documentation
Wikipedia: Random Forest
Machine Learning Mastery: Introduction to Random Forest
Kaggle: Random Forest Guide
Towards Data Science: Understanding Random Forests

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# Regression
* Regression is a supervised machine learning technique which is used to predict continuous values.
> Now, Supervised learning is a category of machine learning that uses labeled datasets to train algorithms to predict outcomes and recognize patterns.
* Regression is a statistical method used to model the relationship between a dependent variable (often denoted as 'y') and one or more independent variables (often denoted as 'x'). The goal of regression analysis is to understand how the dependent variable changes as the independent variables change.
# Types Of Regression
1. Linear Regression
2. Polynomial Regression
3. Stepwise Regression
4. Decision Tree Regression
5. Random Forest Regression
6. Ridge Regression
7. Lasso Regression
8. ElasticNet Regression
9. Bayesian Linear Regression
10. Support Vector Regression
But, we'll first start with Linear Regression
# Linear Regression
* Linear regression is a fundamental statistical method used to model the relationship between a dependent variable (often denoted as
𝑌) and one or more independent variables (often denoted as
𝑋). The relationship is assumed to be linear, meaning that changes in the independent variables are associated with changes in the dependent variable in a straight-line fashion.
The basic form of linear regression for a single independent variable is:
**𝑌=𝛽0+𝛽1𝑋+𝜖**
Where:
* Y is the dependent variable.
* X is the independent variable.
* 𝛽0 is the intercept, representing the value of Y when X is zero
* 𝛽1 is the slope coefficient, representing the change in Y for a one-unit change in X
* ϵ is the error term, representing the variability in Y that is not explained by the linear relationship with X.
# Basic Code of Linear Regression
* This line imports the numpy library, which is widely used for numerical operations in Python. We use np as an alias for numpy, making it easier to reference functions and objects from the library.
```
import numpy as np
```
* This line imports the LinearRegression class from the linear_model module of the scikit-learn library.scikit-learn is a powerful library for machine learning tasks in Python, and LinearRegression is a class provided by it for linear regression.
```
from sklearn.linear_model import LinearRegression
```
* This line creates a NumPy array X containing the independent variable values. In this example, we have a simple one-dimensional array representing the independent variable. The reshape(-1, 1) method reshapes the array into a column vector, necessary for use with scikit-learn
```
X = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)
```
* This line creates a NumPy array Y containing the corresponding dependent variable values. These are the observed values of the dependent variable corresponding to the independent variable values in X.
```
Y = np.array([2, 4, 5, 8, 5])
```
* This line creates an instance of the LinearRegression class, which represents the linear regression model. We'll use this object to train the model and make predictions.
```
model = LinearRegression()
```
* This line fits the linear regression model to the data. The fit() method takes two arguments: the independent variable (X) and the dependent variable (Y). This method estimates the coefficients of the linear regression equation that best fit the given data.
```
model.fit(X, Y)
```
* These lines print out the intercept (beta_0) and coefficient (beta_1) of the linear regression model. model.intercept_ gives the intercept value, and model.coef_ gives an array of coefficients, where model.coef_[0] corresponds to the coefficient of the first independent variable (in this case, there's only one).
```
print("Intercept:", model.intercept_)
print("Coefficient:", model.coef_[0])
```
* These lines demonstrate how to use the trained model to make predictions for new data.
* We create a new NumPy array new_data containing the values of the independent variable for which we want to predict the dependent variable values.
* We then use the predict() method of the model to obtain the predictions for these new data points. Finally, we print out the predicted values.
```
new_data = np.array([[6], [7]])
predictions = model.predict(new_data)
print("Predictions:", predictions)
```
# Assumptions of Linear Regression
# Linearity:
* To assess the linearity assumption, we can visually inspect a scatter plot of the observed values versus the predicted values.
* If the relationship between them appears linear, it suggests that the linearity assumption is reasonable.
```
import matplotlib.pyplot as plt
predictions = model.predict(X)
plt.scatter(predictions,Y)
plt.xlabel("Predicted Values")
plt.ylabel("Observed Values")
plt.title("Linearity Check: Observed vs Predicted")
plt.show()
```
# Homoscedasticity:
* Homoscedasticity refers to the constant variance of the residuals across all levels of the independent variable(s). We can visually inspect a plot of residuals versus predicted values to check for homoscedasticity.
```
residuals = Y - predictions
plt.scatter(predictions, residuals)
plt.xlabel("Predicted Values")
plt.ylabel("Residuals")
plt.title("Homoscedasticity Check: Residuals vs Predicted Values")
plt.axhline(y=0, color='red', linestyle='--') # Add horizontal line at y=0
plt.show()
```
# Normality of Residuals:
* To assess the normality of residuals, we can visually inspect a histogram or a Q-Q plot of the residuals.
```
import seaborn as sns
sns.histplot(residuals, kde=True)
plt.xlabel("Residuals")
plt.ylabel("Frequency")
plt.title("Normality of Residuals: Histogram")
plt.show()
import scipy.stats as stats
stats.probplot(residuals, dist="norm", plot=plt)
plt.title("Normal Q-Q Plot")
plt.show()
```
# Metrics for Regression
# Mean Absolute Error (MAE)
* MAE measures the average magnitude of the errors in a set of predictions, without considering their direction. It is the average of the absolute differences between predicted and actual values.
```
from sklearn.metrics import mean_absolute_error
mae = mean_absolute_error(Y, predictions)
print(f"Mean Absolute Error (MAE): {mae}")
```
# Mean Squared Error (MSE)
* MSE measures the average of the squares of the errors. It gives more weight to larger errors, making it sensitive to outliers.
```
from sklearn.metrics import mean_squared_error
mse = mean_squared_error(Y, predictions)
print(f"Mean Squared Error (MSE): {mse}")
```
# Root Mean Squared Error (RMSE)
* RMSE is the square root of the MSE. It provides an error metric that is in the same units as the dependent variable, making it more interpretable.
```
rmse = np.sqrt(mse)
print(f"Root Mean Squared Error (RMSE): {rmse}")
```
# R-squared (Coefficient of Determination)
* R-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, where 1 indicates a perfect fit.
```
from sklearn.metrics import r2_score
r2 = r2_score(Y, predictions)
print(f"R-squared (R^2): {r2}")
```
> In this tutorial, The sample dataset is there for learning purpose only

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# scikit-learn (sklearn) Python Library
## Overview
scikit-learn, also known as sklearn, is a popular open-source Python library that provides simple and efficient tools for data mining and data analysis. It is built on NumPy, SciPy, and matplotlib. The library is designed to interoperate with the Python numerical and scientific libraries.
## Key Features
- **Classification**: Identifying which category an object belongs to. Example algorithms include SVM, nearest neighbors, random forest.
- **Regression**: Predicting a continuous-valued attribute associated with an object. Example algorithms include support vector regression (SVR), ridge regression, Lasso.
- **Clustering**: Automatic grouping of similar objects into sets. Example algorithms include k-means, spectral clustering, mean-shift.
- **Dimensionality Reduction**: Reducing the number of random variables to consider. Example algorithms include PCA, feature selection, non-negative matrix factorization.
- **Model Selection**: Comparing, validating, and choosing parameters and models. Example methods include grid search, cross-validation, metrics.
- **Preprocessing**: Feature extraction and normalization.
## When to Use scikit-learn
- **Use scikit-learn if**:
- You are working on machine learning tasks such as classification, regression, clustering, dimensionality reduction, model selection, and preprocessing.
- You need an easy-to-use, well-documented library.
- You require tools that are compatible with NumPy and SciPy.
- **Do not use scikit-learn if**:
- You need to perform deep learning tasks. In such cases, consider using TensorFlow or PyTorch.
- You need out-of-the-box support for large-scale data. scikit-learn is designed to work with in-memory data, so for very large datasets, you might want to consider libraries like Dask-ML.
## Installation
You can install scikit-learn using pip:
```bash
pip install scikit-learn
```
Or via conda:
```bash
conda install scikit-learn
```
## Basic Usage with Code Snippets
### Importing the Library
```python
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import accuracy_score
```
### Loading Data
For illustration, let's create a simple synthetic dataset:
```python
from sklearn.datasets import make_classification
X, y = make_classification(n_samples=1000, n_features=20, n_classes=2, random_state=42)
```
### Splitting Data
Split the dataset into training and testing sets:
```python
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
```
### Preprocessing
Standardizing the features:
```python
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)
```
### Training a Model
Train a Logistic Regression model:
```python
model = LogisticRegression()
model.fit(X_train, y_train)
```
### Making Predictions
Make predictions on the test set:
```python
y_pred = model.predict(X_test)
```
### Evaluating the Model
Evaluate the accuracy of the model:
```python
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy * 100:.2f}%")
```
### Putting it All Together
Here is a complete example from data loading to model evaluation:
```python
import numpy as np
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import accuracy_score
# Load data
X, y = make_classification(n_samples=1000, n_features=20, n_classes=2, random_state=42)
# Split data
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)
# Preprocess data
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)
# Train model
model = LogisticRegression()
model.fit(X_train, y_train)
# Make predictions
y_pred = model.predict(X_test)
# Evaluate model
accuracy = accuracy_score(y_test, y_pred)
print(f"Accuracy: {accuracy * 100:.2f}%")
```
## Conclusion
scikit-learn is a powerful and versatile library that can be used for a wide range of machine learning tasks. It is particularly well-suited for beginners due to its easy-to-use interface and extensive documentation. Whether you are working on a simple classification task or a more complex clustering problem, scikit-learn provides the tools you need to build and evaluate your models effectively.

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## Support Vector Machine
Support Vector Machine or SVM is one of the most popular Supervised Learning algorithms, which is used for Classification as well as Regression problems. However, primarily, it is used for Classification problems in Machine Learning.
SVM can be of two types -
1. Linear SVM: Linear SVM is used for linearly separable data, which means if a dataset can be classified into two classes by using a single straight line, then such data is termed as linearly separable data, and classifier is used called as Linear SVM classifier.
2. Non-linear SVM: Non-Linear SVM is used for non-linearly separated data, which means if a dataset cannot be classified by using a straight line, then such data is termed as non-linear data and classifier used is called as Non-linear SVM classifier.
Working of SVM - The goal of SVM is to find a hyperplane that separates the data points into different classes. A hyperplane is a line in 2D space, a plane in 3D space, or a higher-dimensional surface in n-dimensional space. The hyperplane is chosen in such a way that it maximizes the margin, which is the distance between the hyperplane and the closest data points of each class. The closest data points are called the support vectors.
The distance between the hyperplane and a data point "x" can be calculated using the formula −
```
distance = (w . x + b) / ||w||
```
where "w" is the weight vector, "b" is the bias term, and "||w||" is the Euclidean norm of the weight vector. The weight vector "w" is perpendicular to the hyperplane and determines its orientation, while the bias term "b" determines its position.
The optimal hyperplane is found by solving an optimization problem, which is to maximize the margin subject to the constraint that all data points are correctly classified. In other words, we want to find the hyperplane that maximizes the margin between the two classes while ensuring that no data point is misclassified. This is a convex optimization problem that can be solved using quadratic programming. If the data points are not linearly separable, we can use a technique called kernel trick to map the data points into a higher-dimensional space where they become separable. The kernel function computes the inner product between the mapped data points without computing the mapping itself. This allows us to work with the data points in the higherdimensional space without incurring the computational cost of mapping them.
1. Hyperplane:
There can be multiple lines/decision boundaries to segregate the classes in n-dimensional space, but we need to find out the best decision boundary that helps to classify the data points. This best boundary is known as the hyperplane of SVM.
The dimensions of the hyperplane depend on the features present in the dataset, which means if there are 2 features, then hyperplane will be a straight line. And if there are 3 features, then hyperplane will be a 2-dimension plane. We always create a hyperplane that has a maximum margin, which means the maximum distance between the data points.
2. Support Vectors:
The data points or vectors that are the closest to the hyperplane and which affect the position of the hyperplane are termed as Support Vector. Since these vectors support the hyperplane, hence called a Support vector.
3. Margin:
It may be defined as the gap between two lines on the closet data points of different classes. It can be calculated as the perpendicular distance from the line to the support vectors. Large margin is considered as a good margin and small margin is considered as a bad margin.
We will use the famous Iris dataset, which contains the sepal length, sepal width, petal length, and petal width of three species of iris flowers: Iris setosa, Iris versicolor, and Iris virginica. The goal is to classify the flowers into their respective species based on these four features. We load the iris dataset using load_iris and split the data into training and testing sets using train_test_split. We use a test size of 0.2, which means that 20% of the data will be used for testing and 80% for training. We set the random state to 42 to ensure reproducibility of the results.
### Implemetation of SVM in Python
```python
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
from sklearn.metrics import accuracy_score
# load the iris dataset
iris = load_iris()
# split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(iris.data,
iris.target, test_size=0.2, random_state=42)
# create an SVM classifier with a linear kernel
svm = SVC(kernel='linear')
# train the SVM classifier on the training set
svm.fit(X_train, y_train)
# make predictions on the testing set
y_pred = svm.predict(X_test)
# calculate the accuracy of the classifier
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)
```
#### Output
```
Accuracy: 1
```

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# TensorFlow
Developed by the Google Brain team, TensorFlow is an open-source library that provides a comprehensive ecosystem for building and deploying machine learning models. It supports deep learning and neural networks and offers tools for both beginners and experts.
## Key Features
- **Flexible and comprehensive ecosystem**
- **Scalable for both production and research**
- **Supports CPUs, GPUs, and TPUs**
## Basic Example: Linear Regression
Let's start with a simple linear regression example in TensorFlow.
```python
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
# Generate synthetic data
X = np.array([1, 2, 3, 4, 5], dtype=np.float32)
Y = np.array([2, 4, 6, 8, 10], dtype=np.float32)
# Define the model
model = tf.keras.Sequential([
tf.keras.layers.Dense(units=1, input_shape=[1])
])
# Compile the model
model.compile(optimizer='sgd', loss='mean_squared_error')
# Train the model
history = model.fit(X, Y, epochs=500)
# Predict
predictions = model.predict(X)
# Plot the results
plt.plot(X, Y, 'ro', label='Original data')
plt.plot(X, predictions, 'b-', label='Fitted line')
plt.legend()
plt.show()
```
In this example:
1. We define a simple dataset with a linear relationship.
2. We build a sequential model with one dense layer (linear regression).
3. We compile the model with stochastic gradient descent (SGD) optimizer and mean squared error loss.
4. We train the model for 500 epochs and then plot the original data and the fitted line.
## When to Use TensorFlow
TensorFlow is a great choice if you:
- **Need to deploy machine learning models in production:** TensorFlow’s robust deployment options, including TensorFlow Serving, TensorFlow Lite, and TensorFlow.js, make it ideal for production environments.
- **Work on large-scale deep learning projects:** TensorFlow’s comprehensive ecosystem supports distributed training and has tools like TensorBoard for visualization.
- **Require high performance and scalability:** TensorFlow is optimized for performance and can leverage GPUs and TPUs for accelerated computing.
- **Want extensive support and documentation:** TensorFlow has a large community and extensive documentation, which can be very helpful for both beginners and advanced users.
## Example Use Cases
- Building and deploying complex neural networks for image recognition, natural language processing, or recommendation systems.
- Developing models that need to be run on mobile or embedded devices.

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# Transformers
## Introduction
A transformer is a deep learning architecture developed by Google and based on the multi-head attention mechanism. It is based on the softmax-based attention
mechanism. Before transformers, predecessors of attention mechanism were added to gated recurrent neural networks, such as LSTMs and gated recurrent units (GRUs), which processed datasets sequentially. Dependency on previous token computations prevented them from being able to parallelize the attention mechanism.
Transformers are a revolutionary approach to natural language processing (NLP). Unlike older models, they excel at understanding long-range connections between words. This "attention" mechanism lets them grasp the context of a sentence, making them powerful for tasks like machine translation, text summarization, and question answering. Introduced in 2017, transformers are now the backbone of many large language models, including tools you might use every day. Their ability to handle complex relationships in language is fueling advancements in AI across various fields.
## Model Architecture
![Model Architecture](assets/transformer-architecture.png)
Source: [Attention Is All You Need](https://arxiv.org/pdf/1706.03762)
### Encoder
The encoder is composed of a stack of identical layers. Each layer has two sub-layers. The first is a multi-head self-attention mechanism, and the second is a simple, positionwise fully connected feed-forward network. Each encoder consists of two major components: a self-attention mechanism and a feed-forward neural network. The self-attention mechanism accepts input encodings from the previous encoder and weights their relevance to each other to generate output encodings. The feed-forward neural network further processes each output encoding individually. These output encodings are then passed to the next encoder as its input, as well as to the decoders.
### Decoder
The decoder is also composed of a stack of identical layers. In addition to the two sub-layers in each encoder layer, the decoder inserts a third sub-layer, which performs multi-head attention over the output of the encoder stack. The decoder functions in a similar fashion to the encoder, but an additional attention mechanism is inserted which instead draws relevant information from the encodings generated by the encoders. This mechanism can also be called the encoder-decoder attention.
### Attention
#### Scaled Dot-Product Attention
The input consists of queries and keys of dimension $d_k$ , and values of dimension $d_v$. We compute the dot products of the query with all keys, divide each by $\sqrt {d_k}$ , and apply a softmax function to obtain the weights on the values.
$$Attention(Q, K, V) = softmax(\dfrac{QK^T}{\sqrt{d_k}}) \times V$$
#### Multi-Head Attention
Instead of performing a single attention function with $d_{model}$-dimensional keys, values and queries, it is beneficial to linearly project the queries, keys and values h times with different, learned linear projections to $d_k$ , $d_k$ and $d_v$ dimensions, respectively.
Multi-head attention allows the model to jointly attend to information from different representation
subspaces at different positions. With a single attention head, averaging inhibits this.
$$MultiHead(Q, K, V) = Concat(head_1, _{...}, head_h) \times W^O$$
where,
$$head_i = Attention(QW_i^Q, KW_i^K, VW_i^V)$$
where the projections are parameter matrices.
#### Masked Attention
It may be necessary to cut out attention links between some word-pairs. For example, the decoder for token position
$t$ should not have access to token position $t+1$.
$$MaskedAttention(Q, K, V) = softmax(M + \dfrac{QK^T}{\sqrt{d_k}}) \times V$$
### Feed-Forward Network
Each of the layers in the encoder and decoder contains a fully connected feed-forward network, which is applied to each position separately and identically. This
consists of two linear transformations with a ReLU activation in between.
$$FFN(x) = max(0, xW_1 + b_1)W_2 + b_2$$
### Positional Encoding
A positional encoding is a fixed-size vector representation that encapsulates the relative positions of tokens within a target sequence: it provides the transformer model with information about where the words are in the input sequence.
The sine and cosine functions of different frequencies:
$$PE<sub>(pos,2i)</sub> = \sin({\dfrac{pos}{10000^{\dfrac{2i}{d_{model}}}}})$$
$$PE<sub>(pos,2i)</sub> = \cos({\dfrac{pos}{10000^{\dfrac{2i}{d_{model}}}}})$$
## Implementation
### Theory
Text is converted to numerical representations called tokens, and each token is converted into a vector via looking up from a word embedding table.
At each layer, each token is then contextualized within the scope of the context window with other tokens via a parallel multi-head attention mechanism
allowing the signal for key tokens to be amplified and less important tokens to be diminished.
The transformer uses an encoder-decoder architecture. The encoder extracts features from an input sentence, and the decoder uses the features to produce an output sentence. Some architectures use full encoders and decoders, autoregressive encoders and decoders, or combination of both. This depends on the usage and context of the input.
### Tensorflow
TensorFlow is a free and open-source software library for machine learning and artificial intelligence. It can be used across a range of tasks but has a particular focus on training and inference of deep neural networks. It was developed by the Google Brain team for Google's internal use in research and production.
Tensorflow provides the transformer encoder and decoder block that can be implemented by the specification of the user. Although, the transformer is not provided as a standalone to be imported and executed, the user has to create the model first. They also have a tutorial on how to implement the transformer from scratch for machine translation and can be found [here](https://www.tensorflow.org/text/tutorials/transformer).
More information on [encoder](https://www.tensorflow.org/api_docs/python/tfm/nlp/layers/TransformerEncoderBlock) and [decoder](https://www.tensorflow.org/api_docs/python/tfm/nlp/layers/TransformerDecoderBlock) block mentioned in the code.
Imports:
```python
import tensorflow as tf
import tensorflow_models as tfm
```
Adding word embeddings and positional encoding:
```python
class PositionalEmbedding(tf.keras.layers.Layer):
def __init__(self, vocab_size, d_model):
super().__init__()
self.d_model = d_model
self.embedding = tf.keras.layers.Embedding(vocab_size, d_model, mask_zero=True)
self.pos_encoding = tfm.nlp.layers.RelativePositionEmbedding(hidden_size=d_model)
def compute_mask(self, *args, **kwargs):
return self.embedding.compute_mask(*args, **kwargs)
def call(self, x):
length = tf.shape(x)[1]
x = self.embedding(x)
x = x + self.pos_encoding[tf.newaxis, :length, :]
return x
```
Creating the encoder for the transformer:
```python
class Encoder(tf.keras.layers.Layer):
def __init__(self, num_layers, d_model, num_heads,
dff, vocab_size, dropout_rate=0.1):
super().__init__()
self.d_model = d_model
self.num_layers = num_layers
self.pos_embedding = PositionalEmbedding(
vocab_size=vocab_size, d_model=d_model)
self.enc_layers = [
tfm.nlp.layers.TransformerEncoderBlock(output_last_dim=d_model,
num_attention_heads=num_heads,
inner_dim=dff,
inner_activation="relu",
inner_dropout=dropout_rate)
for _ in range(num_layers)]
self.dropout = tf.keras.layers.Dropout(dropout_rate)
def call(self, x):
x = self.pos_embedding(x, length=2048)
x = self.dropout(x)
for i in range(self.num_layers):
x = self.enc_layers[i](x)
return x
```
Creating the decoder for the transformer:
```python
class Decoder(tf.keras.layers.Layer):
def __init__(self, num_layers, d_model, num_heads, dff, vocab_size,
dropout_rate=0.1):
super(Decoder, self).__init__()
self.d_model = d_model
self.num_layers = num_layers
self.pos_embedding = PositionalEmbedding(vocab_size=vocab_size,
d_model=d_model)
self.dropout = tf.keras.layers.Dropout(dropout_rate)
self.dec_layers = [
tfm.nlp.layers.TransformerDecoderBlock(num_attention_heads=num_heads,
intermediate_size=dff,
intermediate_activation="relu",
dropout_rate=dropout_rate)
for _ in range(num_layers)]
def call(self, x, context):
x = self.pos_embedding(x)
x = self.dropout(x)
for i in range(self.num_layers):
x = self.dec_layers[i](x, context)
return x
```
Combining the encoder and decoder to create the transformer:
```python
class Transformer(tf.keras.Model):
def __init__(self, num_layers, d_model, num_heads, dff,
input_vocab_size, target_vocab_size, dropout_rate=0.1):
super().__init__()
self.encoder = Encoder(num_layers=num_layers, d_model=d_model,
num_heads=num_heads, dff=dff,
vocab_size=input_vocab_size,
dropout_rate=dropout_rate)
self.decoder = Decoder(num_layers=num_layers, d_model=d_model,
num_heads=num_heads, dff=dff,
vocab_size=target_vocab_size,
dropout_rate=dropout_rate)
self.final_layer = tf.keras.layers.Dense(target_vocab_size)
def call(self, inputs):
context, x = inputs
context = self.encoder(context)
x = self.decoder(x, context)
logits = self.final_layer(x)
return logits
```
Model initialization that be used for training and inference:
```python
transformer = Transformer(
num_layers=num_layers,
d_model=d_model,
num_heads=num_heads,
dff=dff,
input_vocab_size=64,
target_vocab_size=64,
dropout_rate=dropout_rate
)
```
Sample:
```python
src = tf.random.uniform((64, 40))
tgt = tf.random.uniform((64, 50))
output = transformer((src, tgt))
```
O/P:
```
<tf.Tensor: shape=(64, 50, 64), dtype=float32, numpy=
array([[[ 0.78274703, -1.2312567 , 0.7272992 , ..., 2.1805947 ,
1.3511044 , -1.275499 ],
[ 0.82658154, -1.2863302 , 0.76494133, ..., 2.39311 ,
1.0973787 , -1.3414565 ],
[ 0.57013685, -1.3958443 , 1.0213287 , ..., 2.3791933 ,
0.58439416, -0.93464035],
...,
[ 0.82214123, -0.51090807, 0.25897795, ..., 2.1979148 ,
1.4126635 , -0.5771998 ],
[ 0.6371507 , -0.36584622, 0.40954843, ..., 2.0241373 ,
1.6503414 , -0.74359566],
[ 0.6739802 , -0.39973688, 0.3338765 , ..., 1.6819229 ,
1.7505672 , -1.0763712 ]],
[[ 0.78274703, -1.2312567 , 0.7272992 , ..., 2.1805947 ,
1.3511044 , -1.275499 ],
[ 0.82658154, -1.2863302 , 0.76494133, ..., 2.39311 ,
1.0973787 , -1.3414565 ],
[ 0.57013685, -1.3958443 , 1.0213287 , ..., 2.3791933 ,
0.58439416, -0.93464035],
...,
[ 0.82214123, -0.51090807, 0.25897795, ..., 2.1979148 ,
1.4126635 , -0.5771998 ],
[ 0.6371507 , -0.36584622, 0.40954843, ..., 2.0241373 ,
1.6503414 , -0.74359566],
[ 0.6739802 , -0.39973688, 0.3338765 , ..., 1.6819229 ,
1.7505672 , -1.0763712 ]],
[[ 0.78274703, -1.2312567 , 0.7272992 , ..., 2.1805947 ,
1.3511044 , -1.275499 ],
[ 0.82658154, -1.2863302 , 0.76494133, ..., 2.39311 ,
1.0973787 , -1.3414565 ],
[ 0.57013685, -1.3958443 , 1.0213287 , ..., 2.3791933 ,
0.58439416, -0.93464035],
...,
[ 0.82214123, -0.51090807, 0.25897795, ..., 2.1979148 ,
1.4126635 , -0.5771998 ],
[ 0.6371507 , -0.36584622, 0.40954843, ..., 2.0241373 ,
1.6503414 , -0.74359566],
[ 0.6739802 , -0.39973688, 0.3338765 , ..., 1.6819229 ,
1.7505672 , -1.0763712 ]],
...,
[[ 0.78274703, -1.2312567 , 0.7272992 , ..., 2.1805947 ,
1.3511044 , -1.275499 ],
[ 0.82658154, -1.2863302 , 0.76494133, ..., 2.39311 ,
1.0973787 , -1.3414565 ],
[ 0.57013685, -1.3958443 , 1.0213287 , ..., 2.3791933 ,
0.58439416, -0.93464035],
...,
[ 0.82214123, -0.51090807, 0.25897795, ..., 2.1979148 ,
1.4126635 , -0.5771998 ],
[ 0.6371507 , -0.36584622, 0.40954843, ..., 2.0241373 ,
1.6503414 , -0.74359566],
[ 0.6739802 , -0.39973688, 0.3338765 , ..., 1.6819229 ,
1.7505672 , -1.0763712 ]],
[[ 0.78274703, -1.2312567 , 0.7272992 , ..., 2.1805947 ,
1.3511044 , -1.275499 ],
[ 0.82658154, -1.2863302 , 0.76494133, ..., 2.39311 ,
1.0973787 , -1.3414565 ],
[ 0.57013685, -1.3958443 , 1.0213287 , ..., 2.3791933 ,
0.58439416, -0.93464035],
...,
[ 0.82214123, -0.51090807, 0.25897795, ..., 2.1979148 ,
1.4126635 , -0.5771998 ],
[ 0.6371507 , -0.36584622, 0.40954843, ..., 2.0241373 ,
1.6503414 , -0.74359566],
[ 0.6739802 , -0.39973688, 0.3338765 , ..., 1.6819229 ,
1.7505672 , -1.0763712 ]],
[[ 0.78274703, -1.2312567 , 0.7272992 , ..., 2.1805947 ,
1.3511044 , -1.275499 ],
[ 0.82658154, -1.2863302 , 0.76494133, ..., 2.39311 ,
1.0973787 , -1.3414565 ],
[ 0.57013685, -1.3958443 , 1.0213287 , ..., 2.3791933 ,
0.58439416, -0.93464035],
...,
[ 0.82214123, -0.51090807, 0.25897795, ..., 2.1979148 ,
1.4126635 , -0.5771998 ],
[ 0.6371507 , -0.36584622, 0.40954843, ..., 2.0241373 ,
1.6503414 , -0.74359566],
[ 0.6739802 , -0.39973688, 0.3338765 , ..., 1.6819229 ,
1.7505672 , -1.0763712 ]]], dtype=float32)>
```
```
>>> output.shape
TensorShape([64, 50, 64])
```
### PyTorch
PyTorch is a machine learning library based on the Torch library, used for applications such as computer vision and natural language processing, originally developed by Meta AI and now part of the Linux Foundation umbrella.
Unlike Tensorflow, PyTorch provides the full implementation of the transformer model that can be executed on the go. More information can be found [here](https://pytorch.org/docs/stable/_modules/torch/nn/modules/transformer.html#Transformer). A full implementation of the model can be found [here](https://github.com/pytorch/examples/tree/master/word_language_model).
Imports:
```python
import torch
import torch.nn as nn
```
Initializing the model:
```python
transformer = nn.Transformer(nhead=16, num_encoder_layers=8)
```
Sample:
```python
src = torch.rand((10, 32, 512))
tgt = torch.rand((20, 32, 512))
output = transformer(src, tgt)
```
O/P:
```
tensor([[[ 0.2938, -0.4824, -0.7816, ..., 0.0742, 0.5162, 0.3632],
[-0.0786, -0.5241, 0.6384, ..., 0.3462, -0.0618, 0.9943],
[ 0.7827, 0.1067, -0.1637, ..., -1.7730, -0.3322, -0.0029],
...,
[-0.3202, 0.2341, -0.0896, ..., -0.9714, -0.1251, -0.0711],
[-0.1663, -0.5047, -0.0404, ..., -0.9339, 0.3963, 0.1018],
[ 1.2834, -0.4400, 0.0486, ..., -0.6876, -0.4752, 0.0180]],
[[ 0.9869, -0.7384, -1.0704, ..., -0.9417, 1.3279, -0.1665],
[ 0.3445, -0.2454, -0.3644, ..., -0.4856, -1.1004, -0.6819],
[ 0.7568, -0.3151, -0.5034, ..., -1.2081, -0.7119, 0.3775],
...,
[-0.0451, -0.7596, 0.0168, ..., -0.8267, -0.3272, 1.0457],
[ 0.3150, -0.6588, -0.1840, ..., 0.1822, -0.0653, 0.9053],
[ 0.8692, -0.3519, 0.3128, ..., -1.8446, -0.2325, -0.8662]],
[[ 0.9719, -0.3113, 0.4637, ..., -0.4422, 1.2348, 0.8274],
[ 0.3876, -0.9529, -0.7810, ..., -0.5843, -1.1439, -0.3366],
[-0.5774, 0.3789, -0.2819, ..., -1.4057, 0.4352, 0.1474],
...,
[ 0.6899, -0.1146, -0.3297, ..., -1.7059, -0.1750, 0.4203],
[ 0.3689, -0.5174, -0.1253, ..., 0.1417, 0.4159, 0.7560],
[ 0.5024, -0.7996, 0.1592, ..., -0.8344, -1.1125, 0.4736]],
...,
[[ 0.0704, -0.3971, -0.2768, ..., -1.9929, 0.8608, 1.2264],
[ 0.4013, -0.0962, -0.0965, ..., -0.4452, -0.8682, -0.4593],
[ 0.1656, 0.5224, -0.1723, ..., -1.5785, 0.3219, 1.1507],
...,
[-0.9443, 0.4653, 0.2936, ..., -0.9840, -0.0142, -0.1595],
[-0.6544, -0.3294, -0.0803, ..., 0.1623, -0.5061, 0.9824],
[-0.0978, -1.0023, -0.6915, ..., -0.2296, -0.0594, -0.4715]],
[[ 0.6531, -0.9285, -0.0331, ..., -1.1481, 0.7768, -0.7321],
[ 0.3325, -0.6683, -0.6083, ..., -0.4501, 0.2289, 0.3573],
[-0.6750, 0.4600, -0.8512, ..., -2.0097, -0.5159, 0.2773],
...,
[-1.4356, -1.0135, 0.0081, ..., -1.2985, -0.3715, -0.2678],
[ 0.0546, -0.2111, -0.0965, ..., -0.3822, -0.4612, 1.6217],
[ 0.7700, -0.5309, -0.1754, ..., -2.2807, -0.0320, -1.5551]],
[[ 0.2399, -0.9659, 0.1086, ..., -1.1756, 0.4063, 0.0615],
[-0.2202, -0.7972, -0.5024, ..., -0.9126, -1.5248, 0.2418],
[ 0.5215, 0.4540, 0.0036, ..., -0.2135, 0.2145, 0.6638],
...,
[-0.2190, -0.4967, 0.7149, ..., -0.3324, 0.3502, 1.0624],
[-0.0108, -0.9205, -0.1315, ..., -1.0153, 0.2989, 1.1415],
[ 1.1284, -0.6560, 0.6755, ..., -1.2157, 0.8580, -0.5022]]],
grad_fn=<NativeLayerNormBackward0>)
```
```
>> output.shape
torch.Size([20, 32, 512])
```
### HuggingFace
Hugging Face, Inc. is a French-American company incorporated under the Delaware General Corporation Law and based in New York City that develops computation tools for building applications using machine learning.
It has a wide-range of models that can implemented in Tensorflow, PyTorch and other development backends as well. The models are already trained on a dataset and can be pretrained on custom dataset for customized use, according to the user. The information for training the model and loading the pretrained model can be found [here](https://huggingface.co/docs/transformers/en/training).
In HuggingFace, `pipeline` is used to run inference from the trained model available in the Hub. This is very beginner friendly. The model is downloaded to the local system on running the script before running the inference. It has to be made sure that the model downloaded does not exceed your available data plan.
Imports:
```python
from transformers import pipeline
```
Initialization:
The model used here is BART (large) which was trained on MultiNLI dataset, which consist of sentence paired with its textual entailment.
```python
classifier = pipeline(model="facebook/bart-large-mnli")
```
Sample:
The first argument is the sentence which needs to be analyzed. The second argument, `candidate_labels`, is the list of labels which most likely the first argument sentence belongs to. The output dictionary will have a key as `score`, where the highest index is the textual entailment of the sentence with the index of the label in the list.
```python
output = classifier(
"I need to leave but later",
candidate_labels=["urgent", "not urgent", "sleep"],
)
```
O/P:
```
{'sequence': 'I need to leave but later',
'labels': ['not urgent', 'urgent', 'sleep'],
'scores': [0.8889380097389221, 0.10631518065929413, 0.00474683940410614]}
```
## Application
The transformer has had great success in natural language processing (NLP). Many large language models such as GPT-2, GPT-3, GPT-4, Claude, BERT, XLNet, RoBERTa and ChatGPT demonstrate the ability of transformers to perform a wide variety of such NLP-related tasks, and have the potential to find real-world applications.
These may include:
- Machine translation
- Document summarization
- Text generation
- Biological sequence analysis
- Computer code generation
## Bibliography
- [Attention Is All You Need](https://arxiv.org/pdf/1706.03762)
- [Tensorflow Tutorial](https://www.tensorflow.org/text/tutorials/transformer)
- [Tensorflow Models Docs](https://www.tensorflow.org/api_docs/python/tfm/nlp/layers)
- [Wikipedia](https://en.wikipedia.org/wiki/Transformer_(deep_learning_architecture))
- [HuggingFace](https://huggingface.co/docs/transformers/en/index)
- [PyTorch](https://pytorch.org/docs/stable/generated/torch.nn.Transformer.html)

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---
# Optimizers in Machine Learning
Optimizers are algorithms or methods used to change the attributes of your neural network such as weights and learning rate in order to reduce the losses. Optimization algorithms help to minimize (or maximize) an objective function (also called a loss function) which is simply a mathematical function dependent on the model's internal learnable parameters which are used in computing the target values from the set of features.
## Types of Optimizers
### 1. Gradient Descent
**Explanation:**
Gradient Descent is the simplest and most commonly used optimization algorithm. It works by iteratively updating the model parameters in the opposite direction of the gradient of the objective function with respect to the parameters. The idea is to find the minimum of a function by taking steps proportional to the negative of the gradient of the function at the current point.
**Mathematical Formulation:**
The update rule for the parameter vector θ in gradient descent is represented by the equation:
- $$\theta_{\text{new}} = \theta_{\text{old}} - \alpha \cdot \nabla J(\theta)$$
Where:
- θold is the old parameter vector.
- θnew is the updated parameter vector.
- alpha(α) is the learning rate.
- ∇J(θ) is the gradient of the objective function with respect to the parameters.
**Intuition:**
- At each iteration, we calculate the gradient of the cost function.
- The parameters are updated in the opposite direction of the gradient.
- The size of the step is controlled by the learning rate α.
**Advantages:**
- Simple to implement.
- Suitable for convex problems.
**Disadvantages:**
- Can be slow for large datasets.
- May get stuck in local minima for non-convex problems.
- Requires careful tuning of the learning rate.
**Python Implementation:**
```python
import numpy as np
def gradient_descent(X, y, lr=0.01, epochs=1000):
m, n = X.shape
theta = np.zeros(n)
for epoch in range(epochs):
gradient = np.dot(X.T, (np.dot(X, theta) - y)) / m
theta -= lr * gradient
return theta
```
### 2. Stochastic Gradient Descent (SGD)
**Explanation:**
SGD is a variation of gradient descent where we use only one training example to calculate the gradient and update the parameters. This introduces noise into the parameter updates, which can help to escape local minima but may cause the loss to fluctuate.
**Mathematical Formulation:**
- $$θ = θ - α \cdot \frac{∂J (θ; xᵢ, yᵢ)}{∂θ}$$
- xᵢ, yᵢ are a single training example and its target.
**Intuition:**
- At each iteration, a random training example is selected.
- The gradient is calculated and the parameters are updated for this single example.
- This process is repeated for a specified number of epochs.
**Advantages:**
- Faster updates compared to batch gradient descent.
- Can handle large datasets.
- Helps to escape local minima due to the noise in updates.
**Disadvantages:**
- Loss function may fluctuate.
- Requires more iterations to converge.
**Python Implementation:**
```python
def stochastic_gradient_descent(X, y, lr=0.01, epochs=1000):
m, n = X.shape
theta = np.zeros(n)
for epoch in range(epochs):
for i in range(m):
rand_index = np.random.randint(0, m)
xi = X[rand_index:rand_index+1]
yi = y[rand_index:rand_index+1]
gradient = np.dot(xi.T, (np.dot(xi, theta) - yi))
theta -= lr * gradient
return theta
```
### 3. Mini-Batch Gradient Descent
**Explanation:**
Mini-Batch Gradient Descent is a variation where instead of a single training example or the whole dataset, a mini-batch of examples is used to compute the gradient. This reduces the variance of the parameter updates, leading to more stable convergence.
**Mathematical Formulation:**
- $$θ = θ - α \cdot \frac{1}{k} \sum_{i=1}^{k} \frac{∂J (θ; xᵢ, yᵢ)}{∂θ}$$
Where:
- \( k \) is the batch size.
**Intuition:**
- At each iteration, a mini-batch of training examples is selected.
- The gradient is calculated for this mini-batch.
- The parameters are updated based on the average gradient of the mini-batch.
**Advantages:**
- More stable updates compared to SGD.
- Faster convergence than batch gradient descent.
- Efficient on large datasets.
**Disadvantages:**
- Requires tuning of batch size.
- Computationally more expensive than SGD per iteration.
**Python Implementation:**
```python
def mini_batch_gradient_descent(X, y, lr=0.01, epochs=1000, batch_size=32):
m, n = X.shape
theta = np.zeros(n)
for epoch in range(epochs):
indices = np.random.permutation(m)
X_shuffled = X[indices]
y_shuffled = y[indices]
for i in range(0, m, batch_size):
X_i = X_shuffled[i:i+batch_size]
y_i = y_shuffled[i:i+batch_size]
gradient = np.dot(X_i.T, (np.dot(X_i, theta) - y_i)) / batch_size
theta -= lr * gradient
return theta
```
### 4. Momentum
**Explanation:**
Momentum helps accelerate gradient vectors in the right directions, thus leading to faster converging. It accumulates a velocity vector in directions of persistent reduction in the objective function, which helps to smooth the path towards the minimum.
**Mathematical Formulation:**
- $$v_t = γ \cdot v_{t-1} + α \cdot ∇J(θ)$$
- $$θ = θ - v_t$$
where:
- \( v_t \) is the velocity.
- γ is the momentum term, typically set between 0.9 and 0.99.
**Intuition:**
- At each iteration, the gradient is calculated.
- The velocity is updated based on the current gradient and the previous velocity.
- The parameters are updated based on the velocity.
**Advantages:**
- Faster convergence.
- Reduces oscillations in the parameter updates.
**Disadvantages:**
- Requires tuning of the momentum term.
**Python Implementation:**
```python
def momentum_gradient_descent(X, y, lr=0.01, epochs=1000, gamma=0.9):
m, n = X.shape
theta = np.zeros(n)
v = np.zeros(n)
for epoch in range(epochs):
gradient = np.dot(X.T, (np.dot(X, theta) - y)) / m
v = gamma * v + lr * gradient
theta -= v
return theta
```
### 5. Nesterov Accelerated Gradient (NAG)
**Explanation:**
NAG is a variant of the gradient descent with momentum. It looks ahead by a step and calculates the gradient at that point, thus providing more accurate updates. This method helps to correct the overshooting problem seen in standard momentum.
**Mathematical Formulation:**
- $$v_t = γv_{t-1} + α \cdot ∇J(θ - γ \cdot v_{t-1})$$
- $$θ = θ - v_t$$
**Intuition:**
- At each iteration, the parameters are temporarily updated using the previous velocity.
- The gradient is calculated at this lookahead position.
- The velocity and parameters are then updated based on this gradient.
**Advantages:**
- More accurate updates compared to standard momentum.
- Faster convergence.
**Disadvantages:**
- Requires tuning of the momentum term.
**Python Implementation:**
```python
def nesterov_accelerated_gradient(X, y, lr=0.01, epochs=1000, gamma=0.9):
m, n = X.shape
theta = np.zeros(n)
v = np.zeros(n)
for epoch in range(epochs):
lookahead_theta = theta - gamma * v
gradient = np.dot(X.T, (np.dot(X, lookahead_theta) - y)) / m
v = gamma * v + lr * gradient
theta -= v
return theta
```
### 6. AdaGrad
**Explanation:**
AdaGrad adapts the learning rate to the parameters, performing larger updates for infrequent and smaller updates for frequent parameters. It scales the learning rate inversely proportional to the square root of the sum of all historical squared values of the gradient.
**Mathematical Formulation:**
- $$G_t = G_{t-1} + (∂J(θ)/∂θ)^2$$
- $$θ = θ - \frac{α}{\sqrt{G_t + ε}} \cdot ∇J(θ)$$
Where:
- \(G_t\) is the sum of squares of the gradients up to time step \( t \).
- ε is a small constant to avoid division by zero.
**Intuition:**
- Accumulates the sum of the squares of the gradients for each parameter.
- Uses this accumulated
sum to scale the learning rate.
- Parameters with large gradients in the past have smaller learning rates.
**Advantages:**
- Effective for sparse data.
- Automatically adjusts learning rate.
**Disadvantages:**
- Learning rate decreases continuously, which can lead to premature convergence.
**Python Implementation:**
```python
def adagrad(X, y, lr=0.01, epochs=1000, epsilon=1e-8):
m, n = X.shape
theta = np.zeros(n)
G = np.zeros(n)
for epoch in range(epochs):
gradient = np.dot(X.T, (np.dot(X, theta) - y)) / m
G += gradient**2
adjusted_lr = lr / (np.sqrt(G) + epsilon)
theta -= adjusted_lr * gradient
return theta
```
### 7. RMSprop
**Explanation:**
RMSprop modifies AdaGrad to perform well in non-convex settings by using a moving average of squared gradients to scale the learning rate. It helps to keep the learning rate in check, especially in the presence of noisy gradients.
**Mathematical Formulation:**
- E[g²]ₜ = βE[g²]ₜ₋₁ + (1 - β)(∂J(θ) / ∂θ)²
- $$θ = θ - \frac{α}{\sqrt{E[g^2]_t + ε}} \cdot ∇J(θ)$$
Where:
- \( E[g^2]_t \) is the exponentially decaying average of past squared gradients.
- β is the decay rate.
**Intuition:**
- Keeps a running average of the squared gradients.
- Uses this average to scale the learning rate.
- Parameters with large gradients have their learning rates reduced.
**Advantages:**
- Effective for non-convex problems.
- Reduces oscillations in parameter updates.
**Disadvantages:**
- Requires tuning of the decay rate.
**Python Implementation:**
```python
def rmsprop(X, y, lr=0.01, epochs=1000, beta=0.9, epsilon=1e-8):
m, n = X.shape
theta = np.zeros(n)
E_g = np.zeros(n)
for epoch in range(epochs):
gradient = np.dot(X.T, (np.dot(X, theta) - y)) / m
E_g = beta * E_g + (1 - beta) * gradient**2
adjusted_lr = lr / (np.sqrt(E_g) + epsilon)
theta -= adjusted_lr * gradient
return theta
```
### 8. Adam
**Explanation:**
Adam (Adaptive Moment Estimation) combines the advantages of both RMSprop and AdaGrad by keeping an exponentially decaying average of past gradients and past squared gradients.
**Mathematical Formulation:**
- $$m_t = β_1m_{t-1} + (1 - β_1)(∂J(θ)/∂θ)$$
- $$v_t = β_2v_{t-1} + (1 - β_2)(∂J(θ)/∂θ)^2$$
- $$\hat{m}_t = \frac{m_t}{1 - β_1^t}$$
- $$\hat{v}_t = \frac{v_t}{1 - β_2^t}$$
- $$θ = θ - \frac{α\hat{m}_t}{\sqrt{\hat{v}_t} + ε}$$
Where:
- \( m<sub>t \) is the first moment (mean) of the gradient.
- \( v<sub>t \) is the second moment (uncentered variance) of the gradient.
- β_1.β_2 are the decay rates for the moment estimates.
**Intuition:**
- Keeps track of both the mean and the variance of the gradients.
- Uses these to adaptively scale the learning rate.
- Provides a balance between AdaGrad and RMSprop.
**Advantages:**
- Efficient for large datasets.
- Well-suited for non-convex optimization.
- Handles sparse gradients well.
**Disadvantages:**
- Requires careful tuning of hyperparameters.
- Can be computationally intensive.
**Python Implementation:**
```python
def adam(X, y, lr=0.01, epochs=1000, beta1=0.9, beta2=0.999, epsilon=1e-8):
m, n = X.shape
theta = np.zeros(n)
m_t = np.zeros(n)
v_t = np.zeros(n)
for epoch in range(1, epochs+1):
gradient = np.dot(X.T, (np.dot(X, theta) - y)) / m
m_t = beta1 * m_t + (1 - beta1) * gradient
v_t = beta2 * v_t + (1 - beta2) * gradient**2
m_t_hat = m_t / (1 - beta1**epoch)
v_t_hat = v_t / (1 - beta2**epoch)
theta -= lr * m_t_hat / (np.sqrt(v_t_hat) + epsilon)
return theta
```
These implementations are basic examples of how these optimizers can be implemented in Python using NumPy. In practice, libraries like TensorFlow and PyTorch provide highly optimized and more sophisticated implementations of these and other optimization algorithms.
---

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# Rock Paper Scissors Game
This is a simple implementation of the classic rock-paper-scissors game in Python.
## Code Explanation:
In this section, we import the required libraries (`tkinter` for GUI and `random` for generating computer choices) and define two functions:
- `determine_winner(user_choice, computer_choice)`:
- This function determines the winner of the game based on the choices made by the user and the computer.
- It returns a tuple containing the result of the game and the computer's choice.
- `play_game()`:
- This function handles the gameplay logic.
- It gets the user's choice from the radio buttons, generates a random choice for the computer, determines the winner using the `determine_winner()` function, and updates the result and computer pick labels accordingly.
### Imports and Function Definitions:
```python
import tkinter as tk
import random
def determine_winner(user_choice, computer_choice):
"""Determine the winner of the game."""
if user_choice == computer_choice:
return "It's a tie!", computer_choice
elif (user_choice == "rock" and computer_choice == "scissors") or \
(user_choice == "paper" and computer_choice == "rock") or \
(user_choice == "scissors" and computer_choice == "paper"):
return "You win!", computer_choice
else:
return "Computer wins!", computer_choice
def play_game():
"""Play the game and display the result."""
user_choice = user_var.get()
computer_choice = random.choice(["rock", "paper", "scissors"])
result, computer_pick = determine_winner(user_choice, computer_choice)
result_label.config(text=result)
computer_label.config(text=f"Computer picked: {computer_pick}")
```
### GUI Setup:
```python
# Create main window
root = tk.Tk()
root.title("Rock Paper Scissors")
# User choice options
user_var = tk.StringVar()
user_var.set("rock") # Default choice
choices = ["rock", "paper", "scissors"]
for choice in choices:
rb = tk.Radiobutton(root, text=choice, variable=user_var, value=choice)
rb.pack()
```
- Here, we create the main window for the game using `tkinter.Tk()`. We set the title to "Rock Paper Scissors".
- We define a `StringVar` to store the user's choice and set the default choice to "rock".
- We create radio buttons for the user to choose from ("rock", "paper", "scissors") and pack them into the main window.
```
```
### Play Button and Result Labels:
```python
# Play button
play_button = tk.Button(root, text="Play", command=play_game)
play_button.pack()
# Result label
result_label = tk.Label(root, text="", font=("Helvetica", 16))
result_label.pack()
# Computer pick label
computer_label = tk.Label(root, text="", font=("Helvetica", 12))
computer_label.pack()
```
- We create a "Play" button that triggers the `play_game()` function when clicked, using `tkinter.Button`.
- We create two labels to display the result of the game (`result_label`) and the computer's choice (`computer_label`). Both labels initially display no text and are packed into the main window.
```
```
### Mainloop:
```python
root.mainloop()
```
- Finally, we start the Tkinter event loop using `root.mainloop()`, which keeps the GUI window open and responsive until the user closes it.
-

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## Dice Roller
The aim of this project is to replicate a dice and generate a random number from the numbers 1 to 6.
For this first we will import the random library which will help make random choices.
```
import random
def dice():
dice_no = random.choice([1,2,3,4,5,6])
return "You got " + str(dice_no)
```
The above snippet of code defines a function called `dice()` which makes the random choice and returns the number that is generated.
```
def roll_dice():
print("Hey Guys, you will now roll a single dice using Python!")
while True:
start=input("Type \'k\' to roll the dice: ").lower()
if start != 'k':
print("Invalid input. Please try again.")
continue
print(dice())
roll_again = input("Do you want to reroll? (Yes/No): ").lower()
if roll_again != 'yes':
break
print("Thanks for rolling the dice.")
roll_dice()
```
The above code defines a function called `roll_dice()` which interacts with the user.
It prompts the user to give an input and if the input is `k`,the code proceeds further to generate a random number or gives the message of invalid input and asks the user to try again.
After the dice has been rolled once, the function asks the user whether they want a reroll in the form of a `yes` or `no` question. The dice is rolled again if the user gives `yes` as an answer and exits the code if the user replies with anything other than yes.

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# Hangman - Movies Edition
The Hangman game script is a simple Python program designed to let players guess movie titles. It starts by importing the random module to select a movie from a predefined list. The game displays the movie title as underscores and reveals correctly guessed letters. Players have six attempts to guess the entire title, entering one letter at a time. The script checks if the input is valid, updates the list of guessed letters, and adjusts the number of attempts based on the correctness of the guess. The game continues until the player either guesses the title correctly or runs out of attempts. Upon completion, it congratulates the player for a correct guess or reveals the movie title if the attempts are exhausted. The main execution block ensures the game runs only when the script is executed directly.Below is first the code and then an explanation of the code and its components.
## Code
```
import random
def choose_movie():
movies = ['avatar', 'titanic', 'inception', 'jurassicpark', 'thegodfather', 'forrestgump', 'interstellar', 'pulpfiction', 'shawshank']
return random.choice(movies)
def display_word(movie, guessed_letters):
display = ""
for letter in movie:
if letter in guessed_letters:
display += letter + " "
else:
display += "_ "
return display
def hangman_movies():
movie = choose_movie()
guessed_letters = []
attempts = 6
print("Welcome to Hangman - Movies Edition!")
print("Try to guess the name of the movie. You have 6 attempts.")
while attempts > 0:
print("\n" + display_word(movie, guessed_letters))
guess = input("Guess a letter: ").lower()
if len(guess) != 1 or not guess.isalpha():
print("Please enter a single letter.")
continue
if guess in guessed_letters:
print("You've already guessed that letter.")
continue
guessed_letters.append(guess)
if guess not in movie:
attempts -= 1
print(f"Sorry, '{guess}' is not in the movie name. You have {attempts} attempts left.")
else:
print(f"Good guess! '{guess}' is in the movie name.")
if "_" not in display_word(movie, guessed_letters):
print(f"\nCongratulations! You guessed the movie '{movie.capitalize()}' correctly!")
break
if attempts == 0:
print(f"\nSorry, you ran out of attempts. The movie was '{movie.capitalize()}'.")
if __name__ == "__main__":
hangman_movies()
```
## Code Explanation
### Importing the Random Module
```python
import random
```
The `random` module is imported to use the `choice` function, which will help in selecting a random movie from a predefined list.
### Choosing a Movie
```python
def choose_movie():
movies = ['avatar', 'titanic', 'inception', 'jurassicpark', 'thegodfather', 'forrestgump', 'interstellar', 'pulpfiction', 'shawshank']
return random.choice(movies)
```
The `choose_movie` function returns a random movie title from the `movies` list.
### Displaying the Word
```python
def display_word(movie, guessed_letters):
display = ""
for letter in movie:
if letter in guessed_letters:
display += letter + " "
else:
display += "_ "
return display
```
The `display_word` function takes the movie title and a list of guessed letters as arguments. It constructs a string where correctly guessed letters are shown in their positions, and unknown letters are represented by underscores (`_`).
### Hangman Game Logic
```python
def hangman_movies():
movie = choose_movie()
guessed_letters = []
attempts = 6
print("Welcome to Hangman - Movies Edition!")
print("Try to guess the name of the movie. You have 6 attempts.")
while attempts > 0:
print("\n" + display_word(movie, guessed_letters))
guess = input("Guess a letter: ").lower()
if len(guess) != 1 or not guess.isalpha():
print("Please enter a single letter.")
continue
if guess in guessed_letters:
print("You've already guessed that letter.")
continue
guessed_letters.append(guess)
if guess not in movie:
attempts -= 1
print(f"Sorry, '{guess}' is not in the movie name. You have {attempts} attempts left.")
else:
print(f"Good guess! '{guess}' is in the movie name.")
if "_" not in display_word(movie, guessed_letters):
print(f"\nCongratulations! You guessed the movie '{movie.capitalize()}' correctly!")
break
if attempts == 0:
print(f"\nSorry, you ran out of attempts. The movie was '{movie.capitalize()}'.")
```
The `hangman_movies` function manages the game's flow:
1. It selects a random movie title using `choose_movie`.
2. Initializes an empty list `guessed_letters` and sets the number of attempts to 6.
3. Prints a welcome message and the initial game state.
4. Enters a loop that continues until the player runs out of attempts or guesses the movie title.
5. Displays the current state of the movie title with guessed letters revealed.
6. Prompts the player to guess a letter.
7. Validates the player's input:
- Ensures it is a single alphabetic character.
- Checks if the letter has already been guessed.
8. Adds the guessed letter to `guessed_letters`.
9. Updates the number of attempts if the guessed letter is not in the movie title.
10. Congratulates the player if they guess the movie correctly.
11. Informs the player of the correct movie title if they run out of attempts.
### Main Execution Block
```python
if __name__ == "__main__":
hangman_movies()
```
## Conclusion
This block ensures that the game runs only when the script is executed directly, not when it is imported as a module.
## Output Screenshots:
![image](https://github.com/Aditi22Bansal/learn-python/assets/142652964/a7af1f7e-c80e-4f83-b1f7-c7c5c72158b4)
![image](https://github.com/Aditi22Bansal/learn-python/assets/142652964/082e54dc-ce68-48fd-85da-3252d7629df8)
## Conclusion
This script provides a simple yet entertaining Hangman game focused on guessing movie titles. It demonstrates the use of functions, loops, conditionals, and user input handling in Python.

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# List of sections
- [Section title](filename.md)
- [Dice Roller](dice_roller.md)
- [Rock Paper Scissors Game](Rock_Paper_Scissors_Game.md)
- [Password strength checker](password_strength_checker.md)
- [Path Finder](path-finder.md)
- [Hangman Game Based on Movies](hangman_game.md)
- [Tic-tac-toe](tic-tac-toe.md)

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# about password strength
> This code is a simple password strength checker.
It evaluates the strength of a user's password based on the presence of
uppercase letters, lowercase letters, digits, spaces, and special characters.
### About the code:
- The codebase is break down in two file `password_strength_checker.py` and `main.py`.
`password_strength_checker.py` The function evaluates password strength based on character types (uppercase, lowercase, digits, spaces, special characters) and provides feedback on its security.
and `main.py` contains basic code.
```
import string
class password_checker:
def __init__(self, password):
self.password = password
def check_password_strength(self):
"""This function prompts the user to enter a password and then evaluates its strength."""
password_strength = 0
upper_count = 0
lower_count = 0
num_count = 0
space_count = 0
specialcharacter_count = 0
review = ""
for char in list(password):
if char in string.ascii_uppercase:
upper_count += 1
elif char in string.ascii_lowercase:
lower_count += 1
elif char in string.digits:
num_count += 1
elif char == " ":
space_count += 1
else:
specialcharacter_count += 1
if upper_count >= 1:
password_strength += 1
if lower_count >= 1:
password_strength += 1
if num_count >= 1:
password_strength += 1
if space_count >= 1:
password_strength += 1
if specialcharacter_count >= 1:
password_strength += 1
if password_strength == 1:
review = "That's a very easy password, Not good for use"
elif password_strength == 2:
review = (
"That's a weak password, You should change it to some strong password."
)
elif password_strength == 3:
review = "Your password is just okay, you may change it."
elif password_strength == 4:
review = "Your password is hard to guess."
elif password_strength == 5:
review = "Its the strong password, No one can guess this password "
about_password = {
"uppercase_letters ": upper_count,
"lowercase_letters": lower_count,
"space_count": space_count,
"specialcharacter_count": specialcharacter_count,
"password_strength": password_strength,
"about_password_strength": review,
}
print(about_password)
def check_password():
"""This function prompts the user to decide if they want to check their password strength."""
choice = input("Do you want to check your password's strength? (Y/N): ")
if choice.upper() == "Y":
return True
elif choice.upper() == "N":
return False
else:
print("Invalid input. Please enter 'Y' for Yes or 'N' for No.")
return password_checker.check_password()
```
### Here's the implementation of 'main.py'
```
import password_checker from password_strength_checker
while password_checker.check_password():
password = input("Enter your password: ")
p = password_checker(password)
p.check_password_strength()
```

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# Path Finder
This Python script uses the curses library to visualize the process of finding a path through a maze in real-time within a terminal window. The program represents the maze as a list of lists, where each list represents a row in the maze, and each string element in the lists represents a cell in the maze. The maze includes walls (#), a start point (O), and an end point (X), with empty spaces ( ) that can be traversed.
## The script includes the following main components:
- Visualization Functions: <br>
print_maze(maze, stdscr, path=[]): This function is used to display the maze in the terminal. It utilizes color pairs to distinguish between the maze walls, the path, and unexplored spaces. The current path being explored is displayed with a different color to make it stand out.
- Utility Functions: <br>
find_start(maze, start): This function searches the maze for the starting point (marked as O) and returns its position as a tuple (row, col). <br>
find_neighbors(maze, row, col): This function identifies the valid adjacent cells (up, down, left, right) that can be moved to from the current position,
ignoring any walls or out-of-bound positions.
- Pathfinding Logic: <br>
find_path(maze, stdscr): This function implements a Breadth-First Search (BFS) algorithm to find a path from the start point to the end point (X). It uses a
queue to explore each possible path sequentially. As it explores the maze, it updates the display in real-time, allowing the viewer to follow the progress
visually. Each visited position is marked and not revisited, ensuring the algorithm efficiently covers all possible paths without repetition.
Overall, the script demonstrates an effective use of the curses library to create a dynamic visual representation of the BFS algorithm solving a maze, providing both an educational tool for understanding pathfinding and an example of real-time data visualization in a terminal.
#### Below is the code of the path finder
```python
import curses
from curses import wrapper
import queue
import time
# Define the structure of the maze as a list of lists where each inner list represents a row.
maze = [
["#", "O", "#", "#", "#", "#", "#", "#", "#"],
["#", " ", " ", " ", " ", " ", " ", " ", "#"],
["#", " ", "#", "#", " ", "#", "#", " ", "#"],
["#", " ", "#", " ", " ", " ", "#", " ", "#"],
["#", " ", "#", " ", "#", " ", "#", " ", "#"],
["#", " ", "#", " ", "#", " ", "#", " ", "#"],
["#", " ", "#", " ", "#", " ", "#", "#", "#"],
["#", " ", " ", " ", " ", " ", " ", " ", "#"],
["#", "#", "#", "#", "#", "#", "#", "X", "#"]
]
# Function to print the current state of the maze in the terminal.
def print_maze(maze, stdscr, path=[]):
BLUE = curses.color_pair(1) # Color pair for walls and free paths
RED = curses.color_pair(2) # Color pair for the current path
for i, row in enumerate(maze):
for j, value in enumerate(row):
if (i, j) in path:
stdscr.addstr(i, j*2, "X", RED) # Print path character with red color
else:
stdscr.addstr(i, j*2, value, BLUE) # Print walls and free paths with blue color
# Function to locate the starting point (marked 'O') in the maze.
def find_start(maze, start):
for i, row in enumerate(maze):
for j, value in enumerate(row):
if value == start:
return i, j
return None
# Function to find a path from start ('O') to end ('X') using BFS.
def find_path(maze, stdscr):
start = "O"
end = "X"
start_pos = find_start(maze, start) # Get the start position
q = queue.Queue()
q.put((start_pos, [start_pos])) # Initialize the queue with the start position
visited = set() # Set to keep track of visited positions
while not q.empty():
current_pos, path = q.get() # Get the current position and path
row, col = current_pos
stdscr.clear() # Clear the screen
print_maze(maze, stdscr, path) # Print the current state of the maze
time.sleep(0.2) # Delay for visibility
stdscr.refresh() # Refresh the screen
if maze[row][col] == end: # Check if the current position is the end
return path # Return the path if end is reached
# Get neighbors (up, down, left, right) that are not walls
neighbors = find_neighbors(maze, row, col)
for neighbor in neighbors:
if neighbor not in visited:
r, c = neighbor
if maze[r][c] != "#":
new_path = path + [neighbor]
q.put((neighbor, new_path))
visited.add(neighbor)
# Function to find the valid neighboring cells (not walls or out of bounds).
def find_neighbors(maze, row, col):
neighbors = []
if row > 0: # UP
neighbors.append((row - 1, col))
if row + 1 < len(maze): # DOWN
neighbors.append((row + 1, col))
if col > 0: # LEFT
neighbors.append((row, col - 1))
if col + 1 < len(maze[0]): # RIGHT
neighbors.append((row, col + 1))
return neighbors
# Main function to setup curses and run the pathfinding algorithm.
def main(stdscr):
curses.init_pair(1, curses.COLOR_BLUE, curses.COLOR_BLACK) # Initialize color pair for blue
curses.init_pair(2, curses.COLOR_RED, curses.COLOR_BLACK) # Initialize color pair for red
find_path(maze, stdscr) # Find the path using BFS
stdscr.getch() # Wait for a key press before exiting
wrapper(main) # Use the wrapper to initialize and finalize curses automatically.
```

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# Python Code For The Tic Tac Toe Game
# Tic Tac Toe Game
## Overview
### Objective
- Get three of your symbols (X or O) in a row (horizontally, vertically, or diagonally) on a 3x3 grid.
### Gameplay
- Two players take turns.
- Player 1 uses X, Player 2 uses O.
- Players mark an empty square in each turn.
### Winning
- The first player to align three of their symbols wins.
- If all squares are filled without any player aligning three symbols, the game is a draw.
```python
print("this game should be played by two people player1 takes x player2 takes o")
board = [['1','2','3'],['4','5','6'],['7','8','9']]
x = 'X'
o = 'O'
def displayBoard():
print(f" {board[0][0]} | {board[0][1]} | {board[0][2]}")
print("----------------------------------------")
print(f" {board[1][0]} | {board[1][1]} | {board[1][2]}")
print("----------------------------------------")
print(f" {board[2][0]} | {board[2][1]} | {board[2][2]}")
print("----------------------------------------")
def updateBoard(character,position):
row = (position-1)//3
column = (position-1)%3
board[row][column] = character
def check_win():
for i in range(3):
if board[i][0] == board[i][1] == board[i][2]:
return 1
elif board[0][i] == board[1][i] == board[2][i]:
return 1
if board[0][2] == board[1][1] == board[2][0]:
return 1
elif board[0][0] == board[1][1] == board[2][2]:
return 1
return 0
def check_position(position):
row = (position-1)//3
column = (position-1)%3
if board[row][column] == x or board[row][column] == o:
return 0
return 1
print("==============================welcome to tic tac toe game =====================")
counter = 0
while 1:
if counter % 2 == 0:
displayBoard()
while 1:
choice = int(input(f"player{(counter%2)+1},enter your position('{x}');"))
if choice < 1 or choice > 9:
print("invalid input oplease try againn")
if check_position(choice):
updateBoard(x,choice)
if check_win():
print(f"Congratulations !!!!!!!!!!!Player {(counter % 2)+1} won !!!!!!!!!!")
exit(0)
else :
counter += 1
break
else:
print(f"position{choice} is already occupied.Choose another position")
if counter == 9:
print("the match ended with draw better luck next time")
exit(0)
else:
displayBoard()
while 1:
choice = int(input(f"player{(counter%2)+1},enter your position('{o}'):"))
if choice < 1 or choice > 9:
print("invalid input please try again")
if check_position(choice):
updateBoard(o,choice)
if check_win():
print(f"congratulations !!!!!!!!!!!!!!! player{(counter%2)+1} won !!!!!!!!!!!!!1")
exit(0)
else:
counter += 1
break
else:
print(f"position {choice} is already occupied.choose another position")
print()
```

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# NumPy Array Iteration
Iterating over arrays in NumPy is a common task when processing data. NumPy provides several ways to iterate over elements of an array efficiently.
Understanding these methods is crucial for performing operations on array elements effectively.
## 1. Basic Iteration
- Iterating using basic `for` loop.
### Single-dimensional array
Iterating over a single-dimensional array is straightforward using a basic `for` loop
```python
import numpy as np
arr = np.array([1, 2, 3, 4, 5])
for i in arr:
print(i)
```
#### Output
```python
1
2
3
4
5
```
### Multi-dimensional array
Iterating over multi-dimensional arrays, each iteration returns a sub-array along the first axis.
```python
marr = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
for arr in marr:
print(arr)
```
#### Output
```python
[1 2 3]
[4 5 6]
[7 8 9]
```
## 2. Iterating with `nditer`
- `nditer` is a powerful iterator provided by NumPy for iterating over multi-dimensional arrays.
- In each interation it gives each element.
```python
import numpy as np
arr = np.array([[1, 2, 3], [4, 5, 6]])
for i in np.nditer(arr):
print(i)
```
#### Output
```python
1
2
3
4
5
6
```
## 3. Iterating with `ndenumerate`
- `ndenumerate` allows you to iterate with both the index and the value of each element.
- It gives index and value as output in each iteration
```python
import numpy as np
arr = np.array([[1, 2], [3, 4]])
for index,value in np.ndenumerate(arr):
print(index,value)
```
#### Output
```python
(0, 0) 1
(0, 1) 2
(1, 0) 3
(1, 1) 4
```
## 4. Iterating with flat
- The `flat` attribute returns a 1-D iterator over the array.
```python
import numpy as np
arr = np.array([[1, 2], [3, 4]])
for element in arr.flat:
print(element)
```
#### Output
```python
1
2
3
4
```
Understanding the various ways to iterate over NumPy arrays can significantly enhance your data processing efficiency.
Whether you are working with single-dimensional or multi-dimensional arrays, NumPy provides versatile tools to iterate and manipulate array elements effectively.

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# Basic Mathematics
## What is a Matrix?
A matrix is a collection of numbers ordered in rows and columns. Here is one.
<body>
<table>
<tr>
<td>1</td>
<td>2</td>
<td>3</td>
</tr>
<tr>
<td>4</td>
<td>5</td>
<td>6</td>
</tr>
<tr>
<td>7</td>
<td>8</td>
<td>9</td>
</tr>
</table>
</body>
A matrix is generally written within square brackets[]. The dimensions of a matrix is represented by (Number of rows x Number of columns).The dimensions of the above matrix is 3x3.
Matrices are the main characters in mathematical operations like addition, subtraction etc, especially those used in Pandas and NumPy. They can contain only numbers, symbols or expressions.
In order to refer to a particular element in the matrix we denote it by :
A<sub>ij</sub>
where i represents the ith row and j represents the jth column of the matrix.
## Scalars and Vectors
### Scalars
There exists specific cases of matrices which are also widely used.
A matrix with only one row and column i.e. containing only one element is commonly referred to as a scalar.
The numbers ```[12] ; [-5] ; [0] ; [3.14]``` all represent scalars. Scalars have 0 dimensions.
### Vectors
Vectors are objects with 1 dimension. They sit somewhere between scalars and matrices. They can also be referred to as one dimensional matrices.
```[1 3 5]``` represents a vector with dimension 1x3.
A vector is the simplest linear algebraic object.A matrix can be refered to as a collection of vectors
Vectors are broadly classified into 2 types:
- Row Vectors: Is of the form 1 x n where n refers to the number of columns the vector has.
- Column Vectors: Is of the form m x 1 where m refers to the number of rows the vector has.
m or n are also called as the length of the column and row vector respectively.
## Arrays in Python
To understand arrays, first let us start by declaring scalars, vectors and matrices in Python.
First we need to import numpy. We do so by importing it as 'np' as it provides better readability, namespace clarity and also aligns with the community guidelines.
```python
import numpy as np
```
Next up, we declare a scalar s as,
```
s = 5
```
Now we declare a vector,
```python
v = np.array([5,-2,4])
```
On printing v we get the following output,
```python
array([5,-2,4])
```
By default, a vector is declared as a **'row vector'**.
Finally, we declare matrices,
```python
m=np.array([[5,12,6],[-3,0,14]])
```
On printing m we get,
```python
array([[5,12,6],
[-3,0,14]])
```
> The type() function is used to return the data type of a given variable.
* The type(s) will return **'int'**.
* The type(v) will return **'numpy.ndarray'** which represents a **n-dimensional array**, since it is a 1 dimensional array.
* The type(m) will also return **'numpy.ndarray'** since it is a 2-dimensional array.
These are some ways in which arrays are useful in python.
> The shape() function is used to return the shape of a given variable.
* m.shape() returns (2,3) since we are dealing with a (2,3) matrix.
* v.shape() returns(3,) indicates it has only one dimensional or that it stores 3 elements in order.
* However, 'int' objects do not have shape and therefore s.shape() gives an error.
## What is a Tensor?
A Tensor can be thought of as a collection of matrices. It has dimensions k x m x n.
**NOTE:** Scalars, vectors and matrices are also tensors of rank 0,1,2 respectively.
Tensors can be stored in ndarrays.
Let's create a tensor with 2 matrices,
```python
m1=np.array([[5,12,6],[-3,0,14]])
m2=np.array([[2,1,8],[-6,2,0]])
t=np.array([m1,m2])
```
Upon printing t we get,
```python
array([[[5,12,6],
[-3,0,14]],
[[2,1,8],
[-6,2,0]]])
```
If we check it's shape, we see that is is a **(2,2,3)** object.
If we want to manually create a tensor we write,
```python
t=np.array([[[5,12,6], [-3,0,14]],[[2,1,8], [-6,2,0]]])
```
## Addition and Subtraction in Matrices
### Addition
For 2 matrices to be added to one another they must have **same dimensions**.
If we have 2 matrices say,
```python
A=np.array([[5,12,6],[-3,0,14]])
B=np.array([[2,1,8],[-6,2,0]])
C= A+B
```
The element at position A<sub>ij</sub> gets added to the element at position B<sub>ij</sub>. It's that simple!
The above input will give the resultant C as:
```python
array([[7,13,14],
[-9,2,14]])
```
### Subtraction
As we know, subtraction is a type of addition, the same rules apply here.
If we have 2 matrices say,
```python
A=np.array([[5,12,6],[-3,0,14]])
B=np.array([[2,1,8],[-6,2,0]])
C= A-B
```
The element at position B<sub>ij</sub> gets subtracted from the element at position A<sub>ij</sub>.
The above input will give the resultant C as:
```python
array([[3,11,-2],
[3,-2,14]])
```
Similarly the same operations can be done with **floating point numbers** as well.
In a similar fashion, we can add or subtract vectors as well with the condition that they must be of the **same length**.
```python
A=np.array([1,2,3,4,5])
B=np.array([6,7,8,9,10])
C= A+B
```
The result is a vector of length 5 with C as,
```python
array([7,9,11,13,15])
```
### Addition of scalars with vectors & matrices
Scalars show unique behaviour when added to matrices or vectors.
To demonstrate their behaviour, let's use an example,
Let's declare a matrix,
```python
A=np.array([[5,12,6],[-3,0,14]])
A+1
```
We see that if we perform the above function, i.e. add scalar [1] to the matrix A we get the output,
```python
array([[6,13,7],[-2,1,15]])
```
We see that the scalar is added to the matrix elementwise, i.e. each element gets incremented by 1.
**The same applies to vectors as well.**
Mathematically, it is not allowed as the shape of scalars are different from vectors or matrices but while programming in Python it works.
## Transpose of Matrices & Vectors
### Transposing Vectors
If X is the vector, then the transpose of the vector is represented as X<sup>T</sup>. It changes a vector of dimension n x 1 into a vector of dimension 1 x n, i.e. a row vector to a column vector and vice versa.
> * The values are not changing or transforming ; only their position is.
> * Transposing the same vector (object) twice yields the initial vector (object).
```python
x=np.array([1,2,3))
```
Transposing this in python using ```x.T``` will give
```python
array([1,2,3))
```
which is the same vector as the one taken as input.
> 1-Dimensional arrays don't really get transposed (in the memory of the computer)
To transpose a vector, we need to reshape it first.
```python
x_new= x.reshape(1,3)
x_new.T
```
will now result in the vector getting transposed,
```python
array([[1],
[2],
[3]])
```
### Transposing Matrices
If M is a matrix, then the transpose of the matrix M is represented as M<sup>T</sup>. When transposed, a m x n matrix becomes a n x m matrix.
The element M<sub>ij</sub> of the initial matrix becomes the N<sub>ji</sub> where N is the transposed matrix of M.
Let's understand this further with the help of of an example,
```python
A = np.array([[1,5,-6],[8,-2,0]])
```
The output for the above code snippet will be,
```python
array([[1,5,-6],
[8,-2,0]])
```
> **array.T** returns the transpose of an array (matrix).
```python
A.T
```
will give the output as,
```python
array([[1,8],
[5,-2],
[-6,0]])
```
Hope the following examples have cleared your concept on transposing.
## Dot Product
> **np.dot()** returns the dot product of two objects
> Dot product is represented by ( * ), for example, x(dot)y = x * y
>
### Scalar * Scalar
Let's start with scalar multiplication first.
``` [6] * [5] = [30]
[10] * [-2] = [-20]
```
It is the same multiplication that we are familiar with since learnt as kids.
Therefore, ```np.dot([6]*[5])``` returns ```30```.
### Vector * Vector
To multiply vectors with one another, they must be of **same length**.
Now let's understand this with an example,
```python
x = np.array([2,8,-4])
y = np.array([1,-7,3])
```
The dot product returns the elementwise product of the vector i.e.
x * y = ( x<sub>1</sub> * y<sub>1</sub> ) + ( x<sub>2</sub> * y<sub>2</sub> ) + ( x<sub>3</sub> * y<sub>3</sub> ) in the above example.
Therefore, ```np.dot(x,y)``` gives ```[-66]``` as the input.
We observe that **dot product of 2 vectors returns a scalar**.
### Scalar * Vector
When we multiply a scalar with a vector, we observe that each element of the vector gets multiplied to the scalar individually.
A scalar k when multiplied to a vector v([x1,x2,x3]) gives the product = [(k * x1) + (k * x2) + (k * x3)]
An example would bring further clarity,
```python
y = np.array([1,-7,3])
y*5
```
will give the following output
```python
array[(5,-35,15)]
```
We observe that **dot product of 2 vectors returns a scalar**.
We observe that **dot product of a vector and a scalar returns a vector**.
## Dot Product of Matrices
### Scalar * Matrix
Dot product of a scalar with a matrix works similar to dot product of a vector with a scalar.
Now, we come to a very important concept which will be very useful to us while working in Python.
Each element of the vector gets multiplied to the scalar individually.
```python
A = np.array([[1,5,-6],[8,-2,0]])
B = 3 * A
```
will give the resultant B as
```python
array([[3,15,-18],
[24,-6,0]])
```
Thus each element gets multiplied by 3.
> NOTE: The dot product of a scalar and a matrix gives a matrix of the same shape as the input matrix.
### Matrix * Matrix
A matrix can be multipied to a matrix. However it has certain compatibility measures,
* We can only multiply an m x n matrix with an n x k matrix
* Basically the 2nd dimension of the first matrix has to match the 1st dimension of the 2nd matrix.
> The output of a m x n matrix with a n x k matrix gives a **m x k** matrix.
**Whenever we have a dot product of 2 matrices, we multiply row vectors within one matrix to the column vector of 2nd matrix.**
For example, let's use multiply a row vector to a column vector to understand it further.
```
([[1]
([2 8 4]) * [2] = [(2*1) + (8*2) + (4*3)] = [30]
[3]])
```
Now, let's multiply a 2 x 3 matrix with a 3 x 2 matrix.
```
([[A1,A2,A3], * ([[B1,B2] ([[(A1 * B1 + A2 * B3 + A3 * B5) , (A1 * B2 + A2 * B4 + A3 * B6)]
[A4,A5,A6]]) [B3,B4], = [ (A4 * B1 + A5 * B3 + A6 * B5) , (A4 * B2 + A5 * B4 + A6 * B6)]])
[B5,B6]])
```
Thus we obtain a 2 x 2 matrix.
We use the np.dot() method to directly obtain the dot product of the 2 matrices.
Now let's do an example using python just to solidify our knowledge.
```python
A=np.array([[5,12,6],[-3,0,14]])
B=np.array([[2,-1],[8,0],[3,0]])
np.dot(A,B)
```
The output we obtain is,
```python
array[[124,-5],
[36, 3]])
```

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# Concatenation of Arrays
Concatenation of arrays in NumPy refers to combining multiple arrays into a single array, either along existing axes or by adding new axes. NumPy provides several functions for this purpose.
# Functions of Concatenation
## np.concatenate
Joins two or more arrays along an existing axis.
### Syntax
```python
numpy.concatenate((arr1, arr2, ...), axis)
```
Args:
- arr1, arr2, ...: Sequence of arrays to concatenate.
- axis: Axis along which the arrays will be joined. Default is 0.
### Example
#### Concatenate along axis 0
```python
import numpy as np
#creating 2 arrays
arr1 = np.array([1 2 3],[7 8 9])
arr2 = np.array([4 5 6],[10 11 12])
result_1 = np.concatenate((arr1, arr2), axis=0)
print(result_1)
```
#### Output
```
[[ 1 2 3]
[ 7 8 9]
[ 4 5 6]
[10 11 12]]
```
#### Concatenate along axis 1
```python
result_2 = np.concatenate((arr1, arr2), axis=1)
print(result_2)
```
#### Output
```
[[ 1 2 3 4 5 6 ]
[ 7 8 9 10 11 12]]
```
## np.vstack
Vertical stacking of arrays (row-wise).
### Syntax
```python
numpy.vstack(arrays)
```
Args:
- arrays: Sequence of arrays to stack.
### Example
```python
import numpy as np
#create arrays
arr1= np.array([1 2 3], [7 8 9])
arr2 = np.array([4 5 6],[10 11 12])
result = np.vstack((arr1, arr2))
print(result)
```
#### Output
```
[[ 1 2 3]
[ 7 8 9]
[ 4 5 6]
[10 11 12]]
```
## 3. np.hstack
Stacks arrays horizontally (column-wise).
### Syntax
```python
numpy.hstack(arrays)
```
Args:
- arrays: Sequence of arrays to stack.
### Example
```python
import numpy as np
#create arrays
arr1= np.array([1 2 3], [7 8 9])
arr2 = np.array([4 5 6],[10 11 12])
result = np.hstack((arr1, arr2))
print(result)
```
#### Output
```
[[ 1 2 3] [ 4 5 6]
[ 7 8 9] [10 11 12]]
```
## np.dstack
Stacks arrays along the third axis (depth-wise).
### Syntax
```python
numpy.dstack(arrays)
```
- arrays: Sequence of arrays to stack.
### Example
```python
import numpy as np
#create arrays
arr1= np.array([1 2 3], [7 8 9])
arr2 = np.array([4 5 6],[10 11 12])
result = np.dstack((arr1, arr2))
print(result)
```
#### Output
```
[[[ 1 4]
[ 2 5]
[ 3 6]]
[[ 7 10]
[ 8 11]
[ 9 12]]]
```
## np.stack
Joins a sequence of arrays along a new axis.
```python
numpy.stack(arrays, axis)
```
Args:
- arrays: Sequence of arrays to stack.
### Example
```python
import numpy as np
#create arrays
arr1= np.array([1 2 3], [7 8 9])
arr2 = np.array([4 5 6],[10 11 12])
result = np.stack((arr1, arr2), axis=0)
print(result)
```
#### Output
```
[[[ 1 2 3]
[ 7 8 9]]
[[ 4 5 6]
[10 11 12]]]
```
# Concatenation with Mixed Dimensions
When concatenating arrays with different shapes, it's often necessary to reshape them to have compatible dimensions.
## Example
#### Concatenate along axis 0
```python
arr1 = np.array([[1, 2, 3], [4, 5, 6]])
arr2 = np.array([7, 8, 9])
result_0= np.concatenate((arr1, arr2[np.newaxis, :]), axis=0)
print(result_0)
```
#### Output
```
[[1 2 3]
[4 5 6]
[7 8 9]]
```
#### Concatenate along axis 1
```python
result_1 = np.concatenate((arr1, arr2[:, np.newaxis]), axis=1)
print(result_1)
```
#### Output
```
[[1 2 3 7]
[4 5 6 8]]
```

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# Numpy Data Types
In NumPy, data types play a crcial role in representing and manipulating numerical data.
Numpy supports the following data types:
- `i` - integer
- `b` - boolean
- `u` - unsigned integer
- `f` - float
- `c` - complex float
- `m` - timedelta
- `M` - datetime
- `O` - object
- `S` - string
- `U` - unicode string
_Referred from: W3schools_
## dtype() Function
The `dtype()` function returns the type of the NumPy array object.
Example 1
``` python
import numpy as np
arr = np.array([1, 2, 3, 4])
print(arr.dtype)
# Output: int64
```
Example 2
``` python
import numpy as np
arr = np.array(['apple', 'banana', 'cherry'])
print(arr.dtype)
# Output: <U6
```
## Example for integer type
The NumPy integer array can be defined in two ways.
Way 1: Using function `int_()`
``` python
import numpy as np
arr = np.int_([2,4,6])
# Size: int8, int16, int32, int64
print(arr.dtype())
# Output: int64
```
Way 2: Using `dtype()`
``` python
import numpy as np
arr = np.array([2,4,6], dtype='i4')
# Size: i1, i2, i4, i8
print(arr.dtype)
# Output: int32
```
Note: `np.intc()` has the same function as `int32()`.
## Example for float type
Way 1: Using function `float_()`
``` python
import numpy as np
arr = np.float_(1)
# Size: float8, float16, float32, float64
print(arr)
print(arr.dtype())
# Output:
# 1.0
# float64
```
Way 2: Using `dtype()`
``` python
import numpy as np
arr = np.array([2,4,6], dtype='f4')
# Size: f1, f2, f4, f8
print(arr)
print(arr.dtype)
# Output:
# [1. 2. 3. 4.]
# float32
```
Note: `np.single()` has the same function as `float32()`.
## Example for boolean type
``` python
import numpy as np
x = np.bool_(1)
print(x)
print(x.dtype)
# Output:
# True
# bool
```
## Example for unsigned integer type
``` python
import numpy as np
x = np.uintc(1)
print(x)
print(x.dtype)
# Output:
# 1
# uint32
```
## Example for complex type
Complex type is a combination of real number + imaginary number. The `complex_()` is used to define the complex type NumPy object.
``` python
import numpy as np
x = np.complex_(1)
# Size: complex64, complex128
print(x)
print(x.dtype)
# Output:
# (1+0j)
# complex128
```
## Example for datetime type
The `datetime64()` is used to define the date, month and year.
``` python
import numpy as np
x = np.datetime64('2024-05')
y = np.datetime64('2024-05-20')
z = np.datetime64('2024')
print(x,x.dtype)
print(y,y.dtype)
print(z,z.dtype)
# Output:
# 2024-05 datetime64[M]
# 2024-20-05 datetime64[D]
# 2024 datetime64[Y]
```
## Example for string type
``` python
import numpy as np
arr = np.str_("roopa")
print(arr.dtype)
# Output: <U5
```
## Example for object type
``` python
import numpy as np
arr = np.object_([1, 2, 3, 4])
print(arr)
print(arr.dtype)
# Output:
# [1, 2, 3, 4]
# object
```
## Example for unicode string type
``` python
import numpy as np
arr = np.array(['apple', 'banana', 'cherry'])
print(arr.dtype)
# Output: <U6
```
## Example for timedelta type
The `timedelta64()` used to find the difference between the `datetime64()`. The arguments for timedelta64 are a number, to represent the number of units, and a date/time unit, such as (D)ay, (M)onth, (Y)ear, (h)ours, (m)inutes, or (s)econds. The timedelta64 data type also accepts the string “NAT” in place of the number for a “Not A Time” value.
``` python
import numpy as np
x = np.datetime64('2024-05-20')
y = np.datetime64('2023-05-20')
res = x - y
print(res)
print(res.dtype)
# Output:
# 366 days
# timedelta64[D]
```
## Additional Data Type (`longdouble`)
`longdouble` is a data type that provides higher precision than the standard double-precision floating-point (`float64`) type.
``` python
import numpy as np
arr = np.longdouble([1.222222, 4.44, 45.55])
print(arr, arr.dtype)
# Output:
# [1.222222 4.44 45.55] float128
```
# Data Type Conversion
`astype()` function is used to the NumPy object from one type to another type.
It creates a copy of the array and allows to specify the data type of our choice.
## Example 1
``` python
import numpy as np
x = np.array([1.2, 3.4, 5.6])
y = x.astype(int)
print(y,y.dtype)
# Output:
# [1 3 5] int64
```
## Example 2
``` python
import numpy as np
x = np.array([1, 3, 0])
y = x.astype(bool)
print(y,y.dtype)
# Output:
# [True True False] bool
```

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# List of sections
- [Section title](filename.md)
- [Installing NumPy](installing-numpy.md)
- [Introduction](introduction.md)
- [NumPy Data Types](datatypes.md)
- [Numpy Array Shape and Reshape](reshape-array.md)
- [Basic Mathematics](basic_math.md)
- [Operations on Arrays in NumPy](operations-on-arrays.md)
- [Loading Arrays from Files](loading_arrays_from_files.md)
- [Saving Numpy Arrays into FIles](saving_numpy_arrays_to_files.md)
- [Sorting NumPy Arrays](sorting-array.md)
- [NumPy Array Iteration](array-iteration.md)
- [Concatenation of Arrays](concatenation-of-arrays.md)

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# Installing NumPy
NumPy is the fundamental package for scientific computing in Python.
NumPy is used for working with arrays.
The only prerequisite for installing NumPy is Python itself.
#
**Step 1: Check if PIP is Installed**
Before installing NumPy, it's essential to ensure that PIP (Python Package Installer) is installed on your system. PIP is a package management system used to install and manage Python packages. You can verify if PIP is installed by running a simple command in your terminal or command prompt.
```bash
pip --version
```
If PIP is not currently installed on your system, you can install it by visiting the [pypi.org](https://pypi.org/project/pip/) webpage.
#
**Step 2: Installing PIP**
**get-pip.py**
This is a Python script that uses some bootstrapping logic to install pip.
Open a terminal / command prompt and run:
**Linux**
```bash
python get-pip.py
```
**Windows**
```bash
py get-pip.py
```
**MacOS**
```bash
python get-pip.py
```
#
**Step 3: Installing NumPy**
NumPy can be installed either through conda or pip.
If you use pip, you can install NumPy with:
```bash
pip install numpy
```
If you use conda, you can install NumPy from the defaults or conda-forge channels:
```
# Best practice, use an environment rather than install in the base env
conda create -n my-env
conda activate my-env
```
```
# If you want to install from conda-forge
conda config --env --add channels conda-forge
```
```
# The actual install command
conda install numpy
```
You can find more information about how to install [NumPy](https://numpy.org/install/) on numpy.org.
#
**Step 4: Check if NumPy is Installed**
We can utilize the "pip show" command not only to display the version but also to determine whether NumPy is installed on the system.
```bash
pip show numpy
```

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# Introduction
## What is NumPy?
NumPy is a powerful array-processing library in Python, essential for scientific computing. It provides efficient data structures and tools for working with multidimensional arrays.
## Key Features
1. **Efficient Arrays:** NumPy offers high-performance N-dimensional array objects for swift data manipulation.
2. **Broadcasting:** Advanced broadcasting enables seamless element-wise operations on arrays of varying shapes.
3. **Interoperability:** NumPy seamlessly integrates with C, C++, and Fortran, enhancing performance and versatility.
4. **Mathematical Tools:** Comprehensive support for linear algebra, Fourier transforms, and random number generation.
## Installation
Ensure Python is installed in your system. If not you can install it from here([official Python website](https://www.python.org/)),then install NumPy via:
```bash
pip install numpy
```
## Importing NumPy
To access NumPy functions, import it with the alias `np`.
```python
import numpy as np
```
Using `np` as an alias enhances code readability and is a widely adopted convention.

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# Loading Arrays From Files
Scientific computing and data analysis require the critical feature of being able to load data from different file formats. NumPy has several functionalities for reading data from various file types and converting them into arrays. This part of the content will show how one can load arrays from standard file formats.
## Here are the methods available:
### 1. numpy.loadtxt():
The `loadtxt` function allows you to load data from a text file.You can specify various parameters such as the file name, data type, delimiter,
and more. It reads the file line by line, splits it at the specified delimiter, and converts the values into an array.
- #### Syntax:
```python
numpy.loadtxt(fname, dtype = float, delimiter=None, converters=None, skiprows=0, usecols=None)
```
**fname** : Name of the file <br>
**dtype** : Data type of the resulting array. (By default is float) <br>
**delimiter**: String or character separating columns. (By default is whitespace) <br>
**converters**: Dictionary mapping column number to a function to convert that column's string to a float. <br>
**skiprows**: Number of lines to skip at the beginning of the file. <br>
**usecols**: Which columns to read starting from 0.
- #### Example for `loadtxt`:
**example.txt** <br>
![image](https://github.com/Santhosh-Siddhardha/learn-python/assets/103999924/a0148d29-5fba-45fa-b3f4-058406b3016b)
**Code** <br>
```python
import numpy as np
arr = np.loadtxt("example.txt", dtype=int)
print(arr)
```
**Output**<br>
```python
[1 2 3 4 5]
```
<br>
### 2. numpy.genfromtxt():
The `genfromtxt` function is similar to loadtxt but provides more flexibility. It handles missing values (such as NaNs), allows custom converters
for data parsing, and can handle different data types within the same file. It’s particularly useful for handling complex data formats.
- #### Syntax:
```python
numpy.genfromtxt(fname, dtype=float, delimiter=None, converters=None, missing_values=None, filling_values=None, usecols=None)
```
**fname** : Name of the file <br>
**dtype** : Data type of the resulting array. (By default is float) <br>
**delimiter**: String or character separating columns; default is any whitespace. <br>
**converters**: Dictionary mapping column number to a function to convert that column's string to a float. <br>
**missing_values**: Set of strings corresponding to missing data.<br>
**filling_values**: Value used to fill in missing data. Default is NaN.<br>
**usecols**: Which columns to read starting from 0.
- #### Example for `genfromtxt`:
**example.txt** <br>
![image](https://github.com/Santhosh-Siddhardha/learn-python/assets/103999924/3f9cdd91-4255-4e30-923d-f29c5f237798)
**Code** <br>
```python
import numpy as np
arr = np.genfromtxt("example.txt", dtype='str', usecols=1)
print(arr)
```
**Output**<br>
```python
['Name' 'Kohli' 'Dhoni' 'Rohit']
```
<br>
### 3. numpy.load():
`load` method is used to load arrays saved in NumPy’s native binary format (.npy or .npz). These files preserve the array structure, data types, and metadata.
It’s an efficient way to store and load large arrays.
- #### Syntax:
```python
numpy.load(fname, mmap_mode=None, encoding='ASCII')
```
**fname** : Name of the file <br>
**mmap_mode** : Memory-map the file using the given mode (r, r+, w+, c)(By Default None).Memory-mapping only works with arrays stored in a binary file on disk, not with compressed archives like .npz.<br>
**encoding**:Encoding is used when reading Python2 strings only. (By Default ASCII) <br>
- #### Example for `load`:
**Code** <br>
```python
import numpy as np
arr = np.array(['a','b','c'])
np.savez('example.npz', array=arr) # stores arr in data.npz in NumPy's native binary format
data = np.load('example.npz')
print(data['array'])
```
**Output**<br>
```python
['a' 'b' 'c']
```
<br>
These methods empower users to seamlessly integrate data into their scientific workflows, whether from text files or binary formats.

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# Operations on Arrays
## NumPy Arithmetic Operations
NumPy offers a broad array of operations for arrays, including arithmetic functions.
The arithmetic operations in NumPy are popular for their simplicity and efficiency in handling array calculations.
**Addition**
we can use the `+` operator to perform element-wise addition between two or more NumPy arrays.
**Code**
```python
import numpy as np
array_1 = np.array([9, 10, 11, 12])
array_2 = np.array([1, 3, 5, 7])
result_1 = array_1 + array_2
print("Utilizing the + operator:", result_1)
```
**Output:**
```
Utilizing the + operator: [10 13 16 19]
```
**Subtraction**
we can use the `-` operator to perform element-wise subtraction between two or more NumPy arrays.
**Code**
```python
import numpy as np
array_1 = np.array([9, 10, 11, 12])
array_2 = np.array([1, 3, 5, 7])
result_1 = array_1 - array_2
print("Utilizing the - operator:", result_1)
```
**Output:**
```
Utilizing the - operator: [8 7 6 5]
```
**Multiplication**
we can use the `*` operator to perform element-wise multiplication between two or more NumPy arrays.
**Code**
```python
import numpy as np
array_1 = np.array([9, 10, 11, 12])
array_2 = np.array([1, 3, 5, 7])
result_1 = array_1 * array_2
print("Utilizing the * operator:", result_1)
```
**Output:**
```
Utilizing the * operator: [9 30 55 84]
```
**Division**
we can use the `/` operator to perform element-wise division between two or more NumPy arrays.
**Code**
```python
import numpy as np
array_1 = np.array([9, 10, 11, 12])
array_2 = np.array([1, 3, 5, 7])
result_1 = array_1 / array_2
print("Utilizing the / operator:", result_1)
```
**Output:**
```
Utilizing the / operator: [9. 3.33333333 2.2 1.71428571]
```
**Exponentiation**
we can use the `**` operator to perform element-wise exponentiation between two or more NumPy arrays.
**Code**
```python
import numpy as np
array_1 = np.array([9, 10, 11, 12])
array_2 = np.array([1, 3, 5, 7])
result_1 = array_1 ** array_2
print("Utilizing the ** operator:", result_1)
```
**Output:**
```
Utilizing the ** operator: [9 1000 161051 35831808]
```
**Modulus**
We can use the `%` operator to perform element-wise modulus operations between two or more NumPy arrays.
**Code**
```python
import numpy as np
array_1 = np.array([9, 10, 11, 12])
array_2 = np.array([1, 3, 5, 7])
result_1 = array_1 % array_2
print("Utilizing the % operator:", result_1)
```
**Output:**
```
Utilizing the % operator: [0 1 1 5]
```
<br>
## NumPy Comparision Operations
<br>
NumPy provides various comparison operators that can compare elements across multiple NumPy arrays.
**less than operator**
The `<` operator returns `True` if the value of operand on left is less than the value of operand on right.
**Code**
```python
import numpy as np
array_1 = np.array([12,15,20])
array_2 = np.array([20,15,12])
result_1 = array_1 < array_2
print("array_1 < array_2:",result_1)
```
**Output:**
```
array_1 < array_2 : [True False False]
```
**less than or equal to operator**
The `<=` operator returns `True` if the value of operand on left is lesser than or equal to the value of operand on right.
**Code**
```python
import numpy as np
array_1 = np.array([12,15,20])
array_2 = np.array([20,15,12])
result_1 = array_1 <= array_2
print("array_1 <= array_2:",result_1)
```
**Output:**
```
array_1 <= array_2: [True True False]
```
**greater than operator**
The `>` operator returns `True` if the value of operand on left is greater than the value of operand on right.
**Code**
```python
import numpy as np
array_1 = np.array([12,15,20])
array_2 = np.array([20,15,12])
result_2 = array_1 > array_2
print("array_1 > array_2:",result_2)
```
**Output:**
```
array_1 > array_2 : [False False True]
```
**greater than or equal to operator**
The `>=` operator returns `True` if the value of operand on left is greater than or equal to the value of operand on right.
**Code**
```python
import numpy as np
array_1 = np.array([12,15,20])
array_2 = np.array([20,15,12])
result_2 = array_1 >= array_2
print("array_1 >= array_2:",result_2)
```
**Output:**
```
array_1 >= array_2: [False True True]
```
**equal to operator**
The `==` operator returns `True` if the value of operand on left is same as the value of operand on right.
**Code**
```python
import numpy as np
array_1 = np.array([12,15,20])
array_2 = np.array([20,15,12])
result_3 = array_1 == array_2
print("array_1 == array_2:",result_3)
```
**Output:**
```
array_1 == array_2: [False True False]
```
**not equal to operator**
The `!=` operator returns `True` if the value of operand on left is not equal to the value of operand on right.
**Code**
```python
import numpy as np
array_1 = np.array([12,15,20])
array_2 = np.array([20,15,12])
result_3 = array_1 != array_2
print("array_1 != array_2:",result_3)
```
**Output:**
```
array_1 != array_2: [True False True]
```
<br>
## NumPy Logical Operations
Logical operators perform Boolean algebra. A branch of algebra that deals with `True` and `False` statements.
It illustrates the logical operations of AND, OR, and NOT using np.logical_and(), np.logical_or(), and np.logical_not() functions, respectively.
**Logical AND**
Evaluates the element-wise truth value of `array_1` AND `array_2`
**Code**
```python
import numpy as np
array_1 = np.array([True, False, True])
array_2 = np.array([False, False, True])
print(np.logical_and(array_1, array_2))
```
**Output:**
```
[False False True]
```
**Logical OR**
Evaluates the element-wise truth value of `array_1` OR `array_2`
**Code**
```python
import numpy as np
array_1 = np.array([True, False, True])
array_2 = np.array([False, False, True])
print(np.logical_or(array_1, array_2))
```
**Output:**
```
[True False True]
```
**Logical NOT**
Evaluates the element-wise truth value of `array_1` NOT `array_2`
**Code**
```python
import numpy as np
array_1 = np.array([True, False, True])
array_2 = np.array([False, False, True])
print(np.logical_not(array_1))
```
**Output:**
```
[False True False]
```

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# Numpy Array Shape and Reshape
In NumPy, the primary data structure is the ndarray (N-dimensional array). An array can have one or more dimensions, and it organizes your data efficiently.
Let us create a 2D array
``` python
import numpy as np
numbers = np.array([[1, 2, 3, 4], [5, 6, 7, 8]])
print(numbers)
```
#### Output:
``` python
array([[1, 2, 3, 4],[5, 6, 7, 8]])
```
## Changing Array Shape using `reshape()`
The `reshape()` function allows you to rearrange the data within a NumPy array.
It take 2 arguments, row and columns. The `reshape()` can add or remove the dimensions. For instance, array can convert a 1D array into a 2D array or vice versa.
``` python
arr_1d = np.array([1, 2, 3, 4, 5, 6]) # 1D array
arr_2d = arr_1d.reshape(2, 3) # Reshaping with 2 rows and 3 cols
print(arr_2d)
```
#### Output:
``` python
array([[1, 2, 3],[4, 5, 6]])
```
## Changing Array Shape using `resize()`
The `resize()` function allows you to modify the shape of a NumPy array directly.
It take 2 arguements, row and columns.
``` python
import numpy as np
arr_1d = np.array([1, 2, 3, 4, 5, 6])
arr_1d.resize((2, 3)) # 2 rows and 3 cols
print(arr_1d)
```
#### Output:
``` python
array([[1, 2, 3],[4, 5, 6]])
```

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# Saving NumPy Arrays to Files
- Saving arrays in NumPy is important due to its efficiency in storage and speed, maintaining data integrity and precision, and offering convenience and interoperability.
- NumPy provides several methods to save arrays efficiently, either in binary or text formats.
- The primary methods are `save`, `savez`, and `savetxt`.
### 1. numpy.save():
The `np.save` function saves a single NumPy array to a binary file with a `.npy` extension. This format is efficient and preserves the array's data type and shape.
#### Syntax :
```python
numpy.save(file, arr, allow_pickle=True, fix_imports=True)
```
- **file** : Name of the file.
- **arr** : Array to be saved.
- **allow_pickle** : This is an Optional parameter, Allows saving object arrays using Python pickles.(By Default True)
- **fix_imports** : This is an Optional parameter, Fixes issues for Python 2 to Python 3 compatibility.(By Default True)
#### Example :
```python
import numpy as np
arr = np.array([1,2,3,4,5])
np.save("example.npy",arr) #saves arr into example.npy file in binary format
```
Inorder to load the array from example.npy
```python
arr1 = np.load("example.npy")
print(arr1)
```
**Output** :
```python
[1,2,3,4,5]
```
### 2. numpy.savez():
The `np.savez` function saves multiple NumPy arrays into a single file with a `.npz` extension. Each array is stored with a unique name.
#### Syntax :
```python
numpy.savez(file, *args, **kwds)
```
- **file** : Name of the file.
- **args** : Arrays to be saved.( If arrays are unnamed, they are stored with default names like arr_0, arr_1, etc.)
- **kwds** : Named arrays to be saved.
#### Example :
```python
import numpy as np
arr1 = np.array([1,2,3,4,5])
arr2 = np.array(['a','b','c','d'])
arr3 = np.array([1.2,3.4,5])
np.savez('example.npz', a1=arr1, a2=arr2, a3 = arr3) #saves arrays in npz format
```
Inorder to load the array from example.npz
```python
arr = np.load('example.npz')
print(arr['a1'])
print(arr['a2'])
print(arr['a3'])
```
**Output** :
```python
[1 2 3 4 5]
['a' 'b' 'c' 'd']
[1.2 3.4 5. ]
```
### 3. np.savetxt()
The `np.savetxt` function saves a NumPy array to a text file, such as `.txt` or `.csv`. This format is human-readable and can be used for interoperability with other tools.
#### Syntax :
```python
numpy.savetxt(fname, X, delimiter=' ', newline='\n', header='', footer='', encoding=None)
```
- **fname** : Name of the file.
- **X** : Array to be saved.
- **delimiter** : It is a Optional parameter,This is a character or string that is used to separate columns.(By Default it is " ")
- **newline** : It is a Optional parameter, Character for seperating lines.(By Default it is "\n")
- **header** : It is a Optional parameter, String that is written at beginning of the file.
- **footer** : It is a Optional parameter, String that is written at ending of the file.
- **encoding** : It is a Optional parameter, Encoding of the output file. (By Default it is None)
#### Example :
```python
import numpy as np
arr = np.array([1.1,2.2,3,4.4,5])
np.savetxt("example.txt",arr) #saves the array in example.txt
```
Inorder to load the array from example.txt
```python
arr1 = np.loadtxt("example.txt")
print(arr1)
```
**Output** :
```python
[1.1 2.2 3. 4.4 5. ]
```
By using these methods, you can efficiently save and load NumPy arrays in various formats suitable for your needs.

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# Sorting NumPy Arrays
- Sorting arrays is a common operation in data manipulation and analysis.
- NumPy provides various functions to sort arrays efficiently.
- The primary methods are `numpy.sort`,`numpy.argsort`, and `numpy.lexsort`
### 1. numpy.sort()
The `numpy.sort` function returns a sorted copy of an array.
#### Syntax :
```python
numpy.sort(arr, axis=-1, kind=None, order=None)
```
- **arr** : Array to be sorted.
- **axis** : Axis along which to sort. (By Default is -1)
- **kind** : Sorting algorithm. Options are 'quicksort', 'mergesort', 'heapsort', and 'stable'. (By Default 'quicksort')
- **order** : When arr is an array with fields defined, this argument specifies which fields to compare first.
#### Example :
```python
import numpy as np
arr = np.array([1,7,0,4,6])
sarr = np.sort(arr)
print(sarr)
```
**Output** :
```python
[0 1 4 6 7]
```
### 2. numpy.argsort()
The `numpy.argsort` function returns the indices that would sort an array. Using those indices you can sort the array.
#### Syntax :
```python
numpy.argsort(a, axis=-1, kind=None, order=None)
```
- **arr** : Array to be sorted.
- **axis** : Axis along which to sort. (By Default is -1)
- **kind** : Sorting algorithm. Options are 'quicksort', 'mergesort', 'heapsort', and 'stable'. (By Default 'quicksort')
- **order** : When arr is an array with fields defined, this argument specifies which fields to compare first.
#### Example :
```python
import numpy as np
arr = np.array([2.1,7,4.2,4.3,6])
indices = np.argsort(arr)
print(indices)
s_arr = arr[indices]
print(s_arr)
```
**Output** :
```python
[0 2 3 4 1]
[2.1 4.2 4.3 6. 7. ]
```
### 3. np.lexsort()
The np.lexsort function performs an indirect stable sort using a sequence of keys.
#### Syntax :
```python
numpy.lexsort(keys, axis=-1)
```
- **keys**: Sequence of arrays to sort by. The last key is the primary sort key.
- **axis**: Axis to be indirectly sorted.(By Default -1)
#### Example :
```python
import numpy as np
a = np.array([5,4,3,2])
b = np.array(['a','d','c','b'])
indices = np.lexsort((a,b))
print(indices)
s_arr = a[indices]
print(s_arr)
s_arr = b[indices]
print(s_arr)
```
**Output** :
```python
[0 3 2 1]
[2 3 4 5]
['a' 'b' 'c' 'd']
```
NumPy provides powerful and flexible functions for sorting arrays, including `np.sort`, `np.argsort`, and `np.lexsort`.
These functions support sorting along different axes, using various algorithms, and sorting by multiple keys, making them suitable for a wide range of data manipulation tasks.

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Make,Colour,Odometer,Doors,Price
Toyota,White,150043,4,"$4,000"
Honda,Red,87899,4,"$5,000"
Toyota,Blue,,3,"$7,000"
BMW,Black,11179,5,"$22,000"
Nissan,White,213095,4,"$3,500"
Toyota,Green,,4,"$4,500"
Honda,,,4,"$7,500"
Honda,Blue,,4,
Toyota,White,60000,,
,White,31600,4,"$9,700"
1 Make Colour Odometer Doors Price
2 Toyota White 150043 4 $4,000
3 Honda Red 87899 4 $5,000
4 Toyota Blue 3 $7,000
5 BMW Black 11179 5 $22,000
6 Nissan White 213095 4 $3,500
7 Toyota Green 4 $4,500
8 Honda 4 $7,500
9 Honda Blue 4
10 Toyota White 60000
11 White 31600 4 $9,700

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Make,Colour,Odometer (KM),Doors,Price
Toyota,White,150043,4,"$4,000.00"
Honda,Red,87899,4,"$5,000.00"
Toyota,Blue,32549,3,"$7,000.00"
BMW,Black,11179,5,"$22,000.00"
Nissan,White,213095,4,"$3,500.00"
Toyota,Green,99213,4,"$4,500.00"
Honda,Blue,45698,4,"$7,500.00"
Honda,Blue,54738,4,"$7,000.00"
Toyota,White,60000,4,"$6,250.00"
Nissan,White,31600,4,"$9,700.00"
1 Make Colour Odometer (KM) Doors Price
2 Toyota White 150043 4 $4,000.00
3 Honda Red 87899 4 $5,000.00
4 Toyota Blue 32549 3 $7,000.00
5 BMW Black 11179 5 $22,000.00
6 Nissan White 213095 4 $3,500.00
7 Toyota Green 99213 4 $4,500.00
8 Honda Blue 45698 4 $7,500.00
9 Honda Blue 54738 4 $7,000.00
10 Toyota White 60000 4 $6,250.00
11 Nissan White 31600 4 $9,700.00

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## This folder contains all the Datasets used in the content.

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# Working with Date & Time in Pandas
While working with data, it is common to come across data containing date and time. Pandas is a very handy tool for dealing with such data and provides a wide range of date and time data processing options.
- **Parsing dates and times**: Pandas provides a number of functions for parsing dates and times from strings, including `to_datetime()` and `parse_dates()`. These functions can handle a variety of date and time formats, Unix timestamps, and human-readable formats.
- **Manipulating dates and times**: Pandas provides a number of functions for manipulating dates and times, including `shift()`, `resample()`, and `to_timedelta()`. These functions can be used to add or subtract time periods, change the frequency of a time series, and calculate the difference between two dates or times.
- **Visualizing dates and times**: Pandas provides a number of functions for visualizing dates and times, including `plot()`, `hist()`, and `bar()`. These functions can be used to create line charts, histograms, and bar charts of date and time data.
### `Timestamp` function
The timestamp function in Pandas is used to convert a datetime object to a Unix timestamp. A Unix timestamp is a numerical representation of datetime.
Example for retrieving day, month and year from given date:
```python
import pandas as pd
ts = pd.Timestamp('2024-05-05')
y = ts.year
print('Year is: ', y)
m = ts.month
print('Month is: ', m)
d = ts.day
print('Day is: ', d)
```
Output:
```python
Year is: 2024
Month is: 5
Day is: 5
```
Example for extracting time related data from given date:
```python
import pandas as pd
ts = pd.Timestamp('2024-10-24 12:00:00')
print('Hour is: ', ts.hour)
print('Minute is: ', ts.minute)
print('Weekday is: ', ts.weekday())
print('Quarter is: ', ts.quarter)
```
Output:
```python
Hour is: 12
Minute is: 0
Weekday is: 1
Quarter is: 4
```
### `Timestamp.now()`
Example for getting current date and time:
```python
import pandas as pd
ts = pd.Timestamp.now()
print('Current date and time is: ', ts)
```
Output:
```python
Current date and time is: 2024-05-25 11:48:25.593213
```
### `date_range` function
Example for generating dates' for next five days:
```python
import pandas as pd
ts = pd.date_range(start = pd.Timestamp.now(), periods = 5)
for i in ts:
print(i.date())
```
Output:
```python
2024-05-25
2024-05-26
2024-05-27
2024-05-28
2024-05-29
```
Example for generating dates' for previous five days:
```python
import pandas as pd
ts = pd.date_range(end = pd.Timestamp.now(), periods = 5)
for i in ts:
print(i.date())
```
Output:
```python
2024-05-21
2024-05-22
2024-05-23
2024-05-24
2024-05-25
```
### Built-in vs pandas date & time operations
In `pandas`, you may add a time delta to a full column of dates in a single action, but Python's datetime requires a loop.
Example in Pandas:
```python
import pandas as pd
dates = pd.DataFrame(pd.date_range('2023-01-01', periods=100000, freq='T'))
dates += pd.Timedelta(days=1)
print(dates)
```
Output:
```python
0
0 2023-01-02 00:00:00
1 2023-01-02 00:01:00
2 2023-01-02 00:02:00
3 2023-01-02 00:03:00
4 2023-01-02 00:04:00
... ...
99995 2023-03-12 10:35:00
99996 2023-03-12 10:36:00
99997 2023-03-12 10:37:00
99998 2023-03-12 10:38:00
99999 2023-03-12 10:39:00
```
Example using Built-in datetime library:
```python
from datetime import datetime, timedelta
dates = [datetime(2023, 1, 1) + timedelta(minutes=i) for i in range(100000)]
dates = [date + timedelta(days=1) for date in dates]
```
Why use pandas functions?
- Pandas employs NumPy's datetime64 dtype, which takes up a set amount of bytes (usually 8 bytes per date), to store datetime data more compactly and efficiently.
- Each datetime object in Python takes up extra memory since it contains not only the date and time but also the additional metadata and overhead associated with Python objects.
- Pandas Offers a wide range of convenient functions and methods for date manipulation, extraction, and conversion, such as `pd.to_datetime()`, `date_range()`, `timedelta_range()`, and more. datetime library requires manual implementation for many of these operations, leading to longer and less efficient code.

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## Descriptive Statistics
In the realm of data science, understanding the characteristics of data is fundamental. Descriptive statistics provide the tools and techniques to succinctly summarize and present the key features of a dataset. It serves as the cornerstone for exploring, visualizing, and ultimately gaining insights from data.
Descriptive statistics encompasses a range of methods designed to describe the central tendency, dispersion, and shape of a dataset. Through measures such as mean, median, mode, standard deviation, and variance, descriptive statistics offer a comprehensive snapshot of the data's distribution and variability.
Data scientists utilize descriptive statistics to uncover patterns, identify outliers, and assess the overall structure of data before delving into more advanced analyses. By summarizing large and complex datasets into manageable and interpretable summaries, descriptive statistics facilitate informed decision-making and actionable insights.
```python
import pandas as pd
import numpy as np
df = pd.read_csv("Age-Income-Dataset.csv")
df
```
| | Age | Income |
| --- | ----------- | ------ |
| 0 | Young | 25000 |
| 1 | Middle Age | 54000 |
| 2 | Old | 60000 |
| 3 | Young | 15000 |
| 4 | Young | 45000 |
| 5 | Young | 65000 |
| 6 | Young | 70000 |
| 7 | Young | 30000 |
| 8 | Middle Age | 27000 |
| 9 | Young | 23000 |
| 10 | Young | 48000 |
| 11 | Old | 52000 |
| 12 | Young | 33000 |
| 13 | Old | 80000 |
| 14 | Old | 75000 |
| 15 | Old | 35000 |
| 16 | Middle Age | 29000 |
| 17 | Middle Age | 57000 |
| 18 | Old | 43000 |
| 19 | Middle Age | 56000 |
| 20 | Old | 63000 |
| 21 | Old | 32000 |
| 22 | Old | 45000 |
| 23 | Old | 89000 |
| 24 | Middle Age | 90000 |
| 25 | Middle Age | 93000 |
| 26 | Young | 80000 |
| 27 | Young | 87000 |
| 28 | Young | 38000 |
| 29 | Young | 23000 |
| 30 | Middle Age | 38900 |
| 31 | Middle Age | 53200 |
| 32 | Old | 43800 |
| 33 | Middle Age | 25600 |
| 34 | Middle Age | 65400 |
| 35 | Old | 76800 |
| 36 | Old | 89700 |
| 37 | Old | 41800 |
| 38 | Young | 31900 |
| 39 | Old | 25600 |
| 40 | Middle Age | 45700 |
| 41 | Old | 35600 |
| 42 | Young | 54300 |
| 43 | Middle Age | 65400 |
| 44 | Old | 67800 |
| 45 | Old | 24500 |
| 46 | Middle Age | 34900 |
| 47 | Old | 45300 |
| 48 | Young | 68400 |
| 49 | Middle Age | 51700 |
```python
df.describe()
```
| | Income |
|-------|-------------|
| count | 50.000000 |
| mean | 50966.000000 |
| std | 21096.683268 |
| min | 15000.000000 |
| 25% | 33475.000000 |
| 50% | 46850.000000 |
| 75% | 65400.000000 |
| max | 93000.000000 |
### Mean
The mean, also known as the average, is a measure of central tendency in a dataset. It represents the typical value of a set of numbers. The formula to calculate the mean of a dataset is:
$$ \overline{x} = \frac{\sum\limits_{i=1}^{n} x_i}{n} $$
* $\overline{x}$ (pronounced "x bar") represents the mean value.
* $x_i$ represents the individual value in the dataset (where i goes from 1 to n).
* $\sum$ (sigma) represents the summation symbol, indicating we add up all the values from i=1 to n.
* $n$ represents the total number of values in the dataset.
```python
df['Income'].mean()
```
#### Result
```
50966.0
```
#### Without pandas
```python
def mean_f(df):
for col in df.columns:
if df[col].dtype != 'O':
temp = 0
for i in df[col]:
temp = temp +i
print("Without pandas Library -> ")
print("Average of {} is {}".format(col,(temp/len(df[col]))))
print()
print("With pandas Library -> ")
print(df[col].mean())
mean_f(df)
```
Average of Income:
- Without pandas Library -> 50966.0
- With pandas Library -> 50966.0
### Median
The median is another measure of central tendency in a dataset. Unlike the mean, which is the average value of all data points, the median represents the middle value when the dataset is ordered from smallest to largest. If the dataset has an odd number of observations, the median is the middle value. If the dataset has an even number of observations, the median is the average of the two middle values.
The median represents the "middle" value in a dataset. There are two cases to consider depending on whether the number of observations (n) is odd or even:
**Odd number of observations (n):**
In this case, the median (M) is the value located at the middle position when the data is ordered from least to greatest. We can calculate the position using the following formula:
$$ M = x_{n+1/2} $$
**Even number of observations (n):**
When we have an even number of observations, there isn't a single "middle" value. Instead, the median is the average of the two middle values after ordering the data. Here's the formula to find the median:
$$ M = \frac{x_{n/2} + x_{(n/2)+1}}{2} $$
**Explanation:**
* M represents the median value.
* n represents the total number of observations in the dataset.
* $x$ represents the individual value.
```python
df['Income'].median()
```
#### Result
```
46850.0
```
#### Without pandas
```python
def median_f(df):
for col in df.columns:
if df[col].dtype != 'O':
sorted_data = sorted(df[col])
n = len(df[col])
if n%2 == 0:
x1 =sorted_data[int((n/2))]
x2 =sorted_data[int((n/2))+1]
median=(x1+x2)/2
else:
median = sorted_data[(n+1)/2]
print("Median without library ->")
print("Median of {} is {} ".format(col,median))
print("Median with library ->")
print(df[col].median())
median_f(df)
```
Median of Income:
- Median without library -> 49850.0
- Median with library -> 46850.0
### Mode
The mode is a measure of central tendency that represents the value or values that occur most frequently in a dataset. Unlike the mean and median, which focus on the average or middle value, the mode identifies the most common value(s) in the dataset.
```python
def mode_f(df):
for col in df.columns:
if df[col].dtype == 'O':
print("Column:", col)
arr = df[col].sort_values()
prevcnt = 0
cnt = 0
ans = arr[0]
temp = arr[0]
for i in arr:
if(temp == i) :
cnt += 1
else:
prevcnt = cnt
cnt = 1
temp = i
if(cnt > prevcnt):
ans = i
print("Without pandas Library -> ")
print("Mode of {} is {}".format(col,ans))
print()
print("With pandas Library -> ")
print(df[col].mode())
mode_f(df)
```
#### Result
```
Column: Age
Without pandas Library ->
Mode of Age is Old
With pandas Library ->
0 Old
Name: Age, dtype: object
```
### Standard Deviation
Standard deviation is a measure of the dispersion or spread of a dataset. It quantifies the amount of variation or dispersion of a set of values from the mean. In other words, it indicates how much individual values in a dataset deviate from the mean.
$$s = \sqrt{\frac{\sum(x_i-\overline{x})^{2}}{n-1}}$$
* $s$ represents the standard deviation.
* $\sum$ (sigma) represents the summation symbol, indicating we add up the values for all data points.
* $x_i$ represents the individual value in the dataset.
* $\overline{x}$ (x bar) represents the mean value of the dataset.
* $n$ represents the total number of values in the dataset.
```python
df['Income'].std()
```
#### Result
```
21096.683267707253
```
#### Without pandas
```python
import math
def std_f(df):
for col in df.columns:
if len(df[col]) == 0:
print("Column is empty")
if df[col].dtype != 'O':
sum = 0
mean = df[col].mean()
for i in df[col]:
sum = sum + (i - mean)**2
std = math.sqrt(sum/len(df[col]))
print("Without pandas library ->")
print("Std : " , std)
print("With pandas library: ->")
print("Std : {}".format(np.std(df[col]))) ##ddof = 1
std_f(df)
```
Without pandas library ->
Std : 20884.6509187968 \
With pandas library: ->
Std : 20884.6509187968
### Count
```python
df['Income'].count()
```
#### Result
```
50
```
### Minimum
```python
df['Income'].min()
```
#### Result
```
15000
```
#### Without pandas
```python
def min_f(df):
for col in df.columns:
if df[col].dtype != "O":
sorted_data = sorted(df[col])
min = sorted_data[0]
print("Without pandas Library->",min)
print("With pandas Library->",df[col].min())
min_f(df)
```
Without pandas Library-> 15000 \
With pandas Library-> 15000
### Maximum
```python
df['Income'].max()
```
#### Result
```
93000
```
#### Without pandas
```python
def max_f(df):
for col in df.columns:
if df[col].dtype != "O":
sorted_data = sorted(df[col])
max = sorted_data[len(df[col])-1]
print("Without pandas Library->",max)
print("With pandas Library->",df[col].max())
max_f(df)
```
Without pandas Library-> 93000
With pandas Library-> 93000
### Percentile
```python
df['Income'].quantile(0.25)
```
#### Result
```
33475.0
```
```python
df['Income'].quantile(0.75)
```
#### Result
```
65400.0
```
#### Without pandas
```python
def percentile_f(df,percentile):
for col in df.columns:
if df[col].dtype != 'O':
sorted_data = sorted(df[col])
index = int(percentile*len(df[col]))
percentile_result = sorted_data[index]
print(f"{percentile} Percentile is : ",percentile_result)
percentile_f(df,0.25)
```
0.25 Percentile is : 33000
We have used the method of nearest rank to calculate percentile manually.
Pandas uses linear interpolation of data to calculate percentiles.
## Correlation and Covariance
```python
df = pd.read_csv('Iris.csv')
df.head(5)
```
| | Id | SepalLengthCm | SepalWidthCm | PetalLengthCm | PetalWidthCm | Species |
|---|----|---------------|--------------|---------------|--------------|-------------|
| 0 | 1 | 5.1 | 3.5 | 1.4 | 0.2 | Iris-setosa |
| 1 | 2 | 4.9 | 3.0 | 1.4 | 0.2 | Iris-setosa |
| 2 | 3 | 4.7 | 3.2 | 1.3 | 0.2 | Iris-setosa |
| 3 | 4 | 4.6 | 3.1 | 1.5 | 0.2 | Iris-setosa |
| 4 | 5 | 5.0 | 3.6 | 1.4 | 0.2 | Iris-setosa |
```python
df.drop(['Id','Species'],axis=1,inplace= True)
```
### Covarience
Covariance measures the degree to which two variables change together. If the covariance between two variables is positive, it means that they tend to increase or decrease together. If the covariance is negative, it means that as one variable increases, the other tends to decrease. However, covariance does not provide a standardized measure, making it difficult to interpret the strength of the relationship between variables, especially if the variables are measured in different units.
$$ COV(X,Y) = \frac{\sum\limits_{i=1}^{n} (X_i - \overline{X}) (Y_i - \overline{Y})}{n - 1}$$
**Explanation:**
* $COV(X, Y)$ represents the covariance between variables X and Y.
* $X_i$ and $Y_i$ represent the individual values for variables X and Y in the i-th observation.
* $\overline{X}$ and $\overline{Y}$ represent the mean values for variables X and Y, respectively.
* $n$ represents the total number of observations in the dataset.
```python
df.cov()
```
| | SepalLengthCm | SepalWidthCm | PetalLengthCm | PetalWidthCm |
|-------------------|-------------- |---------------|-----------------|--------------|
| **SepalLengthCm** | 0.685694 | -0.039268 | 1.273682 | 0.516904 |
| **SepalWidthCm** | -0.039268 | 0.188004 | -0.321713 | -0.117981 |
| **PetalLengthCm** | 1.273682 | -0.321713 | 3.113179 | 1.296387 |
| **PetalWidthCm** | 0.516904 | -0.117981 | 1.296387 | 0.582414 |
#### Without pandas
```python
def cov_f(df):
for x in df.columns:
for y in df.columns:
mean_x = df[x].mean()
mean_y = df[y].mean()
sum = 0
n = len(df[x])
for val in range(n):
sum += (df[x].iloc[val] - mean_x)*(df[y].iloc[val] - mean_y)
print("Covariance of {} and {} is : {}".format(x,y, sum/(n-1)))
print()
cov_f(df)
```
#### Result
```
Covariance of SepalLengthCm and SepalLengthCm is : 0.6856935123042504
Covariance of SepalLengthCm and SepalWidthCm is : -0.03926845637583892
Covariance of SepalLengthCm and PetalLengthCm is : 1.2736823266219246
Covariance of SepalLengthCm and PetalWidthCm is : 0.5169038031319911
Covariance of SepalWidthCm and SepalLengthCm is : -0.03926845637583892
Covariance of SepalWidthCm and SepalWidthCm is : 0.1880040268456377
Covariance of SepalWidthCm and PetalLengthCm is : -0.32171275167785235
Covariance of SepalWidthCm and PetalWidthCm is : -0.11798120805369115
Covariance of PetalLengthCm and SepalLengthCm is : 1.2736823266219246
Covariance of PetalLengthCm and SepalWidthCm is : -0.32171275167785235
Covariance of PetalLengthCm and PetalLengthCm is : 3.113179418344519
Covariance of PetalLengthCm and PetalWidthCm is : 1.2963874720357946
Covariance of PetalWidthCm and SepalLengthCm is : 0.5169038031319911
Covariance of PetalWidthCm and SepalWidthCm is : -0.11798120805369115
Covariance of PetalWidthCm and PetalLengthCm is : 1.2963874720357946
Covariance of PetalWidthCm and PetalWidthCm is : 0.5824143176733781
````
### Correlation
Correlation, on the other hand, standardizes the measure of relationship between two variables, making it easier to interpret. It measures both the strength and direction of the linear relationship between two variables. Correlation values range between -1 and 1, where:
$$r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{n(\sum x^2) - (\sum x)^2} \cdot \sqrt{n(\sum y^2) - (\sum y)^2}}$$
* r represents the correlation coefficient.
* n is the number of data points.
```python
df.corr()
```
| | SepalLengthCm | SepalWidthCm | PetalLengthCm | PetalWidthCm |
|-------------------|---------------|--------------|---------------|--------------|
| **SepalLengthCm** | 1.000000 | -0.109369 | 0.871754 | 0.817954 |
| **SepalWidthCm** | -0.109369 | 1.000000 | -0.420516 | -0.356544 |
| **PetalLengthCm** | 0.871754 | -0.420516 | 1.000000 | 0.962757 |
| **PetalWidthCm** | 0.817954 | -0.356544 | 0.962757 | 1.000000 |
#### Without using pandas
```python
import math
def corr_f(df):
for i in df.columns:
for j in df.columns:
n = len(df[i])
sumX = 0
for x in df[i]:
sumX += x
sumY = 0
for y in df[j]:
sumY += y
sumXY = 0
for xy in range(n):
sumXY += (df[i].iloc[xy] * df[j].iloc[xy])
sumX2 = 0
for x in df[i]:
sumX2 += (x**2)
sumY2 = 0
for y in df[j]:
sumY2 += (y**2)
NR = (n * sumXY) - (sumX*sumY)
DR = math.sqrt( ( (n * sumX2) - (sumX**2))*( (n * sumY2) - (sumY ** 2) ) )
print("Correlation of {} and {} :{}".format(i,j,NR/DR))
print()
corr_f(df)
```
#### Result
```
Correlation of SepalLengthCm and SepalLengthCm :1.0
Correlation of SepalLengthCm and SepalWidthCm :-0.10936924995067286
Correlation of SepalLengthCm and PetalLengthCm :0.8717541573048861
Correlation of SepalLengthCm and PetalWidthCm :0.8179536333691775
Correlation of SepalWidthCm and SepalLengthCm :-0.10936924995067286
Correlation of SepalWidthCm and SepalWidthCm :1.0
Correlation of SepalWidthCm and PetalLengthCm :-0.42051609640118826
Correlation of SepalWidthCm and PetalWidthCm :-0.3565440896138223
Correlation of PetalLengthCm and SepalLengthCm :0.8717541573048861
Correlation of PetalLengthCm and SepalWidthCm :-0.42051609640118826
Correlation of PetalLengthCm and PetalLengthCm :1.0
Correlation of PetalLengthCm and PetalWidthCm :0.9627570970509656
Correlation of PetalWidthCm and SepalLengthCm :0.8179536333691775
Correlation of PetalWidthCm and SepalWidthCm :-0.3565440896138223
Correlation of PetalWidthCm and PetalLengthCm :0.9627570970509656
Correlation of PetalWidthCm and PetalWidthCm :1.0
```

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# Pandas DataFrame
The Pandas DataFrame is a two-dimensional, size-mutable, and possibly heterogeneous tabular data format with labelled axes. A data frame is a two-dimensional data structure in which the data can be organised in rows and columns. Pandas DataFrames are comprised of three main components: data, rows, and columns.
In the real world, Pandas DataFrames are formed by importing datasets from existing storage, which can be a Excel file, a SQL database or CSV file. Pandas DataFrames may be constructed from lists, dictionaries, or lists of dictionaries, etc.
Features of Pandas `DataFrame`:
- **Size mutable**: DataFrames are mutable in size, meaning that new rows and columns can be added or removed as needed.
- **Labeled axes**: DataFrames have labeled axes, which makes it easy to keep track of the data.
- **Arithmetic operations**: DataFrames support arithmetic operations on rows and columns.
- **High performance**: DataFrames are highly performant, making them ideal for working with large datasets.
### Installation of libraries
`pip install pandas` <br/>
`pip install xlrd`
- **Note**: The `xlrd` library is used for Excel operations.
Example for reading data from an Excel File:
```python
import pandas as pd
l = pd.read_excel('example.xlsx')
d = pd.DataFrame(l)
print(d)
```
Output:
```python
Name Age
0 John 12
```
Example for Inserting Data into Excel File:
```python
import pandas as pd
l = pd.read_excel('file_name.xlsx')
d = {'Name': ['Bob', 'John'], 'Age': [12, 28]}
d = pd.DataFrame(d)
L = pd.concat([l, d], ignore_index = True)
L.to_excel('file_name.xlsx', index = False)
print(L)
```
Output:
```python
Name Age
0 Bob 12
1 John 28
```
### Usage of Pandas DataFrame:
- Can be used to store and analyze financial data, such as stock prices, trading data, and economic data.
- Can be used to store and analyze sensor data, such as data from temperature sensors, motion sensors, and GPS sensors.
- Can be used to store and analyze log data, such as web server logs, application logs, and system logs

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## Group By Functions
GroupBy is a powerful function in pandas that allows you to split data into distinct groups based on one or more columns and perform operations on each group independently. It's a fundamental technique for data analysis and summarization.
Here's a step-by-step breakdown of how groupby functions work in pandas:
* __Splitting the Data:__ You can group your data based on one or more columns using the .groupby() method. This method takes a column name or a list of column names as input and splits the DataFrame into groups according to the values in those columns.
* __Applying a Function:__ Once the data is grouped, you can apply various functions to each group. Pandas offers a variety of built-in aggregation functions like sum(), mean(), count(), etc., that can be used to summarize the data within each group. You can also use custom functions or lambda functions for more specific operations.
* __Combining the Results:__ After applying the function to each group, the results are combined into a new DataFrame or Series, depending on the input data and the function used. This new data structure summarizes the data by group.
```python
import pandas as pd
import seaborn as sns
import numpy as np
```
```python
iris_data = sns.load_dataset('iris')
```
This code loads the built-in Iris dataset from seaborn and stores it in a pandas DataFrame named iris_data. The Iris dataset contains measurements of flower sepal and petal dimensions for three Iris species (Setosa, Versicolor, Virginica).
```python
iris_data
```
| | sepal_length | sepal_width | petal_length | petal_width | species |
|----|--------------|-------------|--------------|-------------|-----------|
| 0 | 5.1 | 3.5 | 1.4 | 0.2 | setosa |
| 1 | 4.9 | 3.0 | 1.4 | 0.2 | setosa |
| 2 | 4.7 | 3.2 | 1.3 | 0.2 | setosa |
| 3 | 4.6 | 3.1 | 1.5 | 0.2 | setosa |
| 4 | 5.0 | 3.6 | 1.4 | 0.2 | setosa |
| ...| ... | ... | ... | ... | ... |
| 145| 6.7 | 3.0 | 5.2 | 2.3 | virginica |
| 146| 6.3 | 2.5 | 5.0 | 1.9 | virginica |
| 147| 6.5 | 3.0 | 5.2 | 2.0 | virginica |
| 148| 6.2 | 3.4 | 5.4 | 2.3 | virginica |
| 149| 5.9 | 3.0 | 5.1 | 1.8 | virginica |
```python
iris_data.groupby(['species']).count()
```
| species | sepal_length | sepal_width | petal_length | petal_width |
|------------|--------------|-------------|--------------|-------------|
| setosa | 50 | 50 | 50 | 50 |
| versicolor | 50 | 50 | 50 | 50 |
| virginica | 50 | 50 | 50 | 50 |
* We group the data by the 'species' column.
count() is applied to each group, which counts the number of occurrences (rows) in each species category.
* The output (species_counts) is a DataFrame showing the count of each species in the dataset.
```python
iris_data.groupby(["species"])["sepal_length"].mean()
```
species
setosa 5.006\
versicolor 5.936\
virginica 6.588\
Name: sepal_length, dtype: float64
* This groups the data by 'species' and selects the 'sepal_length' column.
mean() calculates the average sepal length for each species group.
* The output (species_means) is a Series containing the mean sepal length for each species.
```python
iris_data.groupby(["species"])["sepal_length"].std()
```
species
setosa 0.352490\
versicolor 0.516171\
virginica 0.635880\
Name: sepal_length, dtype: float64
* Similar to the previous, this groups by 'species' and selects the 'sepal_length' column.
However, it calculates the standard deviation (spread) of sepal length for each species group using std().
* The output (species_std) is a Series containing the standard deviation of sepal length for each species
```python
iris_data.groupby(["species"])["sepal_length"].describe()
```
| species | count | mean | std | min | 25% | 50% | 75% | max |
|------------|-------|-------|----------|------|--------|------|------|------|
| setosa | 50.0 | 5.006 | 0.352490 | 4.3 | 4.800 | 5.0 | 5.2 | 5.8 |
| versicolor | 50.0 | 5.936 | 0.516171 | 4.9 | 5.600 | 5.9 | 6.3 | 7.0 |
| virginica | 50.0 | 6.588 | 0.635880 | 4.9 | 6.225 | 6.5 | 6.9 | 7.9 |
* We have used describe() to generate a more comprehensive summary of sepal length for each species group.
* It provides statistics like count, mean, standard deviation, minimum, maximum, percentiles, etc.
The output (species_descriptions) is a DataFrame containing these descriptive statistics for each species.
```python
iris_data.groupby(["species"])["sepal_length"].quantile(q=0.25)
```
species\
setosa 4.800\
versicolor 5.600\
virginica 6.225\
Name: sepal_length, dtype: float64
```python
iris_data.groupby(["species"])["sepal_length"].quantile(q=0.75)
```
species\
setosa 5.2\
versicolor 6.3\
virginica 6.9\
Name: sepal_length, dtype: float64
* To calculate the quartiles (25th percentile and 75th percentile) of sepal length for each species group.
* quantile(q=0.25) gives the 25th percentile, which represents the value below which 25% of the data points lie.
* quantile(q=0.75) gives the 75th percentile, which represents the value below which 75% of the data points lie.
* The outputs (species_q1 and species_q3) are Series containing the respective quartile values for each species.
## Custom Function For Group By
```python
nc = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width','species']
```
```python
nc
```
['sepal_length', 'sepal_width', 'petal_length', 'petal_width', 'species']
```python
nc = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width']
def species_stats(species_data,species_name):
print("Species Name: {}".format(species_name))
print()
print("Mean:\n",species_data[nc].mean())
print()
print("Median:\n",species_data[nc].median())
print()
print("std:\n",species_data[nc].std())
print()
print("25% percentile:\n",species_data[nc].quantile(0.25))
print()
print("75% percentile:\n",species_data[nc].quantile(0.75))
print()
print("Min:\n",species_data[nc].min())
print()
print("Max:\n",species_data[nc].max())
print()
```
```python
setosa_data = iris_data[iris_data['species'] == 'setosa']
```
```python
versicolor_data = iris_data[iris_data['species'] == 'versicolor']
```
```python
virginica_data = iris_data[iris_data['species'] == 'virginica']
```
```python
species_data_names = ['setosa_data','viginica_data','versicolor_data']
for data in species_data_names:
print("************** Species name {} *****************".format(data))
species_stats(setosa_data,data)
print("------------------------------------")
```
************** Species name setosa_data *****************\
Species Name: setosa_data
Mean:\
sepal_length 5.006\
sepal_width 3.428\
petal_length 1.462\
petal_width 0.246\
dtype: float64
Median:\
sepal_length 5.0\
sepal_width 3.4\
petal_length 1.5\
petal_width 0.2\
dtype: float64
std:\
sepal_length 0.352490\
sepal_width 0.379064\
petal_length 0.173664\
petal_width 0.105386\
dtype: float64
25% percentile:\
sepal_length 4.8\
sepal_width 3.2\
petal_length 1.4\
petal_width 0.2\
Name: 0.25, dtype: float64
75% percentile:\
sepal_length 5.200\
sepal_width 3.675\
petal_length 1.575\
petal_width 0.300\
Name: 0.75, dtype: float64
Min:\
sepal_length 4.3\
sepal_width 2.3\
petal_length 1.0\
petal_width 0.1\
dtype: float64
Max:
sepal_length 5.8\
sepal_width 4.4\
petal_length 1.9\
petal_width 0.6\
dtype: float64
------------------------------------\
************** Species name viginica_data *****************\
Species Name: viginica_data
Mean:\
sepal_length 5.006\
sepal_width 3.428\
petal_length 1.462\
petal_width 0.246\
dtype: float64
Median:\
sepal_length 5.0\
sepal_width 3.4\
petal_length 1.5\
petal_width 0.2\
dtype: float64
std:\
sepal_length 0.352490\
sepal_width 0.379064\
petal_length 0.173664\
petal_width 0.105386\
dtype: float64
25% percentile:\
sepal_length 4.8\
sepal_width 3.2\
petal_length 1.4\
petal_width 0.2\
Name: 0.25, dtype: float64
75% percentile:\
sepal_length 5.200\
sepal_width 3.675\
petal_length 1.575\
petal_width 0.300\
Name: 0.75, dtype: float64
Min:\
sepal_length 4.3\
sepal_width 2.3\
petal_length 1.0\
petal_width 0.1\
dtype: float64
Max:
sepal_length 5.8
sepal_width 4.4
petal_length 1.9
petal_width 0.6
dtype: float64
------------------------------------\
************** Species name versicolor_data *****************\
Species Name: versicolor_data
Mean:\
sepal_length 5.006\
sepal_width 3.428\
petal_length 1.462\
petal_width 0.246\
dtype: float64
Median:\
sepal_length 5.0\
sepal_width 3.4\
petal_length 1.5\
petal_width 0.2\
dtype: float64
std:\
sepal_length 0.352490\
sepal_width 0.379064\
petal_length 0.173664\
petal_width 0.105386\
dtype: float64
25% percentile:\
sepal_length 4.8\
sepal_width 3.2\
petal_length 1.4\
petal_width 0.2\
Name: 0.25, dtype: float64
75% percentile:\
sepal_length 5.200\
sepal_width 3.675\
petal_length 1.575\
petal_width 0.300\
Name: 0.75, dtype: float64
Min:
sepal_length 4.3\
sepal_width 2.3\
petal_length 1.0\
petal_width 0.1\
dtype: float64
Max:\
sepal_length 5.8\
sepal_width 4.4\
petal_length 1.9\
petal_width 0.6\
dtype: float64
------------------------------------

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# Handling Missing Values in Pandas
In real life, many datasets arrive with missing data either because it exists and was not collected or it never existed.
In Pandas missing data is represented by two values:
* `None` : None is simply is `keyword` refer as empty or none.
* `NaN` : Acronym for `Not a Number`.
There are several useful functions for detecting, removing, and replacing null values in Pandas DataFrame:
1. `isnull()`
2. `notnull()`
3. `dropna()`
4. `fillna()`
5. `replace()`
## 2. Checking for missing values using `isnull()` and `notnull()`
Let's import pandas and our fancy car-sales dataset having some missing values.
```python
import pandas as pd
car_sales_missing_df = pd.read_csv("Datasets/car-sales-missing-data.csv")
print(car_sales_missing_df)
```
Make Colour Odometer Doors Price
0 Toyota White 150043.0 4.0 $4,000
1 Honda Red 87899.0 4.0 $5,000
2 Toyota Blue NaN 3.0 $7,000
3 BMW Black 11179.0 5.0 $22,000
4 Nissan White 213095.0 4.0 $3,500
5 Toyota Green NaN 4.0 $4,500
6 Honda NaN NaN 4.0 $7,500
7 Honda Blue NaN 4.0 NaN
8 Toyota White 60000.0 NaN NaN
9 NaN White 31600.0 4.0 $9,700
```python
## Using isnull()
print(car_sales_missing_df.isnull())
```
Make Colour Odometer Doors Price
0 False False False False False
1 False False False False False
2 False False True False False
3 False False False False False
4 False False False False False
5 False False True False False
6 False True True False False
7 False False True False True
8 False False False True True
9 True False False False False
Note here:
* `True` means for `NaN` values
* `False` means for no `Nan` values
If we want to find the number of missing values in each column use `isnull().sum()`.
```python
print(car_sales_missing_df.isnull().sum())
```
Make 1
Colour 1
Odometer 4
Doors 1
Price 2
dtype: int64
You can also check presense of null values in a single column.
```python
print(car_sales_missing_df["Odometer"].isnull())
```
0 False
1 False
2 True
3 False
4 False
5 True
6 True
7 True
8 False
9 False
Name: Odometer, dtype: bool
```python
## using notnull()
print(car_sales_missing_df.notnull())
```
Make Colour Odometer Doors Price
0 True True True True True
1 True True True True True
2 True True False True True
3 True True True True True
4 True True True True True
5 True True False True True
6 True False False True True
7 True True False True False
8 True True True False False
9 False True True True True
Note here:
* `True` means no `NaN` values
* `False` means for `NaN` values
`isnull()` means having null values so it gives boolean `True` for NaN values. And `notnull()` means having no null values so it gives `True` for no NaN value.
## 2. Filling missing values using `fillna()`, `replace()`.
```python
## Filling missing values with a single value using `fillna`
print(car_sales_missing_df.fillna(0))
```
Make Colour Odometer Doors Price
0 Toyota White 150043.0 4.0 $4,000
1 Honda Red 87899.0 4.0 $5,000
2 Toyota Blue 0.0 3.0 $7,000
3 BMW Black 11179.0 5.0 $22,000
4 Nissan White 213095.0 4.0 $3,500
5 Toyota Green 0.0 4.0 $4,500
6 Honda 0 0.0 4.0 $7,500
7 Honda Blue 0.0 4.0 0
8 Toyota White 60000.0 0.0 0
9 0 White 31600.0 4.0 $9,700
```python
## Filling missing values with the previous value using `ffill()`
print(car_sales_missing_df.ffill())
```
Make Colour Odometer Doors Price
0 Toyota White 150043.0 4.0 $4,000
1 Honda Red 87899.0 4.0 $5,000
2 Toyota Blue 87899.0 3.0 $7,000
3 BMW Black 11179.0 5.0 $22,000
4 Nissan White 213095.0 4.0 $3,500
5 Toyota Green 213095.0 4.0 $4,500
6 Honda Green 213095.0 4.0 $7,500
7 Honda Blue 213095.0 4.0 $7,500
8 Toyota White 60000.0 4.0 $7,500
9 Toyota White 31600.0 4.0 $9,700
```python
## illing null value with the next ones using 'bfill()'
print(car_sales_missing_df.bfill())
```
Make Colour Odometer Doors Price
0 Toyota White 150043.0 4.0 $4,000
1 Honda Red 87899.0 4.0 $5,000
2 Toyota Blue 11179.0 3.0 $7,000
3 BMW Black 11179.0 5.0 $22,000
4 Nissan White 213095.0 4.0 $3,500
5 Toyota Green 60000.0 4.0 $4,500
6 Honda Blue 60000.0 4.0 $7,500
7 Honda Blue 60000.0 4.0 $9,700
8 Toyota White 60000.0 4.0 $9,700
9 NaN White 31600.0 4.0 $9,700
#### Filling a null values using `replace()` method
Now we are going to replace the all `NaN` value in the data frame with -125 value
For this we will also need numpy
```python
import numpy as np
print(car_sales_missing_df.replace(to_replace = np.nan, value = -125))
```
Make Colour Odometer Doors Price
0 Toyota White 150043.0 4.0 $4,000
1 Honda Red 87899.0 4.0 $5,000
2 Toyota Blue -125.0 3.0 $7,000
3 BMW Black 11179.0 5.0 $22,000
4 Nissan White 213095.0 4.0 $3,500
5 Toyota Green -125.0 4.0 $4,500
6 Honda -125 -125.0 4.0 $7,500
7 Honda Blue -125.0 4.0 -125
8 Toyota White 60000.0 -125.0 -125
9 -125 White 31600.0 4.0 $9,700
## 3. Dropping missing values using `dropna()`
In order to drop a null values from a dataframe, we used `dropna()` function this function drop Rows/Columns of datasets with Null values in different ways.
#### Dropping rows with at least 1 null value.
```python
print(car_sales_missing_df.dropna(axis = 0)) ##Now we drop rows with at least one Nan value (Null value)
```
Make Colour Odometer Doors Price
0 Toyota White 150043.0 4.0 $4,000
1 Honda Red 87899.0 4.0 $5,000
3 BMW Black 11179.0 5.0 $22,000
4 Nissan White 213095.0 4.0 $3,500
#### Dropping rows if all values in that row are missing.
```python
print(car_sales_missing_df.dropna(how = 'all',axis = 0)) ## If not have leave the row as it is
```
Make Colour Odometer Doors Price
0 Toyota White 150043.0 4.0 $4,000
1 Honda Red 87899.0 4.0 $5,000
2 Toyota Blue NaN 3.0 $7,000
3 BMW Black 11179.0 5.0 $22,000
4 Nissan White 213095.0 4.0 $3,500
5 Toyota Green NaN 4.0 $4,500
6 Honda NaN NaN 4.0 $7,500
7 Honda Blue NaN 4.0 NaN
8 Toyota White 60000.0 NaN NaN
9 NaN White 31600.0 4.0 $9,700
#### Dropping columns with at least 1 null value
```python
print(car_sales_missing_df.dropna(axis = 1))
```
Empty DataFrame
Columns: []
Index: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Now we drop a columns which have at least 1 missing values.
Here the dataset becomes empty after `dropna()` because each column as atleast 1 null value so it remove that columns resulting in an empty dataframe.

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# Importing and Exporting Data in Pandas
## Importing Data from a CSV
We can create `Series` and `DataFrame` in pandas, but often we have to import the data which is in the form of `.csv` (Comma Separated Values), a spreadsheet file or similar tabular data file format.
`pandas` allows for easy importing of this data using functions such as `read_csv()` and `read_excel()` for Microsoft Excel files.
*Note: In case you want to get the information from a **Google Sheet** you can export it as a .csv file.*
The `read_csv()` function can be used to import a CSV file into a pandas DataFrame. The path can be a file system path or a URL where the CSV is available.
```python
import pandas as pd
car_sales_df= pd.read_csv("Datasets/car-sales.csv")
print(car_sales_df)
```
```
Make Colour Odometer (KM) Doors Price
0 Toyota White 150043 4 $4,000.00
1 Honda Red 87899 4 $5,000.00
2 Toyota Blue 32549 3 $7,000.00
3 BMW Black 11179 5 $22,000.00
4 Nissan White 213095 4 $3,500.00
5 Toyota Green 99213 4 $4,500.00
6 Honda Blue 45698 4 $7,500.00
7 Honda Blue 54738 4 $7,000.00
8 Toyota White 60000 4 $6,250.00
9 Nissan White 31600 4 $9,700.00
```
You can find the dataset used above in the `Datasets` folder.
*Note: If you want to import the data from Github you can't directly use its link, you have to first obtain the raw file URL by clicking on the raw button present in the repo*
## Exporting Data to a CSV
`pandas` allows you to export `DataFrame` to `.csv` format using `.to_csv()`, or to a Excel spreadsheet using `.to_excel()`.
```python
car_sales_df.to_csv("exported_car_sales.csv")
```
Running this will save a file called ``exported_car_sales.csv`` to the current folder.

10
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# List of sections
- [Pandas Series Vs NumPy ndarray](pandas_series_vs_numpy_ndarray.md)
- [Pandas Introduction and Dataframes in Pandas](introduction.md)
- [Viewing data in pandas](viewing-data.md)
- [Pandas Series Vs NumPy ndarray](pandas-series-vs-numpy-ndarray.md)
- [Pandas Descriptive Statistics](descriptive-statistics.md)
- [Group By Functions with Pandas](groupby-functions.md)
- [Excel using Pandas DataFrame](excel-with-pandas.md)
- [Working with Date & Time in Pandas](datetime.md)
- [Importing and Exporting Data in Pandas](import-export.md)
- [Handling Missing Values in Pandas](handling-missing-values.md)

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# Introduction_to_Pandas_Library_and_DataFrames
**As you have learnt Python Programming , now it's time for some applications.**
- Machine Learning and Data Science is the emerging field of today's time , to work in this this field your first step should be `Data Science` as Machine Learning is all about data.
- To begin with Data Science your first tool will be `Pandas Library`.
## Introduction of Pandas Library
Pandas is a data analysis and manipulation tool, built on top of the python programming language. Pandas got its name from the term Panel data (‘Pa’ from Panel and ‘da’ from data). Panel data is a data which have rows and columns in it like excel spreadsheets, csv files etc.
**To use Pandas, first we’ve to import it.**
## Why pandas?
* Pandas provides a simple-to-use but very capable set of functions that you can use on your data.
* It is also associate with other machine learning libraries , so it is important to learn it.
* For example - It is highly used to transform tha data which will be use by machine learning model during the training.
```python
# Importing the pandas
import pandas as pd
```
*To import any module in Python use “import 'module name' ” command, I used “pd” as pandas abbreviation because we don’t need to type pandas every time only type “pd” to use pandas.*
```python
# To check available pandas version
print(f"Pandas Version is : {pd.__version__}")
```
Pandas Version is : 2.1.4
## Understanding Pandas data types
Pandas has two main data types : `Series` and `DataFrames`
* `pandas.Series` is a 1-dimensional column of data.
* `pandas.DataFrames` is 2 -dimensional data table having rows and columns.
### 1. Series datatype
**To creeate a series you can use `pd.Series()` and passing a python list inside()**.
Note: S in Series is capital if you use small s it will give you an error.
> Let's create a series
```python
# Creating a series of car companies
cars = pd.Series(["Honda","Audi","Thar","BMW"])
cars
```
0 Honda
1 Audi
2 Thar
3 BMW
dtype: object
The above code creates a Series of cars companies the name of series is “cars” the code “pd.Series([“Honda” , “Audi” , “Thar”, "BMW"])” means Hey! pandas (pd) create a Series of cars named "Honda" , "Audi" , "Thar" and "BMW".
The default index of a series is 0,1,2….(Remember it starts from 0)
To change the index of any series set the “index” parameter accordingly. It takes the list of index values:
```python
cars = pd.Series(["Honda","Audi","Thar","BMW"],index = ["A" , "B" , "C" ,"D"])
cars
```
A Honda
B Audi
C Thar
D BMW
dtype: object
You can see that the index has been changed from numbers to A, B ,C and D.
And the mentioned ‘dtype’ tells us about the type of data we have in the series.
### 2. DataFrames datatype
DataFrame contains rows and columns like a csv file have.
You can also create a DataFrame by using `pd.DataFrame()` and passing it a Python dictionary.
```python
# Let's create
cars_with_colours = pd.DataFrame({"Cars" : ["BMW","Audi","Thar","Honda"],
"Colour" : ["Black","White","Red","Green"]})
print(cars_with_colours)
```
Cars Colour
0 BMW Black
1 Audi White
2 Thar Red
3 Honda Green
The dictionary key is the `column name` and value are the `column data`.
*You can also create a DataFrame with the help of series.*
```python
# Let's create two series
students = pd.Series(["Ram","Mohan","Krishna","Shivam"])
age = pd.Series([19,20,21,24])
students
```
0 Ram
1 Mohan
2 Krishna
3 Shivam
dtype: object
```python
age
```
0 19
1 20
2 21
3 24
dtype: int64
```python
# Now let's create a dataframe with the help of above series
# pass the series name to the dictionary value
record = pd.DataFrame({"Student_Name":students ,
"Age" :age})
print(record)
```
Student_Name Age
0 Ram 19
1 Mohan 20
2 Krishna 21
3 Shivam 24
```python
# To print the list of columns names
record.columns
```
Index(['Student_Name', 'Age'], dtype='object')
### Describe Data
**The good news is that pandas has many built-in functions which allow you to quickly get information about a DataFrame.**
Let's explore the `record` dataframe
#### 1. Use `.dtypes` to find what datatype a column contains
```python
record.dtypes
```
Student_Name object
Age int64
dtype: object
#### 2. use `.describe()` for statistical overview.
```python
print(record.describe()) # It only display the results for numeric data
```
Age
count 4.000000
mean 21.000000
std 2.160247
min 19.000000
25% 19.750000
50% 20.500000
75% 21.750000
max 24.000000
#### 3. Use `.info()` to find information about the dataframe
```python
record.info()
```
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 4 entries, 0 to 3
Data columns (total 2 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 Student_Name 4 non-null object
1 Age 4 non-null int64
dtypes: int64(1), object(1)
memory usage: 196.0+ bytes

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