From 14f425286e720804c7b1e8c606aa50c5cdee279c Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Sun, 2 Jun 2024 15:58:06 +0530 Subject: [PATCH 01/61] Create Dijkstra's_algorithm.md --- contrib/ds-algorithms/Dijkstra's_algorithm.md | 88 +++++++++++++++++++ 1 file changed, 88 insertions(+) create mode 100644 contrib/ds-algorithms/Dijkstra's_algorithm.md diff --git a/contrib/ds-algorithms/Dijkstra's_algorithm.md b/contrib/ds-algorithms/Dijkstra's_algorithm.md new file mode 100644 index 0000000..18845f6 --- /dev/null +++ b/contrib/ds-algorithms/Dijkstra's_algorithm.md @@ -0,0 +1,88 @@ + +# Dijkstra's Algorithm +Dijkstra's algorithm is a graph algorithm that gives the shortest distance of each node from the given node in a weighted, undirected graph. It operates by continually choosing the closest unvisited node and determining the distance to all its unvisited neighboring nodes. This algorithm is similar to BFS in graphs, with the difference being it gives priority to nodes with shorter distances by using a priority queue(min-heap) instead of a FIFO queue. The data structures required would be a distance list (to store the minimum distance of each node), a priority queue or a set, and we assume the adjacency list will be provided. + +## Working +- We will store the minimum distance of each node in the distance list, which has a length equal to the number of nodes in the graph. Thus, the minimum distance of the 2nd node will be stored in the 2nd index of the distance list. We initialize the list with the maximum number possible, say infinity. + +- We now start the traversal from the starting node given and mark its distance as 0. We push this node to the priority queue along with its minimum distance, which is 0, so the structure pushed will be (0, node), a tuple. + +- Now, with the help of the adjacency list, we will add the neighboring nodes to the priority queue with the distance equal to (edge weight + current node distance), and this should be less than the distance list value. We will also update the distance list in the process. + +- When all the nodes are added, we will select the node with the shortest distance and repeat the process. + +## Dry Run +We will now do a manual simulation using an example graph given. First, (0, a) is pushed to the priority queue (pq). +![gssoc photo 1](https://github.com/animator/learn-python/assets/154299201/713cf7dd-fa8a-4f81-829f-00ac33eb12f4) +- **Step1:** The lowest element is popped from the pq, which is (0, a), and all its neighboring nodes are added to the pq while simultaneously checking the distance list. Thus (3, b), (7, c), (1, d) are added to the pq. +![gssoc photo2](https://github.com/animator/learn-python/assets/154299201/9456b701-7877-44dc-854b-da416c5e2e9b) +- **Step2:** Again, the lowest element is popped from the pq, which is (1, d). It has two neighboring nodes, a and e, from which + (0 + 1, a) will not be added to the pq as dist[a] = 0 is less than 1. +![gssoc photo3](https://github.com/animator/learn-python/assets/154299201/83990a40-f3fc-4173-9e21-10eb9e2003cb) + +- **Step3:** Now, the lowest element is popped from the pq, which is (3, b). It has two neighboring nodes, a and c, from which + (0 + 1, a) will not be added to the pq. But the new distance to reach c is 5 (3 + 2), which is less than dist[c] = 7. So (5, c) is added to the pq. +![gssoc photo4](https://github.com/animator/learn-python/assets/154299201/b47eb063-8ce7-4e68-85a5-da98f5ac9a3d) + +- **Step4:** The next smallest element is (5, c). It has neighbors a and e. The new distance to reach a will be 5 + 7 = 12, which is more than dist[a], so it will not be considered. Similarly, the new distance for e is 5 + 3 = 8, which again will not be considered. So, no new tuple has been added to the pq. +![gssoc photo5](https://github.com/animator/learn-python/assets/154299201/c0ef3c2a-1938-4c33-9e07-0929e8e5e631) + +- **Step5:** Similarly, both the elements of the pq will be popped one by one without any new addition. +![gssoc photo6](https://github.com/animator/learn-python/assets/154299201/828739c6-413b-41f6-a09f-b702802b20e1) +![gssoc photo7](https://github.com/animator/learn-python/assets/154299201/488d4c7b-d7bf-4887-a9c5-04accc6c6c89) + +- The distance list we get at the end will be our answer. +- `Output` `dist=[1, 3, 7, 1, 6]` + +## Python Code +```python +import heapq + +def dijkstra(graph, start): + # Create a priority queue + pq = [] + heapq.heappush(pq, (0, start)) + + # Create a dictionary to store distances to each node + dist = {node: float('inf') for node in graph} + dist[start] = 0 + + while pq: + # Get the node with the smallest distance + current_distance, current_node = heapq.heappop(pq) + + # If the current distance is greater than the recorded distance, skip it + if current_distance > dist[current_node]: + continue + + # Update the distances to the neighboring nodes + for neighbor, weight in graph[current_node].items(): + distance = current_distance + weight + # Only consider this new path if it's better + if distance < dist[neighbor]: + dist[neighbor] = distance + heapq.heappush(pq, (distance, neighbor)) + + return dist + +# Example usage: +graph = { + 'A': {'B': 1, 'C': 4}, + 'B': {'A': 1, 'C': 2, 'D': 5}, + 'C': {'A': 4, 'B': 2, 'D': 1}, + 'D': {'B': 5, 'C': 1} +} + +start_node = 'A' +dist = dijkstra(graph, start_node) +print(dist) +``` + +## Complexity Analysis + +- **Time Complexity**: \(O((V + E) log V)\) +- **Space Complexity**: \(O(V + E)\) + + + + From cc85ae3802f2f015a353a81b48f33f1ff5cb6a10 Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Sun, 2 Jun 2024 22:54:56 +0530 Subject: [PATCH 02/61] Update index.md --- contrib/ds-algorithms/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 1d7293b..2263620 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -13,3 +13,4 @@ - [Stacks in Python](stacks.md) - [Sliding Window Technique](sliding-window.md) - [Trie](trie.md) +- [Dijkstra's Algorithm](Dijkstra's_algorithm.md) From ff13658e4ab3cf70a592b27a8a9562847f12f624 Mon Sep 17 00:00:00 2001 From: SAM <8dmasters@gmail.com> Date: Tue, 4 Jun 2024 01:07:24 +0530 Subject: [PATCH 03/61] Create match_case_statement.md --- contrib/advanced-python/match_case_statement.md | 0 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 contrib/advanced-python/match_case_statement.md diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match_case_statement.md new file mode 100644 index 0000000..e69de29 From 3ac978f6a97fa53d1a111d3fb0132984a13ce6de Mon Sep 17 00:00:00 2001 From: SAM <8dmasters@gmail.com> Date: Tue, 4 Jun 2024 01:07:36 +0530 Subject: [PATCH 04/61] Update index.md Added match_case_statement index --- contrib/advanced-python/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/advanced-python/index.md b/contrib/advanced-python/index.md index b31544e..c262aaa 100644 --- a/contrib/advanced-python/index.md +++ b/contrib/advanced-python/index.md @@ -10,3 +10,4 @@ - [Protocols](protocols.md) - [Exception Handling in Python](exception-handling.md) - [Generators](generators.md) +- [Match Case Statement](match_case_statement.md) \ No newline at end of file From a2f8b49b1e77b1d4d9fcc376509e401955b468b7 Mon Sep 17 00:00:00 2001 From: SAM <60264918+SAM-DEV007@users.noreply.github.com> Date: Tue, 4 Jun 2024 15:47:49 +0530 Subject: [PATCH 05/61] Update match_case_statement.md Added introduction and syntax --- .../advanced-python/match_case_statement.md | 22 +++++++++++++++++++ 1 file changed, 22 insertions(+) diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match_case_statement.md index e69de29..d4ad861 100644 --- a/contrib/advanced-python/match_case_statement.md +++ b/contrib/advanced-python/match_case_statement.md @@ -0,0 +1,22 @@ +# Match Case Statements +## Introduction +Match and case statements are introduced in Python 3.10 for structural pattern matching of patterns with associated actions. It offers more readible and +cleaniness to the code as opposed to the traditional `if-else` statements. They also have destructuring, pattern matching and checks for specific properties in +addition to the traditional `switch-case` statements in other languages, which makes them more versatile. + +## Syntax +``` +match : + case : + + case : + + case _: + +``` +A match statement takes a statement which compares it to the various cases and their patterns. If any of the pattern is matched successively, the task is performed accordingly. If an exact match is not confirmed, the last case, a wildcard `_`, if provided, will be used as the matching case. + +## Pattern Matching +As discussed earlier, match case statements use pattern matching where the patterns consist of sequences, mappings, primitive data types as well as class instances. The structural pattern matching uses declarative approach and it nexplicitly states the conditions for the patterns to match with the data. + +### Patterns with a Literal From 55717a47dee55e6d62aa161e52840b7075dc0689 Mon Sep 17 00:00:00 2001 From: SAM <60264918+SAM-DEV007@users.noreply.github.com> Date: Tue, 4 Jun 2024 16:48:03 +0530 Subject: [PATCH 06/61] Update match_case_statement.md Added patterns with a literal section --- .../advanced-python/match_case_statement.md | 57 +++++++++++++++++++ 1 file changed, 57 insertions(+) diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match_case_statement.md index d4ad861..691d23b 100644 --- a/contrib/advanced-python/match_case_statement.md +++ b/contrib/advanced-python/match_case_statement.md @@ -20,3 +20,60 @@ A match statement takes a statement which compares it to the various cases and t As discussed earlier, match case statements use pattern matching where the patterns consist of sequences, mappings, primitive data types as well as class instances. The structural pattern matching uses declarative approach and it nexplicitly states the conditions for the patterns to match with the data. ### Patterns with a Literal +#### Generic Case +`sample text` is passed as a literal in the `match` block. There are two cases and a wildcard case mentioned. +```python +match 'sample text': + case 'sample text': + print('sample text') + case 'sample': + print('sample') + case _: + print('None found') +``` +The `sample text` case is satisfied as it matches with the literal `sample text` described in the `match` block. + +O/P: +``` +sample text +``` + +#### Using OR +Taking another example, `|` can be used as OR to include multiple patterns in a single case statement where the multiple patterns all lead to a similar task. + +The below code snippets can be used interchangebly and generate the similar output. The latter is more consive and readible. +```python +match 'e': + case 'a': + print('vowel') + case 'e': + print('vowel') + case 'i': + print('vowel') + case 'o': + print('vowel') + case 'u': + print('vowel') + case _: + print('consonant') +``` +```python +match 'e': + case 'a' | 'e' | 'i' | 'o' | 'u': + print('vowel') + case _: + print('consonant') +``` +O/P: +``` +vowel +``` + +#### Without wildcard +When in a `match` block, there is no wildcard case present there are be two cases of match being present or not. If the match doesn't exist, the behaviour is a no-op. +```python +match 'c': + case 'a' | 'e' | 'i' | 'o' | 'u': + print('vowel') +``` +The output will be blank as a no-op occurs. From 5f57b24ac03006216a366219e09ea0566e231ab8 Mon Sep 17 00:00:00 2001 From: SAM <60264918+SAM-DEV007@users.noreply.github.com> Date: Tue, 4 Jun 2024 17:44:13 +0530 Subject: [PATCH 07/61] Update match_case_statement.md Added two more sections. Patterns with a literal and a variable, and patterns with classes. --- .../advanced-python/match_case_statement.md | 83 +++++++++++++++++++ 1 file changed, 83 insertions(+) diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match_case_statement.md index 691d23b..57f6bfb 100644 --- a/contrib/advanced-python/match_case_statement.md +++ b/contrib/advanced-python/match_case_statement.md @@ -77,3 +77,86 @@ match 'c': print('vowel') ``` The output will be blank as a no-op occurs. + +### Patterns with a Literal and a Variable +Pattern matching can be done by unpacking the assignments and also bind variables with it. +```python +def get_names(names: str) -> None: + match names: + case ('Bob', y): + print(f'Hello {y}') + case (x, 'John'): + print(f'Hello {x}') + case (x, y): + print(f'Hello {x} and {y}') + case _: + print('Invalid') +``` +Here, the `names` is a tuple that contains two names. The `match` block unpacks the tuple and binds `x` and `y` based on the patterns. A wildcard case prints `Invalid` if the condition is not satisfied. + +O/P: + +In this example, the above code snippet with the parameter `names` as below and the respective output. +``` +>>> get_names(('Bob', 'Max')) +Hello Max + +>>> get_names(('Rob', 'John')) +Hello Rob + +>>> get_names(('Rob', 'Max')) +Hello Rob and Max + +>>> get_names(('Rob', 'Max', 'Bob')) +Invalid +``` + +### Patterns with Classes +Class structures can be used in `match` block for pattern matching. The class members can also be binded with a variable to perform certain operations. For the class structure: +```python +class Person: + def __init__(self, name, age): + self.name = name + self.age = age +``` +The match case example illustrates the generic working as well as the binding of variables with the class members. +```python +def get_class(cls: Person) -> None: + match cls: + case Person(name='Bob', age=18): + print('Hello Bob with age 18') + case Person(name='Max', age=y): + print(f'Age is {y}') + case Person(name=x, age=18): + print(f'Name is {x}') + case Person(name=x, age=y): + print(f'Name and age is {x} and {y}') + case _: + print('Invalid') +``` +O/P: +``` +>>> get_class(Person('Bob', 18)) +Hello Bob with age 18 + +>>> get_class(Person('Max', 21)) +Age is 21 + +>>> get_class(Person('Rob', 18)) +Name is Rob + +>>> get_class(Person('Rob', 21)) +Name and age is Rob and 21 +``` +Now, if a new class is introduced in the above code snippet like below. +```python +class Pet: + def __init__(self, name, animal): + self.name = name + self.animal = animal +``` +The patterns will not match the cases and will trigger the wildcard case for the original code snippet above with `get_class` function. +``` +>>> get_class(Pet('Tommy', 'Dog')) +Invalid +``` From e5c88286d5b72b0e0e51e4f1c889544b41c91ef9 Mon Sep 17 00:00:00 2001 From: SAM <60264918+SAM-DEV007@users.noreply.github.com> Date: Tue, 4 Jun 2024 18:02:50 +0530 Subject: [PATCH 08/61] Update match_case_statement.md Added remaining topic headings --- contrib/advanced-python/match_case_statement.md | 11 +++++++++++ 1 file changed, 11 insertions(+) diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match_case_statement.md index 57f6bfb..6941d98 100644 --- a/contrib/advanced-python/match_case_statement.md +++ b/contrib/advanced-python/match_case_statement.md @@ -160,3 +160,14 @@ The patterns will not match the cases and will trigger the wildcard case for the >>> get_class(Pet('Tommy', 'Dog')) Invalid ``` + +### Nested Patterns + +### Complex Patterns +#### Wildcard + +#### Guard + +## Summary + +## Further Reading From ffcc45ad986b70a5b1b39cc515bb7e7230db3c4d Mon Sep 17 00:00:00 2001 From: SAM <60264918+SAM-DEV007@users.noreply.github.com> Date: Tue, 4 Jun 2024 18:28:39 +0530 Subject: [PATCH 09/61] Update match_case_statement.md Added nested patterns --- .../advanced-python/match_case_statement.md | 27 +++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match_case_statement.md index 6941d98..22eeef9 100644 --- a/contrib/advanced-python/match_case_statement.md +++ b/contrib/advanced-python/match_case_statement.md @@ -162,6 +162,33 @@ Invalid ``` ### Nested Patterns +The patterns can be nested via various means. It can include the mix of the patterns mentioned earlier or can be symmetrical across. A basic of the nested pattern of a list with Patterns with a Literal and Variable is taken. Classes and Iterables can laso be included. +```python +def get_points(points: list) -> None: + match points: + case []: + print('Empty') + case [x]: + print(f'One point {x}') + case [x, y]: + print(f'Two points {x} and {y}') + case _: + print('More than two points') +``` +O/P: +``` +>>> get_points([]) +Empty + +>>> get_points([1]) +One point 1 + +>>> get_points([1, 2]) +Two points 1 and 2 + +>>> get_points([1, 2, 3]) +More than two points +``` ### Complex Patterns #### Wildcard From d345d0339f7a2bd5eea818f5a42bc4e0c5d9f5f7 Mon Sep 17 00:00:00 2001 From: SAM <60264918+SAM-DEV007@users.noreply.github.com> Date: Tue, 4 Jun 2024 19:14:09 +0530 Subject: [PATCH 10/61] Update match_case_statement.md Added the content to remaining sections --- .../advanced-python/match_case_statement.md | 50 +++++++++++++++++++ 1 file changed, 50 insertions(+) diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match_case_statement.md index 22eeef9..cd7bc64 100644 --- a/contrib/advanced-python/match_case_statement.md +++ b/contrib/advanced-python/match_case_statement.md @@ -191,10 +191,60 @@ More than two points ``` ### Complex Patterns +Complex patterns are also supported in the pattern matching sequence. The complex does not mean complex numbers but rather the structure which makes the readibility to seem complex. + #### Wildcard +The wildcard used till now are in the form of `case _` where the wildcard case is used if no match is found. Furthermore, the wildcard `_` can also be used as a placeholder in complex patterns. + +```python +def wildcard(value: tuple) -> None: + match value: + case ('Bob', age, 'Mechanic'): + print(f'Bob is mechanic of age {age}') + case ('Bob', age, _): + print(f'Bob is not a mechanic of age {age}') +``` +O/P: + +The value in the above snippet is a tuple with `(Name, Age, Job)`. If the job is Mechanic and the name is Bob, the first case is triggered. But if the job is different and not a mechanic, then the other case is triggered with the wildcard. +``` +>>> wildcard(('Bob', 18, 'Mechanic')) +Bob is mechanic of age 18 + +>>> wildcard(('Bob', 21, 'Engineer')) +Bob is not a mechanic of age 21 +``` #### Guard +A `guard` is when an `if` is added to a pattern. The evaluation depends on the truth value of the guard. + +`nums` is the tuple which contains two integers. A guard is the first case where it checks whether the first number is greater or equal to the second number in the tuple. If it is false, then it moves to the second case, where it concludes that the first number is smaller than the second number. +```python +def guard(nums: tuple) -> None: + match nums: + case (x, y) if x >= y: + print(f'{x} is greater or equal than {y}') + case (x, y): + print(f'{x} is smaller than {y}') + case _: + print('Invalid') +``` +O/P: +``` +>>> guard((1, 2)) +1 is smaller than 2 + +>>> guard((2, 1)) +2 is greater or equal than 1 + +>>> guard((1, 1)) +1 is greater or equal than 1 +``` ## Summary +The match case statements provide an elegant and readible format to perform operations on pattern matching as compared to `if-else` statements. They are also more versatile as they provide additional functionalities on the pattern matching operations like unpacking, class matching, iterables and iterators. It can also use positional arguments for checking the patterns. They provide a powerful and concise way to handle multiple conditions and perform pattern matching ## Further Reading +- [Python Match Case Statement - GeeksForGeeks](https://www.geeksforgeeks.org/python-match-case-statement/) +- [PEP 634 – Structural Pattern Matching: Specification](https://peps.python.org/pep-0634/) +- [PEP 636 – Structural Pattern Matching: Tutorial](https://peps.python.org/pep-0636/) From fe4ce4a34df72c800d12c624385069b27b689d11 Mon Sep 17 00:00:00 2001 From: SAM <60264918+SAM-DEV007@users.noreply.github.com> Date: Tue, 4 Jun 2024 19:16:29 +0530 Subject: [PATCH 11/61] Update match_case_statement.md Added further reading topic summary --- contrib/advanced-python/match_case_statement.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match_case_statement.md index cd7bc64..b617f7a 100644 --- a/contrib/advanced-python/match_case_statement.md +++ b/contrib/advanced-python/match_case_statement.md @@ -245,6 +245,8 @@ O/P: The match case statements provide an elegant and readible format to perform operations on pattern matching as compared to `if-else` statements. They are also more versatile as they provide additional functionalities on the pattern matching operations like unpacking, class matching, iterables and iterators. It can also use positional arguments for checking the patterns. They provide a powerful and concise way to handle multiple conditions and perform pattern matching ## Further Reading +This article provides a brief introduction to the match case statements and the overview on the pattern matching operations. To know more, the below articles can be used for in-depth understanding of the topic. + - [Python Match Case Statement - GeeksForGeeks](https://www.geeksforgeeks.org/python-match-case-statement/) - [PEP 634 – Structural Pattern Matching: Specification](https://peps.python.org/pep-0634/) - [PEP 636 – Structural Pattern Matching: Tutorial](https://peps.python.org/pep-0636/) From 5542f6ba9d665838d273257859992efe958eca6a Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 22:18:48 +0530 Subject: [PATCH 12/61] Added K-Means --- .../machine-learning/K-Means_Clustering.md | 84 +++++++++++++++++++ 1 file changed, 84 insertions(+) create mode 100644 contrib/machine-learning/K-Means_Clustering.md diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md new file mode 100644 index 0000000..f90e290 --- /dev/null +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -0,0 +1,84 @@ +# K-Means Clustering +Unsupervised Learning Algorithm for Grouping Similar Data. +## Introduction +K-means clustering is a fundamental unsupervised machine learning algorithm that excels at grouping similar data points together. It's a popular choice due to its simplicity and efficiency in uncovering hidden patterns within unlabeled datasets. +## Unsupervised Learning +Unlike supervised learning algorithms that rely on labeled data for training, unsupervised algorithms, like K-means, operate solely on input data (without predefined categories). Their objective is to discover inherent structures or groupings within the data. +## The K-Means Objective +Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. + +![enter image description here](https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQnDTFfxrrAttYMwwjZV0RAA8J8rmUxgrnWc2gU_ArEqrxEMlHm) +## Clusters and Centroids +A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). +## Minimizing In-Cluster Variation +The K-means algorithm strategically assigns each data point to a cluster such that the total variation within each cluster (measured by the sum of squared distances between points and their centroid) is minimized. In simpler terms, K-means strives to create clusters where data points are close to their respective centroids. +## The Meaning Behind "K-Means" +The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. +## K-Means Algorithm in Action +![enter image description here](https://d3i71xaburhd42.cloudfront.net/2f49631bb3103a61fbc3045dd035c3d8f2175887/11-Figure2-1.png) +The K-means algorithm follows an iterative approach to optimize cluster formation: + +1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. +2. **Data Point Assignment:** Each data point is assigned to the closest centroid, effectively creating a preliminary clustering. +3. **Centroid Repositioning:** Once data points are assigned, the centroids are recalculated by averaging the positions of the points within their respective clusters. These new centroids represent the refined centers of the clusters. +4. **Iteration Until Convergence:** Steps 2 and 3 are repeated iteratively until a stopping criterion is met. This criterion can be either: + - **Centroid Stability:** No significant change occurs in the centroids' positions, indicating successful clustering. + - **Reaching Maximum Iterations:** A predefined number of iterations is completed. + ## Code + Following is a simple implementation of K-Means. + + + # Generate and Visualize Sample Data + # import the necessary Libraries + + import numpy as np + import matplotlib.pyplot as plt + + # Create data points for cluster 1 and cluster 2 + X = -2 * np.random.rand(100, 2) + X1 = 1 + 2 * np.random.rand(50, 2) + + # Combine data points from both clusters + X[50:100, :] = X1 + + # Plot data points and display the plot + plt.scatter(X[:, 0], X[:, 1], s=50, c='b') + plt.show() + + # K-Means Model Creation and Training + from sklearn.cluster import KMeans + + # Create KMeans object with 2 clusters + kmeans = KMeans(n_clusters=2) + kmeans.fit(X) # Train the model on the data + + # Visualize Data Points with Centroids + centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) + + plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again + plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 + plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 + plt.show() # Display the plot with centroids + + # Predict Cluster Label for New Data Point + new_data = np.array([-3.0, -3.0]) + new_data_reshaped = new_data.reshape(1, -1) + predicted_cluster = kmeans.predict(new_data_reshaped) + print("Predicted cluster for new data:", predicted_cluster) + + ### Output: + Before Implementing K-Means Clustering : +![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) + + + After Implementing K-Means Clustering:![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) +## Conclusion +**K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. + + + + + + + + From 7259dc7047a0576721b852fc4aeb08ddf5bd8b84 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 22:24:02 +0530 Subject: [PATCH 13/61] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index f90e290..ab5fba9 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -67,11 +67,12 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio print("Predicted cluster for new data:", predicted_cluster) ### Output: - Before Implementing K-Means Clustering : + Before Implementing K-Means Clustering ![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) - After Implementing K-Means Clustering:![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) + After Implementing K-Means Clustering + ![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From e9eb68ab3832ec651264b967de709ee8ae41af5f Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 23:28:27 +0530 Subject: [PATCH 14/61] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index ab5fba9..c6aee6a 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -15,7 +15,6 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![enter image description here](https://d3i71xaburhd42.cloudfront.net/2f49631bb3103a61fbc3045dd035c3d8f2175887/11-Figure2-1.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -66,13 +65,13 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio predicted_cluster = kmeans.predict(new_data_reshaped) print("Predicted cluster for new data:", predicted_cluster) - ### Output: - Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](https://miro.medium.com/v2/resize:fit:640/format:webp/1*jnyQxmEj7rFhazeMH7KXVg.png) + ### Output: +![Before Implementing K-Means Clustering](data:image/png;base64,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) - After Implementing K-Means Clustering - ![enter image description here](https://miro.medium.com/v2/resize:fit:640/format:webp/1*H3L3EH3Jh6kWFmbec0ewKA.png) + + ![After Implementing K-Means Clustering](data:image/png;base64,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+ Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. 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z!s>5(N}+(ZYo14FzRtNg^TU^uiyqHBaGpQV4i=4`3*N;iYFt-VS!I<~R#|10RaRLg arT+(~s&-lbfZ;O$0000 Date: Tue, 4 Jun 2024 23:41:27 +0530 Subject: [PATCH 16/61] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index c6aee6a..82a5c83 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![enter image description here](https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQnDTFfxrrAttYMwwjZV0RAA8J8rmUxgrnWc2gU_ArEqrxEMlHm) +![image](assets/Knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,6 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action +![image](assets/Km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -66,11 +67,11 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio print("Predicted cluster for new data:", predicted_cluster) ### Output: -![Before Implementing K-Means Clustering](data:image/png;base64,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) + Before Implementing K-Means Clustering +![Before Implementing K-Means Clustering](assets/Km_2.png) - - - ![After Implementing K-Means Clustering](data:image/png;base64,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) + After Implementing K-Means Clustering + ![After Implementing K-Means Clustering](assets/Km_3.png) Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From d65dce72e10873a2554cbc37b00fab868fdfb0d5 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Tue, 4 Jun 2024 23:46:20 +0530 Subject: [PATCH 17/61] update k-means --- contrib/machine-learning/K-Means_Clustering.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 82a5c83..bf72ffd 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![image](assets/Knm.png) +![image](assets\knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,7 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![image](assets/Km_.png) +![image](assets\km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -68,10 +68,10 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio ### Output: Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](assets/Km_2.png) +![Before Implementing K-Means Clustering](assets\km_2.png) After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets/Km_3.png) + ![After Implementing K-Means Clustering](assets\km_3.png) Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From 7bc7b0621eb59fa6e85c076885d1e18d2f103847 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Wed, 5 Jun 2024 11:26:57 +0530 Subject: [PATCH 18/61] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index bf72ffd..859636b 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -7,7 +7,7 @@ Unlike supervised learning algorithms that rely on labeled data for training, un ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. -![image](assets\knm.png) +![image](assets/knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). ## Minimizing In-Cluster Variation @@ -15,7 +15,7 @@ The K-means algorithm strategically assigns each data point to a cluster such th ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. ## K-Means Algorithm in Action -![image](assets\km_.png) +![image](assets/km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: 1. **Initial Centroid Placement:** The process begins with randomly selecting k centroids to serve as initial reference points for each cluster. @@ -68,10 +68,11 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio ### Output: Before Implementing K-Means Clustering -![Before Implementing K-Means Clustering](assets\km_2.png) +![Before Implementing K-Means Clustering](assets/km_2.png) After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets\km_3.png) + ![After Implementing K-Means Clustering](assets/km_3.png) + Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. From 92571f619700a05019853aff0230015fe4b85a2d Mon Sep 17 00:00:00 2001 From: saiumasankar Date: Wed, 5 Jun 2024 11:29:23 +0530 Subject: [PATCH 19/61] update dynamic programming Added LIS problem and Tabulation code of LCS and 0-1 Knapsack --- contrib/ds-algorithms/dynamic-programming.md | 124 ++++++++++++++++++- 1 file changed, 121 insertions(+), 3 deletions(-) diff --git a/contrib/ds-algorithms/dynamic-programming.md b/contrib/ds-algorithms/dynamic-programming.md index 43149f8..54c6fcb 100644 --- a/contrib/ds-algorithms/dynamic-programming.md +++ b/contrib/ds-algorithms/dynamic-programming.md @@ -84,8 +84,32 @@ Y = "GXTXAYB" print("Length of Longest Common Subsequence:", longest_common_subsequence(X, Y, len(X), len(Y))) ``` +## Longest Common Subsequence Code in Python (Bottom-Up Approach) + +```python + +def longestCommonSubsequence(X, Y, m, n): + L = [[None]*(n+1) for i in range(m+1)] + for i in range(m+1): + for j in range(n+1): + if i == 0 or j == 0: + L[i][j] = 0 + elif X[i-1] == Y[j-1]: + L[i][j] = L[i-1][j-1]+1 + else: + L[i][j] = max(L[i-1][j], L[i][j-1]) + return L[m][n] + + +S1 = "AGGTAB" +S2 = "GXTXAYB" +m = len(S1) +n = len(S2) +print("Length of LCS is", longestCommonSubsequence(S1, S2, m, n)) +``` + ## Complexity Analysis -- **Time Complexity**: O(m * n) for the top-down approach, where m and n are the lengths of the input sequences +- **Time Complexity**: O(m * n) for both approaches, where m and n are the lengths of the input sequences - **Space Complexity**: O(m * n) for the memoization table
@@ -122,11 +146,105 @@ capacity = 50 n = len(weights) print("Maximum value that can be obtained:", knapsack(weights, values, capacity, n)) ``` +## 0-1 Knapsack Problem Code in Python (Bottom-up Approach) +```python +def knapSack(capacity, weights, values, n): + K = [[0 for x in range(capacity + 1)] for x in range(n + 1)] + for i in range(n + 1): + for w in range(capacity + 1): + if i == 0 or w == 0: + K[i][w] = 0 + elif weights[i-1] <= w: + K[i][w] = max(values[i-1] + + K[i-1][w-weights[i-1]], + K[i-1][w]) + else: + K[i][w] = K[i-1][w] + + return K[n][capacity] + +values = [60, 100, 120] +weights = [10, 20, 30] +capacity = 50 +n = len(weights) +print(knapSack(capacity, weights, values, 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 +- **Time Complexity**: O(n * W) for both approaches, 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 +
+ +# 4. Longest Increasing Subsequence + +The Longest Increasing Subsequence (LIS) is a task is to find the longest subsequence that is strictly increasing, meaning each element in the subsequence is greater than the one before it. This subsequence must maintain the order of elements as they appear in the original sequence but does not need to be contiguous. The goal is to identify the subsequence with the maximum possible length. + +**Algorithm Overview:** +- **Base cases:** If the sequence is empty, the LIS length is 0. +- **Memoization:** Store the results of previously computed subproblems to avoid redundant computations. +- **Recurrence relation:** Compute the LIS length by comparing characters of the sequences and making decisions based on their values. + +## Longest Increasing Subsequence Code in Python (Top-Down Approach using Memoization) + +```python + +import sys + +def f(idx, prev_idx, n, a, dp): + if (idx == n): + return 0 + + if (dp[idx][prev_idx + 1] != -1): + return dp[idx][prev_idx + 1] + + notTake = 0 + f(idx + 1, prev_idx, n, a, dp) + take = -sys.maxsize - 1 + if (prev_idx == -1 or a[idx] > a[prev_idx]): + take = 1 + f(idx + 1, idx, n, a, dp) + + dp[idx][prev_idx + 1] = max(take, notTake) + return dp[idx][prev_idx + 1] + +def longestSubsequence(n, a): + + dp = [[-1 for i in range(n + 1)]for j in range(n + 1)] + return f(0, -1, n, a, dp) + +a = [3, 10, 2, 1, 20] +n = len(a) + +print("Length of lis is", longestSubsequence(n, a)) + +``` + +## Longest Increasing Subsequence Code in Python (Bottom-Up Approach) + +```python +def lis(arr): + n = len(arr) + lis = [1]*n + + for i in range(1, n): + for j in range(0, i): + if arr[i] > arr[j] and lis[i] < lis[j] + 1: + lis[i] = lis[j]+1 + + maximum = 0 + for i in range(n): + maximum = max(maximum, lis[i]) + + return maximum + +arr = [10, 22, 9, 33, 21, 50, 41, 60] +print("Length of lis is", lis(arr)) +``` +## Complexity Analysis +- **Time Complexity**: O(n * n) for both approaches, where n is the length of the array. +- **Space Complexity**: O(n * n) for the memoization table in Top-Down Approach, O(n) in Bottom-Up Approach. + +
+
+
From f742fddff366a0eff24520c8ee292b81d2188d45 Mon Sep 17 00:00:00 2001 From: saiumasankar Date: Wed, 5 Jun 2024 17:28:33 +0530 Subject: [PATCH 20/61] Adding the BeautifulSoup web scrapping --- contrib/web-scrapping/beautifulsoup.md | 206 +++++++++++++++++++++++++ contrib/web-scrapping/index.md | 1 + 2 files changed, 207 insertions(+) create mode 100644 contrib/web-scrapping/beautifulsoup.md diff --git a/contrib/web-scrapping/beautifulsoup.md b/contrib/web-scrapping/beautifulsoup.md new file mode 100644 index 0000000..372b8f2 --- /dev/null +++ b/contrib/web-scrapping/beautifulsoup.md @@ -0,0 +1,206 @@ +# Beautiful Soup Library in Python + +## Table of Contents +1. Introduction +2. Prerequisites +3. Setting Up Environment +4. Beautiful Soup Objects +5. Tag object +6. Children, Parents and Siblings +7. Filter: Findall method +8. Web Scraping the Contents of a Web Page + +## 1. Introduction +Beautiful Soup is a Python library used for web scraping purposes to extract data from HTML and XML files. It creates a parse tree for parsed pages that can be used to extract data easily. + +## 2. Prerequisites +- Understanding of HTTP Requests and Responses. +- Understanding of HTTP methods (GET method). +- Basic Knowledge on HTML. +- Python installed on your machine (version 3.6 or higher). +- pip (Python package installer) installed. + +## 3. Setting Up Environment +1.**Install latest version of Python:** Go to Python.org and Download the latest version of Python. + +2.**Install a IDE:** Install any IDE of your choice to code. VS code is preferred. +>Note: You can use Google Colab without installing Python and IDE. + +3.**Install Beautiful Soup:** +```python +!pip install bs4 +``` + +## 4. Beautiful Soup Objects +Beautiful Soup is a Python library for pulling data out of HTML and XML files. This can be done by presenting the HTML as a set of objects. + +Take the below HTML page as input +``` + + + +Page Title + + +

Title

+

This is the main context of the page

+ + +``` + +lets store the HTML code in a variable +``` +html= " + + + Page Title + + +

Title

+

This is the main context of the page

+ + " +``` + +To parse the HTML document, pass the variable to the `BeautifulSoup` Constructor. +``` +soup = BeautifulSoup(html,'html.parser') +``` +Beautiful Soup transforms a complex HTML document into a complex tree of Python objects. + +## 5. Tags + +The Tag object corresponds to an HTML tag in the original document. + +``` +tag_obj = soup.title +print("tag object:", tag_obj) +print("tag object type:",type(tag_obj)) +``` +``` +Result: +tag object: Page Title + +tag object type: +``` + +## 6. Children, Parent and Siblings + +We can access the child of the tag or navigate down. + +``` +tag_obj = soup.h3 +child = tag_obj.b +print(child) +parent = child.parent +print(parent) +sib = tag_obj.next_sibling +print(sib); +``` +``` +Result: + Title +

Title

+

This is the main context of the page

+``` + +> We need to mention the child to which we want to navigate. It is because there can be more than one child to a tag but only one parent and next sibling. + +**Navigable String:** A string corresponds to a bit of text or content within a tag. Beautiful Soup uses the NavigableString class to contain this text. + +``` +tagstr = child.string +print(tagstr) +``` +``` +Result: +Title +``` + +## 7. Filter + +Filters allow you to find complex patterns, the simplest filter is a string. + +Consider the following HTML code: + +``` + + + + + + Sample Table + + +

Sample Table

+ + + + + + + + + + + + + + + + + + + + + + + + + +
NameAgeCity
John Doe28New York
Jane Smith34Los Angeles
Emily Jones23Chicago
+ + + +``` +Store the above code in a variable. +``` +table = " + + + + + Sample Table +.............. + +table_bs = BeautifulSoup(table, 'html.parser') +" +``` +**Find All:** The find_all() method looks through a tag’s descendants and retrieves all descendants that match your filters. It places all the objects in a list. We can access by indexing. + +## 8. Web Scraping the Contents of a Web Page + +1. Get the URL of the webpage we need to scrape. + +2. Get the HTML content by using `get` method in HTTP request. + +3. Pass the HTML content to the BeautifulSoup Constructor to prepare an object. + +4. Access the HTML elements using Tag name. + +Below is the code to extract the img tags in a wikipedia page. + +``` +import requests +!pip install bs4 +from bs4 import BeautifulSoup + +url = "https://en.wikipedia.org/wiki/Encyclopedia" +data = requests.get(url).text +soup = BeautifulSoup(data,"html.parser") + +for link in soup.find_all('a'): + print(link) + print(link.get('src')) +``` +We can retrieve any data in the webpage by access through the tags. diff --git a/contrib/web-scrapping/index.md b/contrib/web-scrapping/index.md index 276014e..29f558a 100644 --- a/contrib/web-scrapping/index.md +++ b/contrib/web-scrapping/index.md @@ -2,3 +2,4 @@ - [Section title](filename.md) - [Introduction to Flask](flask.md) +- [Web Scrapping Using Beautiful Soup](beautifulsoup.md) From f48a2d70fd60d69d8ad033526f06a0d4a79e4b27 Mon Sep 17 00:00:00 2001 From: rohit Date: Sat, 8 Jun 2024 11:01:07 +0530 Subject: [PATCH 21/61] Added Neural Network Regression in Python --- .../Neural network regression.md | 98 +++++++++++++++++++ contrib/machine-learning/index.md | 1 + 2 files changed, 99 insertions(+) create mode 100644 contrib/machine-learning/Neural network regression.md diff --git a/contrib/machine-learning/Neural network regression.md b/contrib/machine-learning/Neural network regression.md new file mode 100644 index 0000000..36c3b9a --- /dev/null +++ b/contrib/machine-learning/Neural network regression.md @@ -0,0 +1,98 @@ +# Neural Network Regression in Python + +## Overview + +Neural Network Regression is a type of machine learning algorithm used to predict continuous values. Unlike classification, where the goal is to predict a category or class, regression aims to predict a specific numerical value. Neural networks are particularly powerful for regression tasks when dealing with complex, non-linear relationships in data. + +## When to Use Neural Network Regression + +### Suitable Scenarios + +1. **Complex Relationships**: When the relationship between input features and the target variable is non-linear and complex. +2. **Large Datasets**: When you have a large dataset that can support the training of a neural network. +3. **Feature Engineering**: When you can leverage the feature extraction capabilities of neural networks, especially in domains like image or text data. + +### Unsuitable Scenarios + +1. **Small Datasets**: Neural networks require substantial amounts of data to train effectively. For small datasets, simpler models like linear regression or decision trees might perform better. +2. **Real-time Predictions**: If low-latency predictions are required and computational resources are limited, simpler models might be more efficient. +3. **Interpretability**: If model interpretability is crucial, neural networks might not be the best choice due to their "black-box" nature. + +## Implementing Neural Network Regression in Python + +We'll use TensorFlow and Keras, popular libraries for building and training neural networks in Python. + +### Step-by-Step Implementation + +1. **Import Libraries** + +```python +import numpy as np +import pandas as pd +from sklearn.model_selection import train_test_split +from sklearn.preprocessing import StandardScaler +from tensorflow.keras.models import Sequential +from tensorflow.keras.layers import Dense +from tensorflow.keras.optimizers import Adam +``` + +2. **Load and Prepare Data** + +For illustration, let's use a synthetic dataset. + +```python +# Generate synthetic data +np.random.seed(42) +X = np.random.rand(1000, 3) +y = X[:, 0] * 3 + X[:, 1] * -2 + X[:, 2] * 0.5 + np.random.randn(1000) * 0.1 + +# Split the data +X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42) + +# Standardize the data +scaler = StandardScaler() +X_train = scaler.fit_transform(X_train) +X_test = scaler.transform(X_test) +``` + +3. **Build the Neural Network Model** + +```python +model = Sequential() +model.add(Dense(64, input_dim=X_train.shape[1], activation='relu')) +model.add(Dense(64, activation='relu')) +model.add(Dense(1)) # Output layer for regression + +model.compile(optimizer=Adam(learning_rate=0.001), loss='mse', metrics=['mae']) +``` + +4. **Train the Model** + +```python +history = model.fit(X_train, y_train, epochs=100, batch_size=32, validation_split=0.2) +``` + +5. **Evaluate the Model** + +```python +loss, mae = model.evaluate(X_test, y_test) +print(f"Test Mean Absolute Error: {mae}") +``` + +6. **Make Predictions** + +```python +predictions = model.predict(X_test) +``` + +### Explanation + +- **Data Generation and Preparation**: Synthetic data is created and split into training and test sets. The data is standardized to improve the neural network's training efficiency. +- **Model Construction**: A simple feedforward neural network is built using Keras. It consists of two hidden layers with 64 neurons each and ReLU activation functions. The output layer has a single neuron for regression. +- **Training**: The model is trained for 100 epochs with a batch size of 32. The Adam optimizer is used to adjust the weights. +- **Evaluation**: The model's performance is evaluated on the test set, using Mean Absolute Error (MAE) as a metric. +- **Prediction**: Predictions are made on the test data. + +## Conclusion + +Neural Network Regression is a powerful tool for predicting continuous values, particularly in cases involving complex, non-linear relationships. However, they require large datasets and significant computational resources. For smaller datasets or scenarios requiring model interpretability, simpler models might be preferable. By following the steps outlined, you can build, train, and evaluate a neural network for regression tasks in Python using TensorFlow and Keras. \ No newline at end of file diff --git a/contrib/machine-learning/index.md b/contrib/machine-learning/index.md index 0bf39f9..82fbbcc 100644 --- a/contrib/machine-learning/index.md +++ b/contrib/machine-learning/index.md @@ -20,3 +20,4 @@ - [Grid Search](grid-search.md) - [Transformers](transformers.md) - [K-nearest neighbor (KNN)](knn.md) +- [Neural network regression](Neural network regression.md) From 2647dbc3678d8380da938bc2ff02cb2243fc37b1 Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Sat, 8 Jun 2024 11:48:48 +0530 Subject: [PATCH 22/61] Update index.md --- contrib/ds-algorithms/index.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 2263620..b18b79a 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -13,4 +13,6 @@ - [Stacks in Python](stacks.md) - [Sliding Window Technique](sliding-window.md) - [Trie](trie.md) +- [Two Pointer Technique](two-pointer-technique.md) +- [Hashing through Linear Probing](hashing-linear-probing.md) - [Dijkstra's Algorithm](Dijkstra's_algorithm.md) From b2643ad26d31b8e70e3bb41842745bb9f3129716 Mon Sep 17 00:00:00 2001 From: saiumasankar Date: Sat, 8 Jun 2024 15:03:43 +0530 Subject: [PATCH 23/61] deleting unnecessary --- contrib/web-scrapping/beautifulsoup.md | 206 ------------------------- contrib/web-scrapping/index.md | 1 - 2 files changed, 207 deletions(-) delete mode 100644 contrib/web-scrapping/beautifulsoup.md diff --git a/contrib/web-scrapping/beautifulsoup.md b/contrib/web-scrapping/beautifulsoup.md deleted file mode 100644 index 372b8f2..0000000 --- a/contrib/web-scrapping/beautifulsoup.md +++ /dev/null @@ -1,206 +0,0 @@ -# Beautiful Soup Library in Python - -## Table of Contents -1. Introduction -2. Prerequisites -3. Setting Up Environment -4. Beautiful Soup Objects -5. Tag object -6. Children, Parents and Siblings -7. Filter: Findall method -8. Web Scraping the Contents of a Web Page - -## 1. Introduction -Beautiful Soup is a Python library used for web scraping purposes to extract data from HTML and XML files. It creates a parse tree for parsed pages that can be used to extract data easily. - -## 2. Prerequisites -- Understanding of HTTP Requests and Responses. -- Understanding of HTTP methods (GET method). -- Basic Knowledge on HTML. -- Python installed on your machine (version 3.6 or higher). -- pip (Python package installer) installed. - -## 3. Setting Up Environment -1.**Install latest version of Python:** Go to Python.org and Download the latest version of Python. - -2.**Install a IDE:** Install any IDE of your choice to code. VS code is preferred. ->Note: You can use Google Colab without installing Python and IDE. - -3.**Install Beautiful Soup:** -```python -!pip install bs4 -``` - -## 4. Beautiful Soup Objects -Beautiful Soup is a Python library for pulling data out of HTML and XML files. This can be done by presenting the HTML as a set of objects. - -Take the below HTML page as input -``` - - - -Page Title - - -

Title

-

This is the main context of the page

- - -``` - -lets store the HTML code in a variable -``` -html= " - - - Page Title - - -

Title

-

This is the main context of the page

- - " -``` - -To parse the HTML document, pass the variable to the `BeautifulSoup` Constructor. -``` -soup = BeautifulSoup(html,'html.parser') -``` -Beautiful Soup transforms a complex HTML document into a complex tree of Python objects. - -## 5. Tags - -The Tag object corresponds to an HTML tag in the original document. - -``` -tag_obj = soup.title -print("tag object:", tag_obj) -print("tag object type:",type(tag_obj)) -``` -``` -Result: -tag object: Page Title - -tag object type: -``` - -## 6. Children, Parent and Siblings - -We can access the child of the tag or navigate down. - -``` -tag_obj = soup.h3 -child = tag_obj.b -print(child) -parent = child.parent -print(parent) -sib = tag_obj.next_sibling -print(sib); -``` -``` -Result: - Title -

Title

-

This is the main context of the page

-``` - -> We need to mention the child to which we want to navigate. It is because there can be more than one child to a tag but only one parent and next sibling. - -**Navigable String:** A string corresponds to a bit of text or content within a tag. Beautiful Soup uses the NavigableString class to contain this text. - -``` -tagstr = child.string -print(tagstr) -``` -``` -Result: -Title -``` - -## 7. Filter - -Filters allow you to find complex patterns, the simplest filter is a string. - -Consider the following HTML code: - -``` - - - - - - Sample Table - - -

Sample Table

- - - - - - - - - - - - - - - - - - - - - - - - - -
NameAgeCity
John Doe28New York
Jane Smith34Los Angeles
Emily Jones23Chicago
- - - -``` -Store the above code in a variable. -``` -table = " - - - - - Sample Table -.............. - -table_bs = BeautifulSoup(table, 'html.parser') -" -``` -**Find All:** The find_all() method looks through a tag’s descendants and retrieves all descendants that match your filters. It places all the objects in a list. We can access by indexing. - -## 8. Web Scraping the Contents of a Web Page - -1. Get the URL of the webpage we need to scrape. - -2. Get the HTML content by using `get` method in HTTP request. - -3. Pass the HTML content to the BeautifulSoup Constructor to prepare an object. - -4. Access the HTML elements using Tag name. - -Below is the code to extract the img tags in a wikipedia page. - -``` -import requests -!pip install bs4 -from bs4 import BeautifulSoup - -url = "https://en.wikipedia.org/wiki/Encyclopedia" -data = requests.get(url).text -soup = BeautifulSoup(data,"html.parser") - -for link in soup.find_all('a'): - print(link) - print(link.get('src')) -``` -We can retrieve any data in the webpage by access through the tags. diff --git a/contrib/web-scrapping/index.md b/contrib/web-scrapping/index.md index 29f558a..276014e 100644 --- a/contrib/web-scrapping/index.md +++ b/contrib/web-scrapping/index.md @@ -2,4 +2,3 @@ - [Section title](filename.md) - [Introduction to Flask](flask.md) -- [Web Scrapping Using Beautiful Soup](beautifulsoup.md) From c2c84a09d21445382fc535a99d2745d8a8be0a29 Mon Sep 17 00:00:00 2001 From: Kosuri Indu Date: Sat, 8 Jun 2024 19:10:46 +0530 Subject: [PATCH 24/61] Added Splay Trees in DSA section --- contrib/ds-algorithms/index.md | 3 +- contrib/ds-algorithms/splay-trees.md | 162 +++++++++++++++++++++++++++ 2 files changed, 164 insertions(+), 1 deletion(-) create mode 100644 contrib/ds-algorithms/splay-trees.md diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 9c05b15..e099f97 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -15,4 +15,5 @@ - [Trie](trie.md) - [Two Pointer Technique](two-pointer-technique.md) - [Hashing through Linear Probing](hashing-linear-probing.md) -- [Hashing through Chaining](hashing-chaining.md) \ No newline at end of file +- [Hashing through Chaining](hashing-chaining.md) +- [Splay Trees](splay-trees.md) \ No newline at end of file diff --git a/contrib/ds-algorithms/splay-trees.md b/contrib/ds-algorithms/splay-trees.md new file mode 100644 index 0000000..ee900ed --- /dev/null +++ b/contrib/ds-algorithms/splay-trees.md @@ -0,0 +1,162 @@ +# Splay Tree + +In Data Structures and Algorithms, a **Splay Tree** is a self-adjusting binary search tree with the additional property that recently accessed elements are quick to access again. It performs basic operations such as insertion, search, and deletion in O(log n) amortized time. This is achieved by a process called **splaying**, where the accessed node is moved to the root through a series of tree rotations. + +## Points to be Remembered + +- **Splaying**: Moving the accessed node to the root using rotations. +- **Rotations**: Tree rotations (left and right) are used to balance the tree during splaying. +- **Self-adjusting**: The tree adjusts itself with each access, keeping frequently accessed nodes near the root. + +## Real Life Examples of Splay Trees + +- **Cache Implementation**: Frequently accessed data is kept near the top of the tree, making repeated accesses faster. +- **Networking**: Routing tables in network switches can use splay trees to prioritize frequently accessed routes. + +## Applications of Splay Trees + +Splay trees are used in various applications in Computer Science: + +- **Cache Implementations** +- **Garbage Collection Algorithms** +- **Data Compression Algorithms (e.g., LZ78)** + +Understanding these applications is essential for Software Development. + +## Operations in Splay Tree + +Key operations include: + +- **INSERT**: Insert a new element into the splay tree. +- **SEARCH**: Find the position of an element in the splay tree. +- **DELETE**: Remove an element from the splay tree. + +## Implementing Splay Tree in Python + +```python +class SplayTreeNode: + def __init__(self, key): + self.key = key + self.left = None + self.right = None + +class SplayTree: + def __init__(self): + self.root = None + + def insert(self, key): + self.root = self.splay_insert(self.root, key) + + def search(self, key): + self.root = self.splay_search(self.root, key) + return self.root + + def splay(self, root, key): + if not root or root.key == key: + return root + + if root.key > key: + if not root.left: + return root + if root.left.key > key: + root.left.left = self.splay(root.left.left, key) + root = self.rotateRight(root) + elif root.left.key < key: + root.left.right = self.splay(root.left.right, key) + if root.left.right: + root.left = self.rotateLeft(root.left) + return root if not root.left else self.rotateRight(root) + + else: + if not root.right: + return root + if root.right.key > key: + root.right.left = self.splay(root.right.left, key) + if root.right.left: + root.right = self.rotateRight(root.right) + elif root.right.key < key: + root.right.right = self.splay(root.right.right, key) + root = self.rotateLeft(root) + return root if not root.right else self.rotateLeft(root) + + def splay_insert(self, root, key): + if not root: + return SplayTreeNode(key) + + root = self.splay(root, key) + + if root.key == key: + return root + + new_node = SplayTreeNode(key) + + if root.key > key: + new_node.right = root + new_node.left = root.left + root.left = None + else: + new_node.left = root + new_node.right = root.right + root.right = None + + return new_node + + def splay_search(self, root, key): + return self.splay(root, key) + + def rotateRight(self, node): + temp = node.left + node.left = temp.right + temp.right = node + return temp + + def rotateLeft(self, node): + temp = node.right + node.right = temp.left + temp.left = node + return temp + + def preOrder(self, root): + if root: + print(root.key, end=' ') + self.preOrder(root.left) + self.preOrder(root.right) + +#Example usage: +splay_tree = SplayTree() +splay_tree.insert(50) +splay_tree.insert(30) +splay_tree.insert(20) +splay_tree.insert(40) +splay_tree.insert(70) +splay_tree.insert(60) +splay_tree.insert(80) + +print("Preorder traversal of the Splay tree is:") +splay_tree.preOrder(splay_tree.root) + +splay_tree.search(60) + +print("\nSplay tree after search operation for key 60:") +splay_tree.preOrder(splay_tree.root) +``` + +## Output + +```markdown +Preorder traversal of the Splay tree is: +50 30 20 40 70 60 80 + +Splay tree after search operation for key 60: +60 50 30 20 40 70 80 +``` + +## Complexity Analysis + +The worst-case time complexities of the main operations in a Splay Tree are as follows: + +- **Insertion**: (O(n)). In the worst case, insertion may take linear time if the tree is highly unbalanced. +- **Search**: (O(n)). In the worst case, searching for a node may take linear time if the tree is highly unbalanced. +- **Deletion**: (O(n)). In the worst case, deleting a node may take linear time if the tree is highly unbalanced. + +While these operations can take linear time in the worst case, the splay operation ensures that the tree remains balanced over a sequence of operations, leading to better average-case performance. \ No newline at end of file From 0b301cb533e10345a68b98de1d8d2c4ee076102f Mon Sep 17 00:00:00 2001 From: Saimanjari777 Date: Sat, 8 Jun 2024 21:14:05 +0530 Subject: [PATCH 25/61] Added hash-tables, sets, and maps added --- contrib/ds-algorithms/hash-tables.md | 212 +++++++++++++++++++++++++++ contrib/ds-algorithms/index.md | 3 +- 2 files changed, 214 insertions(+), 1 deletion(-) create mode 100644 contrib/ds-algorithms/hash-tables.md diff --git a/contrib/ds-algorithms/hash-tables.md b/contrib/ds-algorithms/hash-tables.md new file mode 100644 index 0000000..f03b7c5 --- /dev/null +++ b/contrib/ds-algorithms/hash-tables.md @@ -0,0 +1,212 @@ +# Data Structures: Hash Tables, Hash Sets, and Hash Maps + +## Table of Contents +- [Introduction](#introduction) +- [Hash Tables](#hash-tables) + - [Overview](#overview) + - [Operations](#operations) +- [Hash Sets](#hash-sets) + - [Overview](#overview-1) + - [Operations](#operations-1) +- [Hash Maps](#hash-maps) + - [Overview](#overview-2) + - [Operations](#operations-2) +- [Conclusion](#conclusion) + +## Introduction +This document provides an overview of three fundamental data structures in computer science: hash tables, hash sets, and hash maps. These structures are widely used for efficient data storage and retrieval operations. + +## Hash Tables + +### Overview +A **hash table** is a data structure that stores key-value pairs. It uses a hash function to compute an index into an array of buckets or slots, from which the desired value can be found. + +### Operations +1. **Insertion**: Add a new key-value pair to the hash table. +2. **Deletion**: Remove a key-value pair from the hash table. +3. **Search**: Find the value associated with a given key. +4. **Update**: Modify the value associated with a given key. + +**Example Code (Python):** +```python +class Node: + def __init__(self, key, value): + self.key = key + self.value = value + self.next = None + + +class HashTable: + def __init__(self, capacity): + self.capacity = capacity + self.size = 0 + self.table = [None] * capacity + + def _hash(self, key): + return hash(key) % self.capacity + + def insert(self, key, value): + index = self._hash(key) + + if self.table[index] is None: + self.table[index] = Node(key, value) + self.size += 1 + else: + current = self.table[index] + while current: + if current.key == key: + current.value = value + return + current = current.next + new_node = Node(key, value) + new_node.next = self.table[index] + self.table[index] = new_node + self.size += 1 + + def search(self, key): + index = self._hash(key) + + current = self.table[index] + while current: + if current.key == key: + return current.value + current = current.next + + raise KeyError(key) + + def remove(self, key): + index = self._hash(key) + + previous = None + current = self.table[index] + + while current: + if current.key == key: + if previous: + previous.next = current.next + else: + self.table[index] = current.next + self.size -= 1 + return + previous = current + current = current.next + + raise KeyError(key) + + def __len__(self): + return self.size + + def __contains__(self, key): + try: + self.search(key) + return True + except KeyError: + return False + + +# Driver code +if __name__ == '__main__': + + ht = HashTable(5) + + ht.insert("apple", 3) + ht.insert("banana", 2) + ht.insert("cherry", 5) + + + print("apple" in ht) + print("durian" in ht) + + print(ht.search("banana")) + + ht.insert("banana", 4) + print(ht.search("banana")) # 4 + + ht.remove("apple") + + print(len(ht)) # 3 +``` + +# Insert elements +hash_table["key1"] = "value1" +hash_table["key2"] = "value2" + +# Search for an element +value = hash_table.get("key1") + +# Delete an element +del hash_table["key2"] + +# Update an element +hash_table["key1"] = "new_value1" + +## Hash Sets + +### Overview +A **hash set** is a collection of unique elements. It is implemented using a hash table where each bucket can store only one element. + +### Operations +1. **Insertion**: Add a new element to the set. +2. **Deletion**: Remove an element from the set. +3. **Search**: Check if an element exists in the set. +4. **Union**: Combine two sets to form a new set with elements from both. +5. **Intersection**: Find common elements between two sets. +6. **Difference**: Find elements present in one set but not in the other. + +**Example Code (Python):** +```python +# Create a hash set +hash_set = set() + +# Insert elements +hash_set.add("element1") +hash_set.add("element2") + +# Search for an element +exists = "element1" in hash_set + +# Delete an element +hash_set.remove("element2") + +# Union of sets +another_set = {"element3", "element4"} +union_set = hash_set.union(another_set) + +# Intersection of sets +intersection_set = hash_set.intersection(another_set) + +# Difference of sets +difference_set = hash_set.difference(another_set) +``` +## Hash Maps + +### Overview +A **hash map** is similar to a hash table but often provides additional functionalities and more user-friendly interfaces for developers. It is a collection of key-value pairs where each key is unique. + +### Operations +1. **Insertion**: Add a new key-value pair to the hash map. +2. **Deletion**: Remove a key-value pair from the hash map. +3. **Search**: Retrieve the value associated with a given key. +4. **Update**: Change the value associated with a given key. + +**Example Code (Python):** +```python +# Create a hash map +hash_map = {} + +# Insert elements +hash_map["key1"] = "value1" +hash_map["key2"] = "value2" + +# Search for an element +value = hash_map.get("key1") + +# Delete an element +del hash_map["key2"] + +# Update an element +hash_map["key1"] = "new_value1" + +``` +## Conclusion +Hash tables, hash sets, and hash maps are powerful data structures that provide efficient means of storing and retrieving data. Understanding these structures and their operations is crucial for developing optimized algorithms and applications. \ No newline at end of file diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 9c05b15..9b8c192 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -15,4 +15,5 @@ - [Trie](trie.md) - [Two Pointer Technique](two-pointer-technique.md) - [Hashing through Linear Probing](hashing-linear-probing.md) -- [Hashing through Chaining](hashing-chaining.md) \ No newline at end of file +- [Hashing through Chaining](hashing-chaining.md) +- [Hash Tables, Sets, Maps ](hash-tables.md) \ No newline at end of file From 4f096eb6a64c5e798f04a68740c7a8aae39b048c Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 8 Jun 2024 23:39:18 +0530 Subject: [PATCH 26/61] Update index.md --- contrib/advanced-python/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/advanced-python/index.md b/contrib/advanced-python/index.md index 59ea9b5..b093e44 100644 --- a/contrib/advanced-python/index.md +++ b/contrib/advanced-python/index.md @@ -12,7 +12,7 @@ - [Protocols](protocols.md) - [Exception Handling in Python](exception-handling.md) - [Generators](generators.md) -- [Match Case Statement](match_case_statement.md) +- [Match Case Statement](match-case.md) - [Closures](closures.md) - [Filter](filter-function.md) - [Reduce](reduce-function.md) From 7d18fe39d45bfdd2e4d432c8bc70b4c7496f7e2d Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 8 Jun 2024 23:39:52 +0530 Subject: [PATCH 27/61] Update and rename match_case_statement.md to match-case.md --- .../advanced-python/{match_case_statement.md => match-case.md} | 1 - 1 file changed, 1 deletion(-) rename contrib/advanced-python/{match_case_statement.md => match-case.md} (95%) diff --git a/contrib/advanced-python/match_case_statement.md b/contrib/advanced-python/match-case.md similarity index 95% rename from contrib/advanced-python/match_case_statement.md rename to contrib/advanced-python/match-case.md index b617f7a..1b4f017 100644 --- a/contrib/advanced-python/match_case_statement.md +++ b/contrib/advanced-python/match-case.md @@ -247,6 +247,5 @@ The match case statements provide an elegant and readible format to perform oper ## Further Reading This article provides a brief introduction to the match case statements and the overview on the pattern matching operations. To know more, the below articles can be used for in-depth understanding of the topic. -- [Python Match Case Statement - GeeksForGeeks](https://www.geeksforgeeks.org/python-match-case-statement/) - [PEP 634 – Structural Pattern Matching: Specification](https://peps.python.org/pep-0634/) - [PEP 636 – Structural Pattern Matching: Tutorial](https://peps.python.org/pep-0636/) From 10e40af9e97a57945f5a96ca1c2890ce17844cdb Mon Sep 17 00:00:00 2001 From: Ishita-Jena <167574361+Ishita-Jena@users.noreply.github.com> Date: Sun, 9 Jun 2024 04:01:25 +0530 Subject: [PATCH 28/61] Create binary_tree.md --- contrib/ds-algorithms/binary_tree.md | 71 ++++++++++++++++++++++++++++ 1 file changed, 71 insertions(+) create mode 100644 contrib/ds-algorithms/binary_tree.md diff --git a/contrib/ds-algorithms/binary_tree.md b/contrib/ds-algorithms/binary_tree.md new file mode 100644 index 0000000..fb11230 --- /dev/null +++ b/contrib/ds-algorithms/binary_tree.md @@ -0,0 +1,71 @@ +# Binary Tree + +A binary tree is a non-linear data structure in which each node can have atmost two children, known as the left and the right child. + +```python + A...................Level 0 + / \ + B C.................Level 1 + / \ \ + D E G...............Level 2 +``` + +## Basic Terminologies + +- **Root node:** The topmost node in a tree is the root node. The root node does not have any parent. In the example given above, **A** is the root node. +- **Parent node:** The predecessor of a node is called the parent of that node. **A** is the parent of **B** and **C**, **B** is the parent of **D** and **E** and **C** is the parent of **G**. +- **Child node:** The successor of a node is called the child of that node. **B** and **C** are children of **A**, **D** and **E** are children of **B** and **G** is the right child of **C**. +- **Leaf node:** Nodes without any children are called the leaf nodes. **D**, **E** and **G** are the leaf nodes. +- **Ancestor node:** Predecessor nodes on the path from the root to that node are called ancestor nodes. **A** and **B** are the ancestors of **E**. +- **Descendant node:** Successor nodes on the path from the root to that node are called descendant nodes. **B** and **E** are descendants of **A**. +- **Sibling node:** Nodes having the same parent are called sibling nodes. **B** and **C** are sibling nodes and so are **D** and **E**. +- **Level (Depth) of a node:** Number of edges in the path from the root to that node is the level of that node. The root node is always at level 0. The depth of root node is the depth of the tree. Nodes **D**, **E** and **G** are at level 2. +- **Height of a node:** Number of edges in the path from that node to the deepest leaf. The height of the root is the height of a tree. Height of nodes **B** and **C** are 1. + +## Types Of Binary Trees + +- **Full Binary Tree:** A binary tree where each node has 0 or 2 children is a full binary tree. +```python + A + / \ + B C + / \ + D E +``` +- **Complete Binary Tree:** A binary tree in which all levels are completely filled except the last level is a complete binary tree. Whenever new nodes are inserted, they are inserted from the left side. +```python + A + / \ + / \ + B C + / \ / + D E F +``` +- **Perfect Binary Tree:** A binary tree in which all nodes are completely filled, i.e., each node has two children is called a perfect binary tree. +```python + A + / \ + / \ + B C + / \ / \ + D E F G +``` +- **Skewed Binary Tree:** A binary tree in which each node has either 0 or 1 child is called a skewed binary tree. It is of two types - left skewed binary tree and right skewed binary tree. +```python + A A + \ / + B B + \ / + C C + Right skewed binary tree Left skewed binary tree +``` +- **Balanced Binary Tree:** A binary tree in which the height difference between the left and right subtree is not more than one and the subtrees are also balanced is a balanced binary tree. +```python + A + / \ + B C + / \ + D E +``` + +## Implementation of Binary Tree From ba59ef608ca96405abc6f9a9c14d2b1a26ed5ffe Mon Sep 17 00:00:00 2001 From: Ishita-Jena <167574361+Ishita-Jena@users.noreply.github.com> Date: Sun, 9 Jun 2024 04:02:49 +0530 Subject: [PATCH 29/61] Update index.md --- contrib/ds-algorithms/index.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 9c05b15..ecc4a10 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -15,4 +15,5 @@ - [Trie](trie.md) - [Two Pointer Technique](two-pointer-technique.md) - [Hashing through Linear Probing](hashing-linear-probing.md) -- [Hashing through Chaining](hashing-chaining.md) \ No newline at end of file +- [Hashing through Chaining](hashing-chaining.md) +- [Binary Tree](binary_tree.md) From 65e2aa42f851628e8aa1f5916236edc15aeae99b Mon Sep 17 00:00:00 2001 From: Kosuri Indu Date: Sun, 9 Jun 2024 09:33:07 +0530 Subject: [PATCH 30/61] Added AVL Trees in DSA section --- contrib/ds-algorithms/avl-trees.md | 185 +++++++++++++++++++++++++++++ contrib/ds-algorithms/index.md | 3 +- 2 files changed, 187 insertions(+), 1 deletion(-) create mode 100644 contrib/ds-algorithms/avl-trees.md diff --git a/contrib/ds-algorithms/avl-trees.md b/contrib/ds-algorithms/avl-trees.md new file mode 100644 index 0000000..b87e82c --- /dev/null +++ b/contrib/ds-algorithms/avl-trees.md @@ -0,0 +1,185 @@ +# AVL Tree + +In Data Structures and Algorithms, an **AVL Tree** is a self-balancing binary search tree (BST) where the difference between heights of left and right subtrees cannot be more than one for all nodes. It ensures that the tree remains balanced, providing efficient search, insertion, and deletion operations. + +## Points to be Remembered + +- **Balance Factor**: The difference in heights between the left and right subtrees of a node. It should be -1, 0, or +1 for all nodes in an AVL tree. +- **Rotations**: Tree rotations (left, right, left-right, right-left) are used to maintain the balance factor within the allowed range. + +## Real Life Examples of AVL Trees + +- **Databases**: AVL trees can be used to maintain large indexes for database tables, ensuring quick data retrieval. +- **File Systems**: Some file systems use AVL trees to keep track of free and used memory blocks. + +## Applications of AVL Trees + +AVL trees are used in various applications in Computer Science: + +- **Database Indexing** +- **Memory Allocation** +- **Network Routing Algorithms** + +Understanding these applications is essential for Software Development. + +## Operations in AVL Tree + +Key operations include: + +- **INSERT**: Insert a new element into the AVL tree. +- **SEARCH**: Find the position of an element in the AVL tree. +- **DELETE**: Remove an element from the AVL tree. + +## Implementing AVL Tree in Python + +```python +class AVLTreeNode: + def __init__(self, key): + self.key = key + self.left = None + self.right = None + self.height = 1 + +class AVLTree: + def insert(self, root, key): + if not root: + return AVLTreeNode(key) + + if key < root.key: + root.left = self.insert(root.left, key) + else: + root.right = self.insert(root.right, key) + + root.height = 1 + max(self.getHeight(root.left), self.getHeight(root.right)) + balance = self.getBalance(root) + + if balance > 1 and key < root.left.key: + return self.rotateRight(root) + if balance < -1 and key > root.right.key: + return self.rotateLeft(root) + if balance > 1 and key > root.left.key: + root.left = self.rotateLeft(root.left) + return self.rotateRight(root) + if balance < -1 and key < root.right.key: + root.right = self.rotateRight(root.right) + return self.rotateLeft(root) + + return root + + def search(self, root, key): + if not root or root.key == key: + return root + + if key < root.key: + return self.search(root.left, key) + + return self.search(root.right, key) + + def delete(self, root, key): + if not root: + return root + + if key < root.key: + root.left = self.delete(root.left, key) + elif key > root.key: + root.right = self.delete(root.right, key) + else: + if root.left is None: + temp = root.right + root = None + return temp + elif root.right is None: + temp = root.left + root = None + return temp + + temp = self.getMinValueNode(root.right) + root.key = temp.key + root.right = self.delete(root.right, temp.key) + + if root is None: + return root + + root.height = 1 + max(self.getHeight(root.left), self.getHeight(root.right)) + balance = self.getBalance(root) + + if balance > 1 and self.getBalance(root.left) >= 0: + return self.rotateRight(root) + if balance < -1 and self.getBalance(root.right) <= 0: + return self.rotateLeft(root) + if balance > 1 and self.getBalance(root.left) < 0: + root.left = self.rotateLeft(root.left) + return self.rotateRight(root) + if balance < -1 and self.getBalance(root.right) > 0: + root.right = self.rotateRight(root.right) + return self.rotateLeft(root) + + return root + + def rotateLeft(self, z): + y = z.right + T2 = y.left + y.left = z + z.right = T2 + z.height = 1 + max(self.getHeight(z.left), self.getHeight(z.right)) + y.height = 1 + max(self.getHeight(y.left), self.getHeight(y.right)) + return y + + def rotateRight(self, z): + y = z.left + T3 = y.right + y.right = z + z.left = T3 + z.height = 1 + max(self.getHeight(z.left), self.getHeight(z.right)) + y.height = 1 + max(self.getHeight(y.left), self.getHeight(y.right)) + return y + + def getHeight(self, root): + if not root: + return 0 + return root.height + + def getBalance(self, root): + if not root: + return 0 + return self.getHeight(root.left) - self.getHeight(root.right) + + def getMinValueNode(self, root): + if root is None or root.left is None: + return root + return self.getMinValueNode(root.left) + + def preOrder(self, root): + if not root: + return + print(root.key, end=' ') + self.preOrder(root.left) + self.preOrder(root.right) + +#Example usage +avl_tree = AVLTree() +root = None + +root = avl_tree.insert(root, 10) +root = avl_tree.insert(root, 20) +root = avl_tree.insert(root, 30) +root = avl_tree.insert(root, 40) +root = avl_tree.insert(root, 50) +root = avl_tree.insert(root, 25) + +print("Preorder traversal of the AVL tree is:") +avl_tree.preOrder(root) +``` + +## Output + +```markdown +Preorder traversal of the AVL tree is: +30 20 10 25 40 50 +``` + +## Complexity Analysis + +- **Insertion**: O(logn). Inserting a node involves traversing the height of the tree, which is logarithmic due to the balancing property. +- **Search**: O(logn). Searching for a node involves traversing the height of the tree. +- **Deletion**: O(log⁡n). Deleting a node involves traversing and potentially rebalancing the tree, maintaining the logarithmic height. \ No newline at end of file diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index 9c05b15..d3dbe73 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -15,4 +15,5 @@ - [Trie](trie.md) - [Two Pointer Technique](two-pointer-technique.md) - [Hashing through Linear Probing](hashing-linear-probing.md) -- [Hashing through Chaining](hashing-chaining.md) \ No newline at end of file +- [Hashing through Chaining](hashing-chaining.md) +- [AVL Trees](avl-trees.md) \ No newline at end of file From 6726d30e5590c5ed97ffbbc3b0d2c6d941656d3c Mon Sep 17 00:00:00 2001 From: Yogesh Vishwakarma <103316955+Yogeshkarma@users.noreply.github.com> Date: Sun, 9 Jun 2024 09:54:56 +0530 Subject: [PATCH 31/61] Create Universal-Functions.md Added Universal Functions file --- contrib/numpy/Universal-Functions.md | 130 +++++++++++++++++++++++++++ 1 file changed, 130 insertions(+) create mode 100644 contrib/numpy/Universal-Functions.md diff --git a/contrib/numpy/Universal-Functions.md b/contrib/numpy/Universal-Functions.md new file mode 100644 index 0000000..090f33c --- /dev/null +++ b/contrib/numpy/Universal-Functions.md @@ -0,0 +1,130 @@ +# Universal functions (ufunc) + +--- + +A `ufunc`, short for "`universal function`," is a fundamental concept in NumPy, a powerful library for numerical computing in Python. Universal functions are highly optimized, element-wise functions designed to perform operations on data stored in NumPy arrays. + + + +## Uses of Ufuncs in NumPy + +Universal functions (ufuncs) in NumPy provide a wide range of functionalities for efficient and powerful numerical computations. Below is a detailed explanation of their uses: + +### 1. **Element-wise Operations** +Ufuncs perform operations on each element of the arrays independently. + +```python +import numpy as np + +A = np.array([1, 2, 3, 4]) +B = np.array([5, 6, 7, 8]) + +# Element-wise addition +np.add(A, B) # Output: array([ 6, 8, 10, 12]) +``` + +### 2. **Broadcasting** +Ufuncs support broadcasting, allowing operations on arrays with different shapes, making it possible to perform operations without explicitly reshaping arrays. + +```python +C = np.array([1, 2, 3]) +D = np.array([[1], [2], [3]]) + +# Broadcasting addition +np.add(C, D) # Output: array([[2, 3, 4], [3, 4, 5], [4, 5, 6]]) +``` + +### 3. **Vectorization** +Ufuncs are vectorized, meaning they are implemented in low-level C code, allowing for fast execution and avoiding the overhead of Python loops. + +```python +# Vectorized square root +np.sqrt(A) # Output: array([1., 1.41421356, 1.73205081, 2.]) +``` + +### 4. **Type Flexibility** +Ufuncs handle various data types and perform automatic type casting as needed. + +```python +E = np.array([1.0, 2.0, 3.0]) +F = np.array([4, 5, 6]) + +# Addition with type casting +np.add(E, F) # Output: array([5., 7., 9.]) +``` + +### 5. **Reduction Operations** +Ufuncs support reduction operations, such as summing all elements of an array or finding the product of all elements. + +```python +# Summing all elements +np.add.reduce(A) # Output: 10 + +# Product of all elements +np.multiply.reduce(A) # Output: 24 +``` + +### 6. **Accumulation Operations** +Ufuncs can perform accumulation operations, which keep a running tally of the computation. + +```python +# Cumulative sum +np.add.accumulate(A) # Output: array([ 1, 3, 6, 10]) +``` + +### 7. **Reduceat Operations** +Ufuncs can perform segmented reductions using the `reduceat` method, which applies the ufunc at specified intervals. + +```python +G = np.array([0, 1, 2, 3, 4, 5, 6, 7]) +indices = [0, 2, 5] +np.add.reduceat(G, indices) # Output: array([ 1, 9, 18]) +``` + +### 8. **Outer Product** +Ufuncs can compute the outer product of two arrays, producing a matrix where each element is the result of applying the ufunc to each pair of elements from the input arrays. + +```python +# Outer product +np.multiply.outer([1, 2, 3], [4, 5, 6]) +# Output: array([[ 4, 5, 6], +# [ 8, 10, 12], +# [12, 15, 18]]) +``` + +### 9. **Out Parameter** +Ufuncs can use the `out` parameter to store results in a pre-allocated array, saving memory and improving performance. + +```python +result = np.empty_like(A) +np.multiply(A, B, out=result) # Output: array([ 5, 12, 21, 32]) +``` + +# Create Your Own Ufunc + +You can create custom ufuncs for specific needs using np.frompyfunc or np.vectorize, allowing Python functions to behave like ufuncs. + +Here, we are using `frompyfunc()` which takes three argument: + +1. function - the name of the function. +2. inputs - the number of input (arrays). +3. outputs - the number of output arrays. + +```python +def my_add(x, y): + return x + y + +my_add_ufunc = np.frompyfunc(my_add, 2, 1) +my_add_ufunc(A, B) # Output: array([ 6, 8, 10, 12], dtype=object) +``` +# Some Common Ufunc are + +Here are some commonly used ufuncs in NumPy: + +- **Arithmetic**: `np.add`, `np.subtract`, `np.multiply`, `np.divide` +- **Trigonometric**: `np.sin`, `np.cos`, `np.tan` +- **Exponential and Logarithmic**: `np.exp`, `np.log`, `np.log10` +- **Comparison**: `np.maximum`, `np.minimum`, `np.greater`, `np.less` +- **Logical**: `np.logical_and`, `np.logical_or`, `np.logical_not` + +For more such Ufunc, address to [Universal functions (ufunc) — NumPy](https://numpy.org/doc/stable/reference/ufuncs.html) From 9b4a621539a461ff0b4d283b4f07b8d5bb81b554 Mon Sep 17 00:00:00 2001 From: Yogesh Vishwakarma <103316955+Yogeshkarma@users.noreply.github.com> Date: Sun, 9 Jun 2024 09:56:16 +0530 Subject: [PATCH 32/61] Update index.md --- contrib/numpy/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/numpy/index.md b/contrib/numpy/index.md index 50e8046..2b0c357 100644 --- a/contrib/numpy/index.md +++ b/contrib/numpy/index.md @@ -11,3 +11,4 @@ - [Sorting NumPy Arrays](sorting-array.md) - [NumPy Array Iteration](array-iteration.md) - [Concatenation of Arrays](concatenation-of-arrays.md) +- [Universal Functions (Ufunc)](Universal-Functions.md) From aefb52e5b3e6a81e55dce1a22f4870b3ef0e2c69 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Sun, 9 Jun 2024 11:48:46 +0530 Subject: [PATCH 33/61] Update K-Means_Clustering.md --- contrib/machine-learning/K-Means_Clustering.md | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 859636b..83fbd80 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -76,6 +76,10 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. +## Reference +[[Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] + +[[A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] From 4e33c752407656390fd2b89398c837c67959bfcb Mon Sep 17 00:00:00 2001 From: Ishita-Jena <167574361+Ishita-Jena@users.noreply.github.com> Date: Sun, 9 Jun 2024 12:08:02 +0530 Subject: [PATCH 34/61] Update binary_tree.md --- contrib/ds-algorithms/binary_tree.md | 168 ++++++++++++++++++++++++++- 1 file changed, 164 insertions(+), 4 deletions(-) diff --git a/contrib/ds-algorithms/binary_tree.md b/contrib/ds-algorithms/binary_tree.md index fb11230..4891204 100644 --- a/contrib/ds-algorithms/binary_tree.md +++ b/contrib/ds-algorithms/binary_tree.md @@ -1,6 +1,6 @@ # Binary Tree -A binary tree is a non-linear data structure in which each node can have atmost two children, known as the left and the right child. +A binary tree is a non-linear data structure in which each node can have atmost two children, known as the left and the right child. It is a heirarchial data structure represented in the following way: ```python A...................Level 0 @@ -12,15 +12,15 @@ A binary tree is a non-linear data structure in which each node can have atmost ## Basic Terminologies -- **Root node:** The topmost node in a tree is the root node. The root node does not have any parent. In the example given above, **A** is the root node. +- **Root node:** The topmost node in a tree is the root node. The root node does not have any parent. In the above example, **A** is the root node. - **Parent node:** The predecessor of a node is called the parent of that node. **A** is the parent of **B** and **C**, **B** is the parent of **D** and **E** and **C** is the parent of **G**. - **Child node:** The successor of a node is called the child of that node. **B** and **C** are children of **A**, **D** and **E** are children of **B** and **G** is the right child of **C**. - **Leaf node:** Nodes without any children are called the leaf nodes. **D**, **E** and **G** are the leaf nodes. - **Ancestor node:** Predecessor nodes on the path from the root to that node are called ancestor nodes. **A** and **B** are the ancestors of **E**. - **Descendant node:** Successor nodes on the path from the root to that node are called descendant nodes. **B** and **E** are descendants of **A**. - **Sibling node:** Nodes having the same parent are called sibling nodes. **B** and **C** are sibling nodes and so are **D** and **E**. -- **Level (Depth) of a node:** Number of edges in the path from the root to that node is the level of that node. The root node is always at level 0. The depth of root node is the depth of the tree. Nodes **D**, **E** and **G** are at level 2. -- **Height of a node:** Number of edges in the path from that node to the deepest leaf. The height of the root is the height of a tree. Height of nodes **B** and **C** are 1. +- **Level (Depth) of a node:** Number of edges in the path from the root to that node is the level of that node. The root node is always at level 0. The depth of root node is the depth of the tree. +- **Height of a node:** Number of edges in the path from that node to the deepest leaf is the height of that node. The height of the root is the height of a tree. Height of node **A** is 2, nodes **B** and **C** is 1 and nodes **D**, **E** and **G** is 0. ## Types Of Binary Trees @@ -68,4 +68,164 @@ A binary tree is a non-linear data structure in which each node can have atmost D E ``` +## Real Life Applications Of Binary Tree + +- **File Systems:** File systems employ binary trees to organize the folders and files, facilitating efficient search and access of files. +- **Decision Trees:** Decision tree, a supervised learning algorithm, utilizes binary trees, with each node representing a decision and its edges showing the possible outcomes. +- **Routing Algorithms:** In routing algorithms, binary trees are used to efficiently transfer data packets from the source to destination through a network of nodes. +- **Searching and sorting Algorithms:** Searching algorithms like binary search and sorting algorithms like heapsort rely heavily on binary trees. + ## Implementation of Binary Tree + +```python +from collections import deque + +class Node: + def __init__(self, data): + self.data = data + self.left = None + self.right = None + +class Binary_tree: + @staticmethod + def insert(root, data): + if root is None: + return Node(data) + q = deque() + q.append(root) + while q: + temp = q.popleft() + if temp.left is None: + temp.left = Node(data) + break + else: + q.append(temp.left) + if temp.right is None: + temp.right = Node(data) + break + else: + q.append(temp.right) + return root + + @staticmethod + def inorder(root): + if not root: + return + b.inorder(root.left) + print(root.data, end=" ") + b.inorder(root.right) + + @staticmethod + def preorder(root): + if not root: + return + print(root.data, end=" ") + b.preorder(root.left) + b.preorder(root.right) + + @staticmethod + def postorder(root): + if not root: + return + b.postorder(root.left) + b.postorder(root.right) + print(root.data, end=" ") + + @staticmethod + def levelorder(root): + if not root: + return + q = deque() + q.append(root) + while q: + temp = q.popleft() + print(temp.data, end=" ") + if temp.left is not None: + q.append(temp.left) + if temp.right is not None: + q.append(temp.right) + + @staticmethod + def delete(root, value): + q = deque() + q.append(root) + while q: + temp = q.popleft() + if temp is value: + temp = None + return + if temp.right: + if temp.right is value: + temp.right = None + return + else: + q.append(temp.right) + if temp.left: + if temp.left is value: + temp.left = None + return + else: + q.append(temp.left) + + @staticmethod + def delete_value(root, value): + if root is None: + return None + if root.left is None and root.right is None: + if root.data == value: + return None + else: + return root + x = None + q = deque() + q.append(root) + temp = None + while q: + temp = q.popleft() + if temp.data == value: + x = temp + if temp.left: + q.append(temp.left) + if temp.right: + q.append(temp.right) + if x: + y = temp.data + x.data = y + b.delete(root, temp) + return root + +b = Binary_tree() +root = None +root = b.insert(root, 10) +root = b.insert(root, 20) +root = b.insert(root, 30) +root = b.insert(root, 40) +root = b.insert(root, 50) +root = b.insert(root, 60) + +print("Preorder traversal:", end=" ") +b.preorder(root) + +print("\nInorder traversal:", end=" ") +b.inorder(root) + +print("\nPostorder traversal:", end=" ") +b.postorder(root) + +print("\nLevel order traversal:", end=" ") +b.levelorder(root) + +root = b.delete_value(root, 20) +print("\nLevel order traversal after deletion:", end=" ") +b.levelorder(root) + + +''' +OUTPUT: +Preorder traversal: 10 20 40 50 30 60 +Inorder traversal: 40 20 50 10 60 30 +Postorder traversal: 40 50 20 60 30 10 +Level order traversal: 10 20 30 40 50 60 +Level order traversal after deletion: 10 60 30 40 50 +''' +``` From eee9f149f251c50fffcaede4c02a3a02610b60cc Mon Sep 17 00:00:00 2001 From: Ishita-Jena <167574361+Ishita-Jena@users.noreply.github.com> Date: Sun, 9 Jun 2024 12:26:28 +0530 Subject: [PATCH 35/61] Update binary_tree.md --- contrib/ds-algorithms/binary_tree.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/ds-algorithms/binary_tree.md b/contrib/ds-algorithms/binary_tree.md index 4891204..867bca0 100644 --- a/contrib/ds-algorithms/binary_tree.md +++ b/contrib/ds-algorithms/binary_tree.md @@ -73,7 +73,7 @@ A binary tree is a non-linear data structure in which each node can have atmost - **File Systems:** File systems employ binary trees to organize the folders and files, facilitating efficient search and access of files. - **Decision Trees:** Decision tree, a supervised learning algorithm, utilizes binary trees, with each node representing a decision and its edges showing the possible outcomes. - **Routing Algorithms:** In routing algorithms, binary trees are used to efficiently transfer data packets from the source to destination through a network of nodes. -- **Searching and sorting Algorithms:** Searching algorithms like binary search and sorting algorithms like heapsort rely heavily on binary trees. +- **Searching and sorting Algorithms:** Searching algorithms like binary search and sorting algorithms like heapsort heavily rely on binary trees. ## Implementation of Binary Tree From b2db560bad79ac5b389cd97e25de22ee26dfaa7b Mon Sep 17 00:00:00 2001 From: rohit Date: Mon, 10 Jun 2024 01:17:11 +0530 Subject: [PATCH 36/61] Added Neural network regression --- .../Neural network regression.md | 64 ++++++++----------- 1 file changed, 25 insertions(+), 39 deletions(-) diff --git a/contrib/machine-learning/Neural network regression.md b/contrib/machine-learning/Neural network regression.md index 36c3b9a..4330120 100644 --- a/contrib/machine-learning/Neural network regression.md +++ b/contrib/machine-learning/Neural network regression.md @@ -1,26 +1,24 @@ -# Neural Network Regression in Python +# Neural Network Regression in Python using Scikit-learn ## Overview -Neural Network Regression is a type of machine learning algorithm used to predict continuous values. Unlike classification, where the goal is to predict a category or class, regression aims to predict a specific numerical value. Neural networks are particularly powerful for regression tasks when dealing with complex, non-linear relationships in data. +Neural Network Regression is used to predict continuous values based on input features. Scikit-learn provides an easy-to-use interface for implementing neural network models, specifically through the `MLPRegressor` class, which stands for Multi-Layer Perceptron Regressor. ## When to Use Neural Network Regression ### Suitable Scenarios -1. **Complex Relationships**: When the relationship between input features and the target variable is non-linear and complex. -2. **Large Datasets**: When you have a large dataset that can support the training of a neural network. -3. **Feature Engineering**: When you can leverage the feature extraction capabilities of neural networks, especially in domains like image or text data. +1. **Complex Relationships**: Ideal when the relationship between features and the target variable is complex and non-linear. +2. **Sufficient Data**: Works well with large datasets that can support training deep learning models. +3. **Feature Extraction**: Useful in cases where the neural network's feature extraction capabilities can be leveraged, such as with image or text data. ### Unsuitable Scenarios -1. **Small Datasets**: Neural networks require substantial amounts of data to train effectively. For small datasets, simpler models like linear regression or decision trees might perform better. -2. **Real-time Predictions**: If low-latency predictions are required and computational resources are limited, simpler models might be more efficient. -3. **Interpretability**: If model interpretability is crucial, neural networks might not be the best choice due to their "black-box" nature. +1. **Small Datasets**: Less effective with small datasets due to overfitting and inability to learn complex patterns. +2. **Low-latency Predictions**: Might not be suitable for real-time applications with strict latency requirements. +3. **Interpretability**: Not ideal when model interpretability is crucial, as neural networks are often seen as "black-box" models. -## Implementing Neural Network Regression in Python - -We'll use TensorFlow and Keras, popular libraries for building and training neural networks in Python. +## Implementing Neural Network Regression in Python with Scikit-learn ### Step-by-Step Implementation @@ -31,9 +29,8 @@ import numpy as np import pandas as pd from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler -from tensorflow.keras.models import Sequential -from tensorflow.keras.layers import Dense -from tensorflow.keras.optimizers import Adam +from sklearn.neural_network import MLPRegressor +from sklearn.metrics import mean_absolute_error ``` 2. **Load and Prepare Data** @@ -55,44 +52,33 @@ X_train = scaler.fit_transform(X_train) X_test = scaler.transform(X_test) ``` -3. **Build the Neural Network Model** +3. **Build and Train the Neural Network Model** ```python -model = Sequential() -model.add(Dense(64, input_dim=X_train.shape[1], activation='relu')) -model.add(Dense(64, activation='relu')) -model.add(Dense(1)) # Output layer for regression +# Create the MLPRegressor model +mlp = MLPRegressor(hidden_layer_sizes=(64, 64), activation='relu', solver='adam', max_iter=500, random_state=42) -model.compile(optimizer=Adam(learning_rate=0.001), loss='mse', metrics=['mae']) +# Train the model +mlp.fit(X_train, y_train) ``` -4. **Train the Model** +4. **Evaluate the Model** ```python -history = model.fit(X_train, y_train, epochs=100, batch_size=32, validation_split=0.2) -``` +# Make predictions +y_pred = mlp.predict(X_test) -5. **Evaluate the Model** - -```python -loss, mae = model.evaluate(X_test, y_test) +# Calculate the Mean Absolute Error +mae = mean_absolute_error(y_test, y_pred) print(f"Test Mean Absolute Error: {mae}") ``` -6. **Make Predictions** - -```python -predictions = model.predict(X_test) -``` - ### Explanation -- **Data Generation and Preparation**: Synthetic data is created and split into training and test sets. The data is standardized to improve the neural network's training efficiency. -- **Model Construction**: A simple feedforward neural network is built using Keras. It consists of two hidden layers with 64 neurons each and ReLU activation functions. The output layer has a single neuron for regression. -- **Training**: The model is trained for 100 epochs with a batch size of 32. The Adam optimizer is used to adjust the weights. -- **Evaluation**: The model's performance is evaluated on the test set, using Mean Absolute Error (MAE) as a metric. -- **Prediction**: Predictions are made on the test data. +- **Data Generation and Preparation**: Synthetic data is created, split into training and test sets, and standardized to improve the efficiency of the neural network training process. +- **Model Construction and Training**: An `MLPRegressor` is created with two hidden layers, each containing 64 neurons and ReLU activation functions. The model is trained using the Adam optimizer for a maximum of 500 iterations. +- **Evaluation**: The model's performance is evaluated on the test set using Mean Absolute Error (MAE) as the performance metric. ## Conclusion -Neural Network Regression is a powerful tool for predicting continuous values, particularly in cases involving complex, non-linear relationships. However, they require large datasets and significant computational resources. For smaller datasets or scenarios requiring model interpretability, simpler models might be preferable. By following the steps outlined, you can build, train, and evaluate a neural network for regression tasks in Python using TensorFlow and Keras. \ No newline at end of file +Neural Network Regression with Scikit-learn's `MLPRegressor` is a powerful method for predicting continuous values in complex, non-linear scenarios. However, it's essential to ensure that you have enough data to train the model effectively and consider the computational resources required. Simpler models may be more appropriate for small datasets or when model interpretability is necessary. By following the steps outlined, you can build, train, and evaluate a neural network for regression tasks in Python using Scikit-learn. \ No newline at end of file From 6a03b12726c158ca77414cfa586f8e40c962da56 Mon Sep 17 00:00:00 2001 From: Lingamuneni Santhosh Siddhardha <103999924+Santhosh-Siddhardha@users.noreply.github.com> Date: Mon, 10 Jun 2024 11:57:56 +0530 Subject: [PATCH 37/61] Create magic-methods.md Added intro Added Commonly used methods Added examples Added Output Added Conclusion --- contrib/advanced-python/magic-methods.md | 151 +++++++++++++++++++++++ 1 file changed, 151 insertions(+) create mode 100644 contrib/advanced-python/magic-methods.md diff --git a/contrib/advanced-python/magic-methods.md b/contrib/advanced-python/magic-methods.md new file mode 100644 index 0000000..447e36b --- /dev/null +++ b/contrib/advanced-python/magic-methods.md @@ -0,0 +1,151 @@ +# Magic Methods + +Magic methods, also known as dunder (double underscore) methods, are special methods in Python that start and end with double underscores (`__`). +These methods allow you to define the behavior of objects for built-in operations and functions, enabling you to customize how your objects interact with the +language's syntax and built-in features. Magic methods make your custom classes integrate seamlessly with Python’s built-in data types and operations. + +**Commonly Used Magic Methods** + +1. **Initialization and Representation** + - `__init__(self, ...)`: Called when an instance of the class is created. Used for initializing the object's attributes. + - `__repr__(self)`: Returns a string representation of the object, useful for debugging and logging. + - `__str__(self)`: Returns a human-readable string representation of the object. + +**Example** : + + ```python + class Person: + def __init__(self, name, age): + self.name = name + self.age = age + + def __repr__(self): + return f"Person({self.name}, {self.age})" + + def __str__(self): + return f"{self.name}, {self.age} years old" + + p = Person("Alice", 30) + print(repr(p)) + print(str(p)) + ``` + +**Output** : +```python +Person("Alice",30) +Alice, 30 years old +``` + +2. **Arithmetic Operations** + - `__add__(self, other)`: Defines behavior for the `+` operator. + - `__sub__(self, other)`: Defines behavior for the `-` operator. + - `__mul__(self, other)`: Defines behavior for the `*` operator. + - `__truediv__(self, other)`: Defines behavior for the `/` operator. + + +**Example** : + + ```python + class Vector: + def __init__(self, x, y): + self.x = x + self.y = y + + def __add__(self, other): + return Vector(self.x + other.x, self.y + other.y) + + def __repr__(self): + return f"Vector({self.x}, {self.y})" + + v1 = Vector(2, 3) + v2 = Vector(1, 1) + v3 = v1 + v2 + print(v3) + ``` + +**Output** : + +```python +Vector(3, 4) +``` + +3. **Comparison Operations** + - `__eq__(self, other)`: Defines behavior for the `==` operator. + - `__lt__(self, other)`: Defines behavior for the `<` operator. + - `__le__(self, other)`: Defines behavior for the `<=` operator. + +**Example** : + + ```python + class Person: + def __init__(self, name, age): + self.name = name + self.age = age + + def __eq__(self, other): + return self.age == other.age + + def __lt__(self, other): + return self.age < other.age + + p1 = Person("Alice", 30) + p2 = Person("Bob", 25) + print(p1 == p2) + print(p1 < p2) + ``` + + **Output** : + + ```python + False + False + ``` + +5. **Container and Sequence Methods** + + - `__len__(self)`: Defines behavior for the `len()` function. + - `__getitem__(self, key)`: Defines behavior for indexing (`self[key]`). + - `__setitem__(self, key, value)`: Defines behavior for item assignment (`self[key] = value`). + - `__delitem__(self, key)`: Defines behavior for item deletion (`del self[key]`). + +**Example** : + + ```python + class CustomList: + def __init__(self, *args): + self.items = list(args) + + def __len__(self): + return len(self.items) + + def __getitem__(self, index): + return self.items[index] + + def __setitem__(self, index, value): + self.items[index] = value + + def __delitem__(self, index): + del self.items[index] + + def __repr__(self): + return f"CustomList({self.items})" + + cl = CustomList(1, 2, 3) + print(len(cl)) + print(cl[1]) + cl[1] = 5 + print(cl) + del cl[1] + print(cl) + ``` + +**Output** : +```python +3 +2 +CustomList([1, 5, 3]) +CustomList([1, 3]) +``` + +Magic methods provide powerful ways to customize the behavior of your objects and make them work seamlessly with Python's syntax and built-in functions. +Use them judiciously to enhance the functionality and readability of your classes. From 120f3eb9e6618508cb9b4244aff94a32e9f02348 Mon Sep 17 00:00:00 2001 From: Lingamuneni Santhosh Siddhardha <103999924+Santhosh-Siddhardha@users.noreply.github.com> Date: Mon, 10 Jun 2024 11:59:05 +0530 Subject: [PATCH 38/61] Update index.md Added Magic Methods section --- contrib/advanced-python/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/advanced-python/index.md b/contrib/advanced-python/index.md index b093e44..387ffd3 100644 --- a/contrib/advanced-python/index.md +++ b/contrib/advanced-python/index.md @@ -18,3 +18,4 @@ - [Reduce](reduce-function.md) - [List Comprehension](list-comprehension.md) - [Eval Function](eval_function.md) +- [Magic Methods](magic-methods.md) From bb38f8fb5a9418a359635dcbec275e77e364c6fa Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Wed, 12 Jun 2024 21:57:30 +0530 Subject: [PATCH 39/61] Update K-Means_Clustering.md --- .../machine-learning/K-Means_Clustering.md | 96 ++++++++++--------- 1 file changed, 53 insertions(+), 43 deletions(-) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/K-Means_Clustering.md index 83fbd80..ee615c3 100644 --- a/contrib/machine-learning/K-Means_Clustering.md +++ b/contrib/machine-learning/K-Means_Clustering.md @@ -1,19 +1,25 @@ # K-Means Clustering Unsupervised Learning Algorithm for Grouping Similar Data. + ## Introduction K-means clustering is a fundamental unsupervised machine learning algorithm that excels at grouping similar data points together. It's a popular choice due to its simplicity and efficiency in uncovering hidden patterns within unlabeled datasets. + ## Unsupervised Learning Unlike supervised learning algorithms that rely on labeled data for training, unsupervised algorithms, like K-means, operate solely on input data (without predefined categories). Their objective is to discover inherent structures or groupings within the data. + ## The K-Means Objective Organize similar data points into clusters to unveil underlying patterns. The main objective is to minimize total intra-cluster variance or the squared function. ![image](assets/knm.png) ## Clusters and Centroids A cluster represents a collection of data points that share similar characteristics. K-means identifies a pre-determined number (k) of clusters within the dataset. Each cluster is represented by a centroid, which acts as its central point (imaginary or real). + ## Minimizing In-Cluster Variation The K-means algorithm strategically assigns each data point to a cluster such that the total variation within each cluster (measured by the sum of squared distances between points and their centroid) is minimized. In simpler terms, K-means strives to create clusters where data points are close to their respective centroids. + ## The Meaning Behind "K-Means" The "means" in K-means refers to the averaging process used to compute the centroid, essentially finding the center of each cluster. + ## K-Means Algorithm in Action ![image](assets/km_.png) The K-means algorithm follows an iterative approach to optimize cluster formation: @@ -24,62 +30,66 @@ The K-means algorithm follows an iterative approach to optimize cluster formatio 4. **Iteration Until Convergence:** Steps 2 and 3 are repeated iteratively until a stopping criterion is met. This criterion can be either: - **Centroid Stability:** No significant change occurs in the centroids' positions, indicating successful clustering. - **Reaching Maximum Iterations:** A predefined number of iterations is completed. - ## Code - Following is a simple implementation of K-Means. + +## Code +Following is a simple implementation of K-Means. - - # Generate and Visualize Sample Data - # import the necessary Libraries - - import numpy as np - import matplotlib.pyplot as plt +```python +# Generate and Visualize Sample Data +# import the necessary Libraries - # Create data points for cluster 1 and cluster 2 - X = -2 * np.random.rand(100, 2) - X1 = 1 + 2 * np.random.rand(50, 2) - - # Combine data points from both clusters - X[50:100, :] = X1 - - # Plot data points and display the plot - plt.scatter(X[:, 0], X[:, 1], s=50, c='b') - plt.show() +import numpy as np +import matplotlib.pyplot as plt - # K-Means Model Creation and Training - from sklearn.cluster import KMeans - - # Create KMeans object with 2 clusters - kmeans = KMeans(n_clusters=2) - kmeans.fit(X) # Train the model on the data +# Create data points for cluster 1 and cluster 2 +X = -2 * np.random.rand(100, 2) +X1 = 1 + 2 * np.random.rand(50, 2) - # Visualize Data Points with Centroids - centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) +# Combine data points from both clusters +X[50:100, :] = X1 + +# Plot data points and display the plot +plt.scatter(X[:, 0], X[:, 1], s=50, c='b') +plt.show() - plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again - plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 - plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 - plt.show() # Display the plot with centroids +# K-Means Model Creation and Training +from sklearn.cluster import KMeans - # Predict Cluster Label for New Data Point - new_data = np.array([-3.0, -3.0]) - new_data_reshaped = new_data.reshape(1, -1) - predicted_cluster = kmeans.predict(new_data_reshaped) - print("Predicted cluster for new data:", predicted_cluster) +# Create KMeans object with 2 clusters +kmeans = KMeans(n_clusters=2) +kmeans.fit(X) # Train the model on the data - ### Output: - Before Implementing K-Means Clustering +# Visualize Data Points with Centroids +centroids = kmeans.cluster_centers_ # Get centroids (cluster centers) + +plt.scatter(X[:, 0], X[:, 1], s=50, c='b') # Plot data points again +plt.scatter(centroids[0, 0], centroids[0, 1], s=200, c='g', marker='s') # Plot centroid 1 +plt.scatter(centroids[1, 0], centroids[1, 1], s=200, c='r', marker='s') # Plot centroid 2 +plt.show() # Display the plot with centroids + +# Predict Cluster Label for New Data Point +new_data = np.array([-3.0, -3.0]) +new_data_reshaped = new_data.reshape(1, -1) +predicted_cluster = kmeans.predict(new_data_reshaped) +print("Predicted cluster for new data:", predicted_cluster) +``` + +### Output: +Before Implementing K-Means Clustering ![Before Implementing K-Means Clustering](assets/km_2.png) - After Implementing K-Means Clustering - ![After Implementing K-Means Clustering](assets/km_3.png) +After Implementing K-Means Clustering +![After Implementing K-Means Clustering](assets/km_3.png) + +Predicted cluster for new data: `[0]` - Predicted cluster for new data: [0] ## Conclusion **K-Means** can be applied to data that has a smaller number of dimensions, is numeric, and is continuous or can be used to find groups that have not been explicitly labeled in the data. As an example, it can be used for Document Classification, Delivery Store Optimization, or Customer Segmentation. -## Reference -[[Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] -[[A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ)] +## References + +- [Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) +- [A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) From cf01273be27a0d9f82c45a41e505fde46360b749 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Wed, 12 Jun 2024 21:58:13 +0530 Subject: [PATCH 40/61] Update and rename K-Means_Clustering.md to kmeans.md --- contrib/machine-learning/{K-Means_Clustering.md => kmeans.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/machine-learning/{K-Means_Clustering.md => kmeans.md} (100%) diff --git a/contrib/machine-learning/K-Means_Clustering.md b/contrib/machine-learning/kmeans.md similarity index 100% rename from contrib/machine-learning/K-Means_Clustering.md rename to contrib/machine-learning/kmeans.md From 8f0e9808356ae8a02937d490f8952f3de28a42e4 Mon Sep 17 00:00:00 2001 From: Revanth <109272714+revanth1718@users.noreply.github.com> Date: Wed, 12 Jun 2024 22:16:20 +0530 Subject: [PATCH 41/61] Update index.md --- contrib/machine-learning/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/machine-learning/index.md b/contrib/machine-learning/index.md index b6945cd..6227561 100644 --- a/contrib/machine-learning/index.md +++ b/contrib/machine-learning/index.md @@ -16,3 +16,4 @@ - [Types_of_Cost_Functions](cost-functions.md) - [Clustering](clustering.md) - [Grid Search](grid-search.md) +- [K-Means](kmeans.md) From 51011db02b624db7723f246984e3a2d9644c5d57 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Thu, 13 Jun 2024 00:38:06 +0530 Subject: [PATCH 42/61] Update kmeans.md --- contrib/machine-learning/kmeans.md | 8 -------- 1 file changed, 8 deletions(-) diff --git a/contrib/machine-learning/kmeans.md b/contrib/machine-learning/kmeans.md index ee615c3..52db92e 100644 --- a/contrib/machine-learning/kmeans.md +++ b/contrib/machine-learning/kmeans.md @@ -90,11 +90,3 @@ Predicted cluster for new data: `[0]` - [Survey of Machine Learning and Data Mining Techniques used in Multimedia System](https://www.researchgate.net/publication/333457161_Survey_of_Machine_Learning_and_Data_Mining_Techniques_used_in_Multimedia_System?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) - [A Clustering Approach for Outliers Detection in a Big Point-of-Sales Database](https://www.researchgate.net/publication/339267868_A_Clustering_Approach_for_Outliers_Detection_in_a_Big_Point-of-Sales_Database?_tp=eyJjb250ZXh0Ijp7ImZpcnN0UGFnZSI6Il9kaXJlY3QiLCJwYWdlIjoiX2RpcmVjdCJ9fQ) - - - - - - - - From 41e41d804d105358a512e7a6aaa0feb1e3db4522 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Thu, 13 Jun 2024 01:33:30 +0530 Subject: [PATCH 43/61] Update dynamic-programming.md --- contrib/ds-algorithms/dynamic-programming.md | 20 +++----------------- 1 file changed, 3 insertions(+), 17 deletions(-) diff --git a/contrib/ds-algorithms/dynamic-programming.md b/contrib/ds-algorithms/dynamic-programming.md index 54c6fcb..0f16d5c 100644 --- a/contrib/ds-algorithms/dynamic-programming.md +++ b/contrib/ds-algorithms/dynamic-programming.md @@ -51,10 +51,6 @@ print(f"The {n}th Fibonacci number is: {fibonacci(n)}.") - **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. @@ -112,10 +108,6 @@ print("Length of LCS is", longestCommonSubsequence(S1, S2, m, n)) - **Time Complexity**: O(m * n) for both approaches, 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. @@ -146,6 +138,7 @@ capacity = 50 n = len(weights) print("Maximum value that can be obtained:", knapsack(weights, values, capacity, n)) ``` + ## 0-1 Knapsack Problem Code in Python (Bottom-up Approach) ```python @@ -170,14 +163,11 @@ capacity = 50 n = len(weights) print(knapSack(capacity, weights, values, n)) ``` + ## Complexity Analysis - **Time Complexity**: O(n * W) for both approaches, where n is the number of items and W is the capacity of the knapsack - **Space Complexity**: O(n * W) for the memoization table -
-
-
- # 4. Longest Increasing Subsequence The Longest Increasing Subsequence (LIS) is a task is to find the longest subsequence that is strictly increasing, meaning each element in the subsequence is greater than the one before it. This subsequence must maintain the order of elements as they appear in the original sequence but does not need to be contiguous. The goal is to identify the subsequence with the maximum possible length. @@ -190,7 +180,6 @@ The Longest Increasing Subsequence (LIS) is a task is to find the longest subseq ## Longest Increasing Subsequence Code in Python (Top-Down Approach using Memoization) ```python - import sys def f(idx, prev_idx, n, a, dp): @@ -241,10 +230,7 @@ def lis(arr): arr = [10, 22, 9, 33, 21, 50, 41, 60] print("Length of lis is", lis(arr)) ``` + ## Complexity Analysis - **Time Complexity**: O(n * n) for both approaches, where n is the length of the array. - **Space Complexity**: O(n * n) for the memoization table in Top-Down Approach, O(n) in Bottom-Up Approach. - -
-
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9961a0c9f80160a2b28db22b802b45c77ff22d1f Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Thu, 13 Jun 2024 22:30:27 +0530 Subject: [PATCH 46/61] Rename Dijkstra's_algorithm photo2.png to Dijkstra's_algorithm_photo2.png --- ...m photo2.png => Dijkstra's_algorithm_photo2.png} | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/ds-algorithms/images/{Dijkstra's_algorithm photo2.png => Dijkstra's_algorithm_photo2.png} (100%) diff --git a/contrib/ds-algorithms/images/Dijkstra's_algorithm photo2.png b/contrib/ds-algorithms/images/Dijkstra's_algorithm_photo2.png similarity index 100% rename from contrib/ds-algorithms/images/Dijkstra's_algorithm photo2.png rename to contrib/ds-algorithms/images/Dijkstra's_algorithm_photo2.png From 3e7e46969390235b3c12fbef8be0522f52dc4155 Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Thu, 13 Jun 2024 22:31:20 +0530 Subject: [PATCH 47/61] Rename Dijkstra's_algorithm photo3.png to Dijkstra's_algorithm_photo3.png --- ...m photo3.png => Dijkstra's_algorithm_photo3.png} | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/ds-algorithms/images/{Dijkstra's_algorithm photo3.png => Dijkstra's_algorithm_photo3.png} (100%) diff --git a/contrib/ds-algorithms/images/Dijkstra's_algorithm photo3.png b/contrib/ds-algorithms/images/Dijkstra's_algorithm_photo3.png similarity index 100% rename from contrib/ds-algorithms/images/Dijkstra's_algorithm photo3.png rename to contrib/ds-algorithms/images/Dijkstra's_algorithm_photo3.png From 77f20e9908d4be3e616e9ccefd4f0e5c9c672648 Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Thu, 13 Jun 2024 22:31:43 +0530 Subject: [PATCH 48/61] Rename Dijkstra's_algorithm photo4.png to Dijkstra's_algorithm_photo4.png --- ...m photo4.png => Dijkstra's_algorithm_photo4.png} | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/ds-algorithms/images/{Dijkstra's_algorithm photo4.png => Dijkstra's_algorithm_photo4.png} (100%) diff --git a/contrib/ds-algorithms/images/Dijkstra's_algorithm photo4.png b/contrib/ds-algorithms/images/Dijkstra's_algorithm_photo4.png similarity index 100% rename from contrib/ds-algorithms/images/Dijkstra's_algorithm photo4.png rename to contrib/ds-algorithms/images/Dijkstra's_algorithm_photo4.png From c32dc12b1a7ea1dd1bcf6e1576f308b01d4e3d56 Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Thu, 13 Jun 2024 22:32:03 +0530 Subject: [PATCH 49/61] Rename Dijkstra's_algorithm photo5.png to Dijkstra's_algorithm_photo5.png --- ...m photo5.png => Dijkstra's_algorithm_photo5.png} | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/ds-algorithms/images/{Dijkstra's_algorithm photo5.png => Dijkstra's_algorithm_photo5.png} (100%) diff --git a/contrib/ds-algorithms/images/Dijkstra's_algorithm photo5.png b/contrib/ds-algorithms/images/Dijkstra's_algorithm_photo5.png similarity index 100% rename from contrib/ds-algorithms/images/Dijkstra's_algorithm photo5.png rename to contrib/ds-algorithms/images/Dijkstra's_algorithm_photo5.png From 01207f441c592d8a00411aa41b89f533458da6ef Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Thu, 13 Jun 2024 22:32:22 +0530 Subject: [PATCH 50/61] Rename Dijkstra's_algorithm photo6.png to Dijkstra's_algorithm_photo6.png --- ...m photo6.png => Dijkstra's_algorithm_photo6.png} | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/ds-algorithms/images/{Dijkstra's_algorithm photo6.png => Dijkstra's_algorithm_photo6.png} (100%) diff --git a/contrib/ds-algorithms/images/Dijkstra's_algorithm photo6.png b/contrib/ds-algorithms/images/Dijkstra's_algorithm_photo6.png similarity index 100% rename from contrib/ds-algorithms/images/Dijkstra's_algorithm photo6.png rename to contrib/ds-algorithms/images/Dijkstra's_algorithm_photo6.png From d98376b7da3417e9b1b8bb60b00e0e0092c86267 Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Thu, 13 Jun 2024 22:32:40 +0530 Subject: [PATCH 51/61] Rename Dijkstra's_algorithm photo7.png to Dijkstra's_algorithm_photo7.png --- ...m photo7.png => Dijkstra's_algorithm_photo7.png} | Bin 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/ds-algorithms/images/{Dijkstra's_algorithm photo7.png => Dijkstra's_algorithm_photo7.png} (100%) diff --git a/contrib/ds-algorithms/images/Dijkstra's_algorithm photo7.png b/contrib/ds-algorithms/images/Dijkstra's_algorithm_photo7.png similarity index 100% rename from contrib/ds-algorithms/images/Dijkstra's_algorithm photo7.png rename to contrib/ds-algorithms/images/Dijkstra's_algorithm_photo7.png From 85ecb2cabcda3c16c72480e6268f1e946d36c76d Mon Sep 17 00:00:00 2001 From: yashasvi232 <154299201+yashasvi232@users.noreply.github.com> Date: Thu, 13 Jun 2024 22:33:49 +0530 Subject: [PATCH 52/61] Update Dijkstra's_algorithm.md --- contrib/ds-algorithms/Dijkstra's_algorithm.md | 16 +++++++++------- 1 file changed, 9 insertions(+), 7 deletions(-) diff --git a/contrib/ds-algorithms/Dijkstra's_algorithm.md b/contrib/ds-algorithms/Dijkstra's_algorithm.md index 18845f6..cea6da4 100644 --- a/contrib/ds-algorithms/Dijkstra's_algorithm.md +++ b/contrib/ds-algorithms/Dijkstra's_algorithm.md @@ -13,23 +13,25 @@ Dijkstra's algorithm is a graph algorithm that gives the shortest distance of ea ## Dry Run We will now do a manual simulation using an example graph given. First, (0, a) is pushed to the priority queue (pq). -![gssoc photo 1](https://github.com/animator/learn-python/assets/154299201/713cf7dd-fa8a-4f81-829f-00ac33eb12f4) +![Photo 1](images/Dijkstra's_algorithm_photo1.png) + - **Step1:** The lowest element is popped from the pq, which is (0, a), and all its neighboring nodes are added to the pq while simultaneously checking the distance list. Thus (3, b), (7, c), (1, d) are added to the pq. -![gssoc photo2](https://github.com/animator/learn-python/assets/154299201/9456b701-7877-44dc-854b-da416c5e2e9b) +![Photo 2](images/Dijkstra's_algorithm_photo2.png) + - **Step2:** Again, the lowest element is popped from the pq, which is (1, d). It has two neighboring nodes, a and e, from which (0 + 1, a) will not be added to the pq as dist[a] = 0 is less than 1. -![gssoc photo3](https://github.com/animator/learn-python/assets/154299201/83990a40-f3fc-4173-9e21-10eb9e2003cb) +![Photo 3](images/Dijkstra's_algorithm_photo3.png) - **Step3:** Now, the lowest element is popped from the pq, which is (3, b). It has two neighboring nodes, a and c, from which (0 + 1, a) will not be added to the pq. But the new distance to reach c is 5 (3 + 2), which is less than dist[c] = 7. So (5, c) is added to the pq. -![gssoc photo4](https://github.com/animator/learn-python/assets/154299201/b47eb063-8ce7-4e68-85a5-da98f5ac9a3d) +![Photo 4](images/Dijkstra's_algorithm_photo4.png) - **Step4:** The next smallest element is (5, c). It has neighbors a and e. The new distance to reach a will be 5 + 7 = 12, which is more than dist[a], so it will not be considered. Similarly, the new distance for e is 5 + 3 = 8, which again will not be considered. So, no new tuple has been added to the pq. -![gssoc photo5](https://github.com/animator/learn-python/assets/154299201/c0ef3c2a-1938-4c33-9e07-0929e8e5e631) +![Photo 5](images/Dijkstra's_algorithm_photo5.png) - **Step5:** Similarly, both the elements of the pq will be popped one by one without any new addition. -![gssoc photo6](https://github.com/animator/learn-python/assets/154299201/828739c6-413b-41f6-a09f-b702802b20e1) -![gssoc photo7](https://github.com/animator/learn-python/assets/154299201/488d4c7b-d7bf-4887-a9c5-04accc6c6c89) +![Photo 6](images/Dijkstra's_algorithm_photo6.png) +![Photo 7](images/Dijkstra's_algorithm_photo7.png) - The distance list we get at the end will be our answer. - `Output` `dist=[1, 3, 7, 1, 6]` From 848af819957763fa9a3231cd62265e2fb6081057 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 15 Jun 2024 23:34:33 +0530 Subject: [PATCH 53/61] Rename Dijkstra's_algorithm.md to dijkstra.md --- contrib/ds-algorithms/{Dijkstra's_algorithm.md => dijkstra.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/ds-algorithms/{Dijkstra's_algorithm.md => dijkstra.md} (100%) diff --git a/contrib/ds-algorithms/Dijkstra's_algorithm.md b/contrib/ds-algorithms/dijkstra.md similarity index 100% rename from contrib/ds-algorithms/Dijkstra's_algorithm.md rename to contrib/ds-algorithms/dijkstra.md From fbc528b00bb794b358064b0585cbc1da23bd0d93 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 15 Jun 2024 23:34:50 +0530 Subject: [PATCH 54/61] Update index.md --- contrib/ds-algorithms/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index e1d12ce..047b3dd 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -18,4 +18,4 @@ - [Hashing through Chaining](hashing-chaining.md) - [AVL Trees](avl-trees.md) - [Splay Trees](splay-trees.md) -- [Dijkstra's Algorithm](Dijkstra's_algorithm.md) \ No newline at end of file +- [Dijkstra's Algorithm](dijkstra.md) From 8be8ae0b6e3ed7eab44655b91ce5790b56d27038 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Tue, 18 Jun 2024 03:15:08 +0530 Subject: [PATCH 55/61] Rename Universal-Functions.md to universal-functions.md --- contrib/numpy/{Universal-Functions.md => universal-functions.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/numpy/{Universal-Functions.md => universal-functions.md} (100%) diff --git a/contrib/numpy/Universal-Functions.md b/contrib/numpy/universal-functions.md similarity index 100% rename from contrib/numpy/Universal-Functions.md rename to contrib/numpy/universal-functions.md From 7f43373d0e9844dbb366e23b559794c3d5301f1f Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Tue, 18 Jun 2024 03:15:29 +0530 Subject: [PATCH 56/61] Update index.md --- contrib/numpy/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/numpy/index.md b/contrib/numpy/index.md index 2b0c357..a61195b 100644 --- a/contrib/numpy/index.md +++ b/contrib/numpy/index.md @@ -11,4 +11,4 @@ - [Sorting NumPy Arrays](sorting-array.md) - [NumPy Array Iteration](array-iteration.md) - [Concatenation of Arrays](concatenation-of-arrays.md) -- [Universal Functions (Ufunc)](Universal-Functions.md) +- [Universal Functions (Ufunc)](universal-functions.md) From 6822f4238aa09e266d340bab9d82950181721d4f Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 15:44:24 +0530 Subject: [PATCH 57/61] Update binary_tree.md --- contrib/ds-algorithms/binary_tree.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/contrib/ds-algorithms/binary_tree.md b/contrib/ds-algorithms/binary_tree.md index 867bca0..03da2cf 100644 --- a/contrib/ds-algorithms/binary_tree.md +++ b/contrib/ds-algorithms/binary_tree.md @@ -2,7 +2,7 @@ A binary tree is a non-linear data structure in which each node can have atmost two children, known as the left and the right child. It is a heirarchial data structure represented in the following way: -```python +``` A...................Level 0 / \ B C.................Level 1 @@ -25,7 +25,7 @@ A binary tree is a non-linear data structure in which each node can have atmost ## Types Of Binary Trees - **Full Binary Tree:** A binary tree where each node has 0 or 2 children is a full binary tree. -```python +``` A / \ B C @@ -33,7 +33,7 @@ A binary tree is a non-linear data structure in which each node can have atmost D E ``` - **Complete Binary Tree:** A binary tree in which all levels are completely filled except the last level is a complete binary tree. Whenever new nodes are inserted, they are inserted from the left side. -```python +``` A / \ / \ @@ -42,7 +42,7 @@ A binary tree is a non-linear data structure in which each node can have atmost D E F ``` - **Perfect Binary Tree:** A binary tree in which all nodes are completely filled, i.e., each node has two children is called a perfect binary tree. -```python +``` A / \ / \ @@ -51,7 +51,7 @@ A binary tree is a non-linear data structure in which each node can have atmost D E F G ``` - **Skewed Binary Tree:** A binary tree in which each node has either 0 or 1 child is called a skewed binary tree. It is of two types - left skewed binary tree and right skewed binary tree. -```python +``` A A \ / B B @@ -60,7 +60,7 @@ A binary tree is a non-linear data structure in which each node can have atmost Right skewed binary tree Left skewed binary tree ``` - **Balanced Binary Tree:** A binary tree in which the height difference between the left and right subtree is not more than one and the subtrees are also balanced is a balanced binary tree. -```python +``` A / \ B C @@ -218,14 +218,14 @@ b.levelorder(root) root = b.delete_value(root, 20) print("\nLevel order traversal after deletion:", end=" ") b.levelorder(root) +``` +#### OUTPUT -''' -OUTPUT: +``` Preorder traversal: 10 20 40 50 30 60 Inorder traversal: 40 20 50 10 60 30 Postorder traversal: 40 50 20 60 30 10 Level order traversal: 10 20 30 40 50 60 Level order traversal after deletion: 10 60 30 40 50 -''' ``` From 00949d96ec517120f7eac1adc946bc1bd9aeaffa Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 15:44:45 +0530 Subject: [PATCH 58/61] Rename binary_tree.md to binary-tree.md --- contrib/ds-algorithms/{binary_tree.md => binary-tree.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/ds-algorithms/{binary_tree.md => binary-tree.md} (100%) diff --git a/contrib/ds-algorithms/binary_tree.md b/contrib/ds-algorithms/binary-tree.md similarity index 100% rename from contrib/ds-algorithms/binary_tree.md rename to contrib/ds-algorithms/binary-tree.md From 1c0d60b5d67b9155c473eb65549fd7850d2369dc Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 15:45:35 +0530 Subject: [PATCH 59/61] Update index.md --- contrib/ds-algorithms/index.md | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/contrib/ds-algorithms/index.md b/contrib/ds-algorithms/index.md index dda6713..f6249d1 100644 --- a/contrib/ds-algorithms/index.md +++ b/contrib/ds-algorithms/index.md @@ -16,8 +16,7 @@ - [Two Pointer Technique](two-pointer-technique.md) - [Hashing through Linear Probing](hashing-linear-probing.md) - [Hashing through Chaining](hashing-chaining.md) -- [Binary Tree](binary_tree.md) +- [Binary Tree](binary-tree.md) - [AVL Trees](avl-trees.md) - [Splay Trees](splay-trees.md) -- [Splay Trees](splay-trees.md) - [Dijkstra's Algorithm](dijkstra.md) From d977cd8d2e683db43181157df219336ab05ea926 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 15:57:59 +0530 Subject: [PATCH 60/61] Rename Neural network regression.md to neural-network-regression.md --- ...eural network regression.md => neural-network-regression.md} | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) rename contrib/machine-learning/{Neural network regression.md => neural-network-regression.md} (99%) diff --git a/contrib/machine-learning/Neural network regression.md b/contrib/machine-learning/neural-network-regression.md similarity index 99% rename from contrib/machine-learning/Neural network regression.md rename to contrib/machine-learning/neural-network-regression.md index 4330120..aa16bc6 100644 --- a/contrib/machine-learning/Neural network regression.md +++ b/contrib/machine-learning/neural-network-regression.md @@ -81,4 +81,4 @@ print(f"Test Mean Absolute Error: {mae}") ## Conclusion -Neural Network Regression with Scikit-learn's `MLPRegressor` is a powerful method for predicting continuous values in complex, non-linear scenarios. However, it's essential to ensure that you have enough data to train the model effectively and consider the computational resources required. Simpler models may be more appropriate for small datasets or when model interpretability is necessary. By following the steps outlined, you can build, train, and evaluate a neural network for regression tasks in Python using Scikit-learn. \ No newline at end of file +Neural Network Regression with Scikit-learn's `MLPRegressor` is a powerful method for predicting continuous values in complex, non-linear scenarios. However, it's essential to ensure that you have enough data to train the model effectively and consider the computational resources required. Simpler models may be more appropriate for small datasets or when model interpretability is necessary. By following the steps outlined, you can build, train, and evaluate a neural network for regression tasks in Python using Scikit-learn. From 61e8ed73707194f7c49aef6b399a3b9dd85ddee7 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 15:58:20 +0530 Subject: [PATCH 61/61] Update index.md --- contrib/machine-learning/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/machine-learning/index.md b/contrib/machine-learning/index.md index 82fbbcc..d3ae109 100644 --- a/contrib/machine-learning/index.md +++ b/contrib/machine-learning/index.md @@ -20,4 +20,4 @@ - [Grid Search](grid-search.md) - [Transformers](transformers.md) - [K-nearest neighbor (KNN)](knn.md) -- [Neural network regression](Neural network regression.md) +- [Neural network regression](neural-network-regression.md)

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