+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**
+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. diff --git a/contrib/api-development/assets/image.png b/contrib/api-development/assets/image.png new file mode 100644 index 0000000..682e9ed Binary files /dev/null and b/contrib/api-development/assets/image.png differ diff --git a/contrib/api-development/assets/image2.png b/contrib/api-development/assets/image2.png new file mode 100644 index 0000000..298a726 Binary files /dev/null and b/contrib/api-development/assets/image2.png differ diff --git a/contrib/api-development/fast-api.md b/contrib/api-development/fast-api.md new file mode 100644 index 0000000..b67c56e --- /dev/null +++ b/contrib/api-development/fast-api.md @@ -0,0 +1,289 @@ + +# 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 + + +Here is how I tested ``POST`` method in UI: + + +That's all for FastAPI for now.... Happy Learning! diff --git a/contrib/api-development/index.md b/contrib/api-development/index.md index 75c702a..8d4dc59 100644 --- a/contrib/api-development/index.md +++ b/contrib/api-development/index.md @@ -1,3 +1,4 @@ # List of sections - [API Methods](api-methods.md) +- [FastAPI](fast-api.md) diff --git a/contrib/database/index.md b/contrib/database/index.md index 82596a2..bc3d7e6 100644 --- a/contrib/database/index.md +++ b/contrib/database/index.md @@ -1,3 +1,4 @@ # List of sections -- [Section title](filename.md) +- [Introduction to MySQL and Queries](intro_mysql_queries.md) +- [SQLAlchemy and Aggregation Functions](sqlalchemy-aggregation.md) diff --git a/contrib/database/intro_mysql_queries.md b/contrib/database/intro_mysql_queries.md new file mode 100644 index 0000000..b955ead --- /dev/null +++ b/contrib/database/intro_mysql_queries.md @@ -0,0 +1,371 @@ +# 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. + + + + diff --git a/contrib/database/sqlalchemy-aggregation.md b/contrib/database/sqlalchemy-aggregation.md new file mode 100644 index 0000000..9fce96c --- /dev/null +++ b/contrib/database/sqlalchemy-aggregation.md @@ -0,0 +1,123 @@ +# 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 diff --git a/contrib/ds-algorithms/divide-and-conquer-algorithm.md b/contrib/ds-algorithms/divide-and-conquer-algorithm.md new file mode 100644 index 0000000..b5a356e --- /dev/null +++ b/contrib/ds-algorithms/divide-and-conquer-algorithm.md @@ -0,0 +1,54 @@ +# 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 + +--- diff --git a/contrib/ds-algorithms/dynamic-programming.md b/contrib/ds-algorithms/dynamic-programming.md new file mode 100644 index 0000000..43149f8 --- /dev/null +++ b/contrib/ds-algorithms/dynamic-programming.md @@ -0,0 +1,132 @@ +# 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 + + +
+ + +# 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 + + +
+ + +# 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 + + +
+ \ No newline at end of file diff --git a/contrib/ds-algorithms/graph.md b/contrib/ds-algorithms/graph.md new file mode 100644 index 0000000..517c90d --- /dev/null +++ b/contrib/ds-algorithms/graph.md @@ -0,0 +1,219 @@ +# 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. + + + + diff --git a/contrib/ds-algorithms/greedy-algorithms.md b/contrib/ds-algorithms/greedy-algorithms.md new file mode 100644 index 0000000..c79ee99 --- /dev/null +++ b/contrib/ds-algorithms/greedy-algorithms.md @@ -0,0 +1,135 @@ +# 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) + + +
+ + +# 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) + + +
+ + +# 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 + + +
+ diff --git a/contrib/ds-algorithms/hashing-linear-probing.md b/contrib/ds-algorithms/hashing-linear-probing.md new file mode 100644 index 0000000..0d27db4 --- /dev/null +++ b/contrib/ds-algorithms/hashing-linear-probing.md @@ -0,0 +1,139 @@ +# 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. \ No newline at end of file diff --git a/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigOh.png b/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigOh.png new file mode 100644 index 0000000..f748094 Binary files /dev/null and b/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigOh.png differ diff --git a/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigOmega.png b/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigOmega.png new file mode 100644 index 0000000..b4faba1 Binary files /dev/null and b/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigOmega.png differ diff --git a/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigTheta.png b/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigTheta.png new file mode 100644 index 0000000..7434906 Binary files /dev/null and b/contrib/ds-algorithms/images/Time-And-Space-Complexity-BigTheta.png differ diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 5b52155..30881ac 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -1,4 +1,16 @@ # 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) diff --git a/contrib/ds-algorithms/linked-list.md b/contrib/ds-algorithms/linked-list.md new file mode 100644 index 0000000..ddbc6d5 --- /dev/null +++ b/contrib/ds-algorithms/linked-list.md @@ -0,0 +1,222 @@ +# 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. diff --git a/contrib/ds-algorithms/queues.md b/contrib/ds-algorithms/queues.md new file mode 100644 index 0000000..2c5c0f0 --- /dev/null +++ b/contrib/ds-algorithms/queues.md @@ -0,0 +1,130 @@ +# 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.
+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.
+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. + +
+ +# 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). + +
+ +# 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. diff --git a/contrib/ds-algorithms/recursion.md b/contrib/ds-algorithms/recursion.md new file mode 100644 index 0000000..4233242 --- /dev/null +++ b/contrib/ds-algorithms/recursion.md @@ -0,0 +1,127 @@ +# 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 +``` + + + diff --git a/contrib/ds-algorithms/searching-algorithms.md b/contrib/ds-algorithms/searching-algorithms.md new file mode 100644 index 0000000..78b86d1 --- /dev/null +++ b/contrib/ds-algorithms/searching-algorithms.md @@ -0,0 +1,161 @@ +# 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) + + +
+ + +# 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) + + +
+ + +# 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) + + +
+ + diff --git a/contrib/ds-algorithms/sliding-window.md b/contrib/ds-algorithms/sliding-window.md new file mode 100644 index 0000000..72aa191 --- /dev/null +++ b/contrib/ds-algorithms/sliding-window.md @@ -0,0 +1,249 @@ +# 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. diff --git a/contrib/ds-algorithms/sorting-algorithms.md b/contrib/ds-algorithms/sorting-algorithms.md index 6423b4b..2edc265 100644 --- a/contrib/ds-algorithms/sorting-algorithms.md +++ b/contrib/ds-algorithms/sorting-algorithms.md @@ -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. - -
- - -# 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. - -
- -# 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. - -
- -# 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. - -
- +## 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. diff --git a/contrib/ds-algorithms/stacks.md b/contrib/ds-algorithms/stacks.md new file mode 100644 index 0000000..428a193 --- /dev/null +++ b/contrib/ds-algorithms/stacks.md @@ -0,0 +1,116 @@ +# 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. diff --git a/contrib/ds-algorithms/time-space-complexity.md b/contrib/ds-algorithms/time-space-complexity.md new file mode 100644 index 0000000..eeadd64 --- /dev/null +++ b/contrib/ds-algorithms/time-space-complexity.md @@ -0,0 +1,243 @@ +# 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: + + + +### 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: + + + +### 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: + + + +## 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. diff --git a/contrib/ds-algorithms/trie.md b/contrib/ds-algorithms/trie.md new file mode 100644 index 0000000..0ccfbaa --- /dev/null +++ b/contrib/ds-algorithms/trie.md @@ -0,0 +1,152 @@ +# 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)) +``` diff --git a/contrib/machine-learning/ann.md b/contrib/machine-learning/ann.md new file mode 100644 index 0000000..c577c94 --- /dev/null +++ b/contrib/machine-learning/ann.md @@ -0,0 +1,153 @@ +# Understanding the Neural Network + +## Table of Contents +
+
+
+
+## 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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diff --git a/contrib/machine-learning/binomial-distribution.md b/contrib/machine-learning/binomial-distribution.md
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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()
diff --git a/contrib/machine-learning/clustering.md b/contrib/machine-learning/clustering.md
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--- /dev/null
+++ b/contrib/machine-learning/clustering.md
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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.
diff --git a/contrib/machine-learning/confusion-matrix.md b/contrib/machine-learning/confusion-matrix.md
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--- /dev/null
+++ b/contrib/machine-learning/confusion-matrix.md
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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
+```
diff --git a/contrib/machine-learning/cost-functions.md b/contrib/machine-learning/cost-functions.md
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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.
diff --git a/contrib/machine-learning/decision-tree.md b/contrib/machine-learning/decision-tree.md
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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(pi * log2(pi))__
+
+where `p``i` 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.
diff --git a/contrib/machine-learning/ensemble-learning.md b/contrib/machine-learning/ensemble-learning.md
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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.
diff --git a/contrib/machine-learning/grid-search.md b/contrib/machine-learning/grid-search.md
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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.
diff --git a/contrib/machine-learning/hierarchical-clustering.md b/contrib/machine-learning/hierarchical-clustering.md
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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.
diff --git a/contrib/machine-learning/index.md b/contrib/machine-learning/index.md
index 82596a2..0bf39f9 100644
--- a/contrib/machine-learning/index.md
+++ b/contrib/machine-learning/index.md
@@ -1,3 +1,22 @@
# 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)
diff --git a/contrib/machine-learning/intro-to-cnn.md b/contrib/machine-learning/intro-to-cnn.md
new file mode 100644
index 0000000..0221ca1
--- /dev/null
+++ b/contrib/machine-learning/intro-to-cnn.md
@@ -0,0 +1,225 @@
+# 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).
+
+
+- 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.
+
+
+- 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').
+
+
+- `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.
+
+
+- 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.
+
+
+- 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,
+ nin = 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,
+ nc = 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.
+Click to expand
+ +- [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) + +
+ 
+
+
+- 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.
+
+
+### 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.
+
+
+- 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!
diff --git a/contrib/machine-learning/knn.md b/contrib/machine-learning/knn.md
new file mode 100644
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+++ b/contrib/machine-learning/knn.md
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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.
diff --git a/contrib/machine-learning/logistic-regression.md b/contrib/machine-learning/logistic-regression.md
new file mode 100644
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+++ b/contrib/machine-learning/logistic-regression.md
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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:
+- β₀ is the intercept.
+- βi are the coefficients for the predictor variables Xi.
+
+
+## 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.
diff --git a/contrib/machine-learning/pytorch.md b/contrib/machine-learning/pytorch.md
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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!
diff --git a/contrib/machine-learning/random-forest.md b/contrib/machine-learning/random-forest.md
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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
diff --git a/contrib/machine-learning/regression.md b/contrib/machine-learning/regression.md
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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
+
+
diff --git a/contrib/machine-learning/sklearn-introduction.md b/contrib/machine-learning/sklearn-introduction.md
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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.
diff --git a/contrib/machine-learning/support-vector-machine.md b/contrib/machine-learning/support-vector-machine.md
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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
+```
+
diff --git a/contrib/machine-learning/tensorflow.md b/contrib/machine-learning/tensorflow.md
new file mode 100644
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--- /dev/null
+++ b/contrib/machine-learning/tensorflow.md
@@ -0,0 +1,64 @@
+# 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.
diff --git a/contrib/machine-learning/transformers.md b/contrib/machine-learning/transformers.md
new file mode 100644
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--- /dev/null
+++ b/contrib/machine-learning/transformers.md
@@ -0,0 +1,443 @@
+# 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
+
+
+
+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:
+
+$$PE(pos,2i) = \sin({\dfrac{pos}{10000^{\dfrac{2i}{d_{model}}}}})$$
+
+$$PE(pos,2i) = \cos({\dfrac{pos}{10000^{\dfrac{2i}{d_{model}}}}})$$
+
+## 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:
+```
+
++ 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:
+ 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).
+ 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:
+ 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. + +``` + + + diff --git a/contrib/mini-projects/tic-tac-toe.md b/contrib/mini-projects/tic-tac-toe.md new file mode 100644 index 0000000..8589e64 --- /dev/null +++ b/contrib/mini-projects/tic-tac-toe.md @@ -0,0 +1,91 @@ +# 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() +``` + diff --git a/contrib/numpy/array-iteration.md b/contrib/numpy/array-iteration.md new file mode 100644 index 0000000..b0a499f --- /dev/null +++ b/contrib/numpy/array-iteration.md @@ -0,0 +1,120 @@ +# 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. diff --git a/contrib/numpy/basic_math.md b/contrib/numpy/basic_math.md new file mode 100644 index 0000000..d19f2f8 --- /dev/null +++ b/contrib/numpy/basic_math.md @@ -0,0 +1,371 @@ +# Basic Mathematics +## What is a Matrix? +A matrix is a collection of numbers ordered in rows and columns. Here is one. + + +
| 1 | +2 | +3 | +
| 4 | +5 | +6 | +
| 7 | +8 | +9 | +
+ **delimiter**: String or character separating columns. (By default is whitespace)
+ **converters**: Dictionary mapping column number to a function to convert that column's string to a float.
+ **skiprows**: Number of lines to skip at the beginning of the file.
+ **usecols**: Which columns to read starting from 0. + +- #### Example for `loadtxt`: + + **example.txt**
+ +  + + **Code**
+ ```python + import numpy as np + + arr = np.loadtxt("example.txt", dtype=int) + print(arr) + ``` + + **Output**
+ ```python + [1 2 3 4 5] + ``` + +
+ +### 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
+ **dtype** : Data type of the resulting array. (By default is float)
+ **delimiter**: String or character separating columns; default is any whitespace.
+ **converters**: Dictionary mapping column number to a function to convert that column's string to a float.
+ **missing_values**: Set of strings corresponding to missing data.
+ **filling_values**: Value used to fill in missing data. Default is NaN.
+ **usecols**: Which columns to read starting from 0. + +- #### Example for `genfromtxt`: + + **example.txt**
+ +  + + + **Code**
+ ```python + import numpy as np + + arr = np.genfromtxt("example.txt", dtype='str', usecols=1) + print(arr) + ``` + + **Output**
+ ```python + ['Name' 'Kohli' 'Dhoni' 'Rohit'] + ``` + +
+ + +### 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
+ **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.
+ **encoding**:Encoding is used when reading Python2 strings only. (By Default ASCII)
+ +- #### Example for `load`: + + **Code**
+ ```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**
+ ```python + ['a' 'b' 'c'] + ``` +
+ +These methods empower users to seamlessly integrate data into their scientific workflows, whether from text files or binary formats. diff --git a/contrib/numpy/operations-on-arrays.md b/contrib/numpy/operations-on-arrays.md new file mode 100644 index 0000000..e3966d2 --- /dev/null +++ b/contrib/numpy/operations-on-arrays.md @@ -0,0 +1,281 @@ +# 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] +``` + +
+ +## NumPy Comparision Operations + +
+ +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] +``` + +
+ +## 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] +``` diff --git a/contrib/numpy/reshape-array.md b/contrib/numpy/reshape-array.md new file mode 100644 index 0000000..91da366 --- /dev/null +++ b/contrib/numpy/reshape-array.md @@ -0,0 +1,57 @@ +# 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]]) +``` diff --git a/contrib/numpy/saving_numpy_arrays_to_files.md b/contrib/numpy/saving_numpy_arrays_to_files.md new file mode 100644 index 0000000..c8935b8 --- /dev/null +++ b/contrib/numpy/saving_numpy_arrays_to_files.md @@ -0,0 +1,126 @@ +# 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. + + diff --git a/contrib/numpy/sorting-array.md b/contrib/numpy/sorting-array.md new file mode 100644 index 0000000..65e9c25 --- /dev/null +++ b/contrib/numpy/sorting-array.md @@ -0,0 +1,104 @@ +# 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. diff --git a/contrib/pandas/Datasets/car-sales-missing-data.csv b/contrib/pandas/Datasets/car-sales-missing-data.csv new file mode 100644 index 0000000..21a3157 --- /dev/null +++ b/contrib/pandas/Datasets/car-sales-missing-data.csv @@ -0,0 +1,11 @@ +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" diff --git a/contrib/pandas/Datasets/car-sales.csv b/contrib/pandas/Datasets/car-sales.csv new file mode 100644 index 0000000..81e534a --- /dev/null +++ b/contrib/pandas/Datasets/car-sales.csv @@ -0,0 +1,11 @@ +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" diff --git a/contrib/pandas/Datasets/readme.md b/contrib/pandas/Datasets/readme.md new file mode 100644 index 0000000..ea2255c --- /dev/null +++ b/contrib/pandas/Datasets/readme.md @@ -0,0 +1 @@ +## This folder contains all the Datasets used in the content. diff --git a/contrib/pandas/datetime.md b/contrib/pandas/datetime.md new file mode 100644 index 0000000..008d6fc --- /dev/null +++ b/contrib/pandas/datetime.md @@ -0,0 +1,158 @@ +# 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. diff --git a/contrib/pandas/descriptive-statistics.md b/contrib/pandas/descriptive-statistics.md new file mode 100644 index 0000000..abdb33b --- /dev/null +++ b/contrib/pandas/descriptive-statistics.md @@ -0,0 +1,573 @@ +## 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 +``` diff --git a/contrib/pandas/excel-with-pandas.md b/contrib/pandas/excel-with-pandas.md new file mode 100644 index 0000000..d325e46 --- /dev/null +++ b/contrib/pandas/excel-with-pandas.md @@ -0,0 +1,63 @@ +# 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`
+`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 diff --git a/contrib/pandas/groupby-functions.md b/contrib/pandas/groupby-functions.md new file mode 100644 index 0000000..00bad79 --- /dev/null +++ b/contrib/pandas/groupby-functions.md @@ -0,0 +1,391 @@ +## 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 + + ------------------------------------ + diff --git a/contrib/pandas/handling-missing-values.md b/contrib/pandas/handling-missing-values.md new file mode 100644 index 0000000..da6c377 --- /dev/null +++ b/contrib/pandas/handling-missing-values.md @@ -0,0 +1,264 @@ +# 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. diff --git a/contrib/pandas/import-export.md b/contrib/pandas/import-export.md new file mode 100644 index 0000000..23d1ad8 --- /dev/null +++ b/contrib/pandas/import-export.md @@ -0,0 +1,46 @@ +# 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. diff --git a/contrib/pandas/index.md b/contrib/pandas/index.md index 5c0f2b4..e5a8353 100644 --- a/contrib/pandas/index.md +++ b/contrib/pandas/index.md @@ -1,3 +1,11 @@ # 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) diff --git a/contrib/pandas/introduction.md b/contrib/pandas/introduction.md new file mode 100644 index 0000000..3552437 --- /dev/null +++ b/contrib/pandas/introduction.md @@ -0,0 +1,244 @@ +# 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() +``` + +
{{ heading }}
+{{ content }}
+ + + ``` + +- **Render the Template**: + ```python + from flask import Flask, render_template + + app = Flask(__name__) + + @app.route('/') + def home(): + return render_template('index.html', title='Home', heading='Welcome to Flask', content='This is a Flask application.') + ``` + +### Serving Static Files +Static files like CSS, JavaScript, and images are placed in the `static` directory. + +- **Create Static Files**: + - `app/static/style.css`: + ```css + body { + font-family: Arial, sans-serif; + } + ``` + +- **Include Static Files in Templates**: + ```html + + + +{{ heading }}
+{{ content }}
+ + + ``` + +## 7. Working with Forms +### Handling Form Data +Forms are used to collect user input. Flask provides utilities to handle form submissions. + +- **Create a Form**: + - `app/templates/form.html`: + ```html + + + +404 - Page Not Found
+The page you are looking for does not exist.
+ + + + + + - **app/templates/500.html:** + + + + +500 - Internal Server Error
+Something went wrong on our end. Please try again later.
+ + + + +## 10. Testing Your Application +Flask applications can be tested using Python's built-in `unittest` framework. + +- **Write a Test Case**: + - `tests/test_app.py`: + ```python + import unittest + from app import create_app + + class BasicTestCase(unittest.TestCase): + def setUp(self): + self.app = create_app() + self.app.config['TESTING'] = True + self.client = self.app.test_client() + + def test_home(self): + response = self.client.get('/') + self.assertEqual(response.status_code, 200) + self.assertIn(b'Hello, World!', response.data) + + if __name__ == '__main__': + unittest.main() + ``` + + - **Run the Tests**: + ``` + python -m unittest discover -s tests + ``` + +## 11. Deploying Your Flask Application +### Using Gunicorn +Gunicorn is a Python WSGI HTTP Server for UNIX. It’s a pre-fork worker model, meaning that it forks multiple worker processes to handle requests. + +- **Install Gunicorn**: + ``` + pip install gunicorn + ``` + +- **Run Your Application with Gunicorn**: + ``` + gunicorn -w 4 run:app + ``` + +### Deploying to Render +Render is a cloud platform for deploying web applications. + +- **Create a `requirements.txt` File**: + ``` + Flask + gunicorn + flask_sqlalchemy + ``` + +- **Create a `render.yaml` File**: + ```yaml + services: + - type: web + name: my-flask-app + env: python + plan: free + buildCommand: pip install -r requirements.txt + startCommand: gunicorn -w 4 run:app + ``` + +- **Deploy Your Application**: + 1. Push your code to a Git repository. + 2. Sign in to Render and create a new Web Service. + 3. Connect your repository and select the branch to deploy. + 4. Render will automatically use the `render.yaml` file to configure and deploy your application. + +## 12. Conclusion +Flask is a powerful and flexible framework for building web applications in Python. It offers simplicity and ease of use, making it a great choice for both beginners and experienced developers. This guide covered the basics of setting up a Flask application, routing, templating, working with forms, integrating databases, error handling, testing, and deployment. + +## 13. Further Reading and Resources +- Flask Documentation: https://flask.palletsprojects.com/en/latest/ +- Jinja2 Documentation: https://jinja.palletsprojects.com/en/latest/ +- SQLAlchemy Documentation: https://docs.sqlalchemy.org/en/latest/ +- Render Documentation: https://render.com/docs diff --git a/contrib/web-scrapping/index.md b/contrib/web-scrapping/index.md index 82596a2..276014e 100644 --- a/contrib/web-scrapping/index.md +++ b/contrib/web-scrapping/index.md @@ -1,3 +1,4 @@ # List of sections - [Section title](filename.md) +- [Introduction to Flask](flask.md)