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docs/python/getting-started-py.md delete mode 100644 docs/python/image-1.png delete mode 100644 docs/python/image-2.png delete mode 100644 docs/python/image.png delete mode 100644 docs/python/intro-py.md delete mode 100644 docs/python/json.md delete mode 100644 docs/python/loops.md delete mode 100644 docs/python/math-in-python.md delete mode 100644 docs/python/pip.md delete mode 100644 docs/python/resource.md diff --git a/docs/Nodemailer/HowtoSecure.md b/docs/Nodemailer/HowtoSecure.md deleted file mode 100644 index 38c8a1a8b..000000000 --- a/docs/Nodemailer/HowtoSecure.md +++ /dev/null @@ -1,57 +0,0 @@ ---- -id: nodemailer-secure -title: Nodemailer Security -sidebar_label: Security -sidebar_position: 4 -description: How to secure the password and mail address. -tags: [Node.Js, NodeMailer, env , SMTP ,JavaScript framework] ---- -How to secure the mail address and Password: - -### Environment Variables (Recommended) - -It's good practice to keep your email credentials secure by using environment variables. You can use the `dotenv` package to manage these variables. - -1. **Install the `dotenv` package**: - ```bash - npm install dotenv - ``` - -2. **Create a `.env` file in your project root** and add your credentials: - ``` - EMAIL=your-email@gmail.com - PASSWORD=your-email-password - ``` - -3. **Modify your `sendEmail.js` file to use `dotenv`**: - ```javascript - const nodemailer = require('nodemailer'); - require('dotenv').config(); - - // Create a transporter object - let transporter = nodemailer.createTransport({ - service: 'gmail', - auth: { - user: process.env.EMAIL, - pass: process.env.PASSWORD - } - }); - - // Define email options - let mailOptions = { - from: process.env.EMAIL, - to: 'recipient@example.com', - subject: 'Test Email', - text: 'Hello, this is a test email sent using Nodemailer!', - html: 'Hello, this is a test email sent using Nodemailer!' - }; - - // Send the email - transporter.sendMail(mailOptions, (error, info) => { - if (error) { - return console.log(error); - } - console.log('Email sent: ' + info.response); - }); - ``` - \ No newline at end of file diff --git a/docs/Nodemailer/Introduction.md b/docs/Nodemailer/Introduction.md deleted file mode 100644 index a13edc951..000000000 --- a/docs/Nodemailer/Introduction.md +++ /dev/null @@ -1,18 +0,0 @@ ---- -id: nodemailer-intro -title: Nodemailer -sidebar_label: Introduction -sidebar_position: 1 -description: Nodemailer is a module for Node.js applications that allows you to send emails. -tags: [Node.Js, NodeMailer, env , SMTP ,JavaScript framework] ---- - -Nodemailer is a module for Node.js applications that allows you to send emails. It is designed to be easy to set up and use, providing a straightforward API for sending emails through various email services and SMTP servers. Here are some key features and components of Nodemailer: - -1. **SMTP Support**: Nodemailer supports sending emails using SMTP (Simple Mail Transfer Protocol), allowing you to use your own email server or a third-party service like Gmail, Outlook, or Yahoo Mail. - -2. **Transporters**: A transporter is an object that defines how emails are sent. Nodemailer provides several built-in transport methods, including SMTP, Sendmail, and more. You can also create custom transport methods if needed. - -3. **Email Formatting**: Nodemailer supports both plain text and HTML email bodies, making it easy to create rich, formatted emails. It also supports attachments, inline images, and various encoding methods. - -4. **Authentication**: Nodemailer supports various authentication mechanisms, including OAuth2, making it secure and flexible for different use cases. diff --git a/docs/Nodemailer/Setup.md b/docs/Nodemailer/Setup.md deleted file mode 100644 index a839fc520..000000000 --- a/docs/Nodemailer/Setup.md +++ /dev/null @@ -1,52 +0,0 @@ ---- -id: nodemailer-installation -title: Installation -sidebar_label: Installation -sidebar_position: 2 -description: How to Install Nodemailer. -tags: [Node.Js, NodeMailer, env , SMTP ,JavaScript framework] ---- - -To install Nodemailer in your Node.js project, follow these steps: - -### Step 1: Initialize Your Project - -First, make sure you have Node.js and npm installed. If not, you can download and install them from the [official Node.js website](https://nodejs.org/). - -1. **Create a new directory for your project** (if you don't already have one): - ```bash - mkdir my-project - cd my-project - ``` - -2. **Initialize a new Node.js project**: - ```bash - npm init -y - ``` - -### Step 2: Install Nodemailer - -You can install Nodemailer using npm. Run the following command in your project directory: - -```bash -npm install nodemailer -``` - -This command will install Nodemailer and add it to your `package.json` file as a dependency. - -### Setp 3: How Import - -Two methods to import the package - -- In node & Express Js -```bash -const nodemailer=require('nodemailer') -``` - -- In another ES6 method - -```bash -import nodemailer from 'nodemailer' -``` - - diff --git a/docs/Nodemailer/_category_.json b/docs/Nodemailer/_category_.json deleted file mode 100644 index 04fecbfe4..000000000 --- a/docs/Nodemailer/_category_.json +++ /dev/null @@ -1,8 +0,0 @@ -{ - "label": "Nodemailer", - "position": 25, - "link": { - "type": "generated-index", - "description": "Nodemailer is a module for Node.js applications that allows you to send emails. It is designed to be easy to set up and use." - } - } \ No newline at end of file diff --git a/docs/dsa/Hash/_category_.json b/docs/dsa/Hash/_category_.json deleted file mode 100644 index 93424d3c3..000000000 --- a/docs/dsa/Hash/_category_.json +++ /dev/null @@ -1,8 +0,0 @@ -{ - "label": "Hash", - "position": 15, - "link": { - "type": "generated-index", - "description": "Hash is a data structure that maps keys to values. It uses a hash function to compute an index into an array of buckets or slots, from which the desired value can be found." - } -} diff --git a/docs/dsa/Hash/hash.md b/docs/dsa/Hash/hash.md deleted file mode 100644 index 398b6dd33..000000000 --- a/docs/dsa/Hash/hash.md +++ /dev/null @@ -1,150 +0,0 @@ -# Hash in DSA (Data Structures and Algorithms) - -Hash in DSA (Data Structures and Algorithms) is a function that takes an input (or "key") and produces a fixed-size string of characters, which is typically a unique representation of the input. Hash functions are commonly used in various applications, such as data indexing, password storage, and digital signatures. - -![alt text](image.png) - -- A hash function takes an input and applies a mathematical algorithm to generate a hash value. The hash value is a fixed-size string that is unique to the input data. It is important to note that even a small change in the input data will result in a completely different hash value. - -![alt text](image-1.png) - -- Hash functions are designed to minimize the occurrence of hash collisions, where two different inputs produce the same hash value. However, it is still possible for collisions to occur due to the limited size of the hash value compared to the potentially infinite input space. - -- One common use of hash functions is in data indexing. Hash tables, also known as hash maps, use hash functions to map keys to specific locations in memory, allowing for efficient retrieval and storage of data. - -Hash functions are also used in password storage. Instead of storing passwords in plain text, they are hashed and the hash value is stored. When a user enters their password, it is hashed and compared to the stored hash value for authentication. - - - -Hash functions are an integral part of digital signatures. They are used to generate a unique hash value for a document or message, which is then encrypted with the sender's private key. The recipient can verify the integrity of the message by decrypting the hash value with the sender's public key and comparing it to the computed hash value of the received message. - -Overall, hash functions play a crucial role in various applications by providing a unique representation of data, enabling efficient data retrieval, ensuring data integrity, and enhancing security. - -## Implementing Hash Functions in Different Programming Languages - -Here's a basic example of how to implement a hash function in different programming languages: - -Python: -```python -import hashlib - -def hash_string(input_string): - hash_object = hashlib.sha256(input_string.encode()) - return hash_object.hexdigest() - -input_string = "Hello, World!" -hashed_string = hash_string(input_string) -print(hashed_string) -``` -Output: `2ef7bde608ce5404e97d5f042f95f89f1c232871` - -Java: -```java -import java.security.MessageDigest; -import java.security.NoSuchAlgorithmException; - -public class HashExample { - public static String hashString(String inputString) throws NoSuchAlgorithmException { - MessageDigest md = MessageDigest.getInstance("SHA-256"); - byte[] hashBytes = md.digest(inputString.getBytes()); - StringBuilder sb = new StringBuilder(); - for (byte b : hashBytes) { - sb.append(String.format("%02x", b)); - } - return sb.toString(); - } - - public static void main(String[] args) throws NoSuchAlgorithmException { - String inputString = "Hello, World!"; - String hashedString = hashString(inputString); - System.out.println(hashedString); - } -} -``` -Output: `2ef7bde608ce5404e97d5f042f95f89f1c232871` - -C++: -```cpp -#include -#include - -std::string hashString(const std::string& inputString) { - unsigned char hash[SHA256_DIGEST_LENGTH]; - SHA256_CTX sha256; - SHA256_Init(&sha256); - SHA256_Update(&sha256, inputString.c_str(), inputString.length()); - SHA256_Final(hash, &sha256); - std::stringstream ss; - for (int i = 0; i < SHA256_DIGEST_LENGTH; i++) { - ss << std::hex << std::setw(2) << std::setfill('0') << (int)hash[i]; - } - return ss.str(); -} - -int main() { - std::string inputString = "Hello, World!"; - std::string hashedString = hashString(inputString); - std::cout << hashedString << std::endl; - return 0; -} -``` -Output: `2ef7bde608ce5404e97d5f042f95f89f1c232871` - -Please note that these examples use the SHA-256 hash function as an illustration. Different hash functions may be used depending on the specific requirements of your application. - -## Example Questions with Code in Python - -Here are some example questions with code in Python to help you practice implementing hash functions: - -1. **Question:** Write a Python function to calculate the MD5 hash of a given string. - -```python -import hashlib - -def calculate_md5_hash(input_string): - hash_object = hashlib.md5(input_string.encode()) - return hash_object.hexdigest() - -input_string = "Hello, World!" -md5_hash = calculate_md5_hash(input_string) -print(md5_hash) -``` - -**Output:** `3e25960a79dbc69b674cd4ec67a72c62` - -2. **Question:** Implement a Python program to find the SHA-1 hash of a file. - -```python -import hashlib - -def calculate_sha1_hash(file_path): - sha1_hash = hashlib.sha1() - with open(file_path, 'rb') as file: - for chunk in iter(lambda: file.read(4096), b''): - sha1_hash.update(chunk) - return sha1_hash.hexdigest() - -file_path = "path/to/file.txt" -sha1_hash = calculate_sha1_hash(file_path) -print(sha1_hash) -``` - -**Output:** `2ef7bde608ce5404e97d5f042f95f89f1c232871` - -3. **Question:** Write a Python function to generate a random salt value for password hashing. - -```python -import os -import hashlib - -def generate_salt(): - salt = os.urandom(16) - return salt.hex() - -salt = generate_salt() -print(salt) -``` - -**Output:** `a5f7b9c8d7e6f5a4b3c2d1e0f9e8d7c6` - -Remember to customize these examples based on your specific requirements and use appropriate hash functions for your application. diff --git a/docs/dsa/Hash/image-1.png b/docs/dsa/Hash/image-1.png deleted file mode 100644 index c0b6d612e0469a3954482eec888501ccd28deca7..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 22802 zcmX`T1wfQr_dWd3ol?@$-O{BXARyhXAl)G_w1hMwAPpj2q9EM}(k+70%}B%GP{RLk z-{1E=*NZpl-@o7` zm6L0a)NIH46~%Vhn%x;g@jNe26@{hd@6CKxufxK^{1v>A2aBEm_T40NU5~zphK8>9 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are a type of binary tree-based data structure that satisfy the heap property. They are commonly used to implement priority queues and efficiently find the maximum or minimum element. Heaps can be either max heaps or min heaps, depending on whether the parent nodes are greater or smaller than their children. Operations like insertion, deletion, and retrieval of the maximum or minimum element can be performed efficiently on heaps." - } - - } - - - diff --git a/docs/dsa/Heaps/heaps.md b/docs/dsa/Heaps/heaps.md deleted file mode 100644 index 8035806d3..000000000 --- a/docs/dsa/Heaps/heaps.md +++ /dev/null @@ -1,134 +0,0 @@ ---- -id: heaps-in-dsa -title: Heaps Data Structure -sidebar_label: Heaps -sidebar_position: 1 -description: "Heaps are a type of binary tree-based data structure commonly used in computer science. They are often used to implement priority queues, where elements with higher priority are dequeued first. Heaps have two main variations: max heaps, where the parent node is always greater than or equal to its children, and min heaps, where the parent node is always less than or equal to its children. Heaps have efficient insertion and deletion operations, making them suitable for applications that require efficient priority-based processing." -tags: [dsa, data-structures, heaps] ---- - - - -## Python - Heaps - -Heap is a special tree structure in which each parent node is less than or equal to its child node. Then it is called a Min Heap. If each parent node is greater than or equal to its child node then it is called a max heap. It is very useful is implementing priority queues where the queue item with higher weightage is given more priority in processing. - -A detailed discussion on heaps is available in our website here. Please study it first if you are new to heap data structure. In this chapter we will see the implementation of heap data structure using python. - -![alt text](image.png) -## Create a Heap - -A heap is created by using python’s inbuilt library named heapq. This library has the relevant functions to carry out various operations on heap data structure. Below is a list of these functions. - -- heapify − This function converts a regular list to a heap. In the resulting heap the smallest element gets pushed to the index position 0. But rest of the data elements are not necessarily sorted. - -- heappush − This function adds an element to the heap without altering the current heap. - -- heappop − This function returns the smallest data element from the heap. - -- heapreplace − This function replaces the smallest data element with a new value supplied in the function. - -## Creating a Heap -A heap is created by simply using a list of elements with the heapify function. In the below example we supply a list of elements and the heapify function rearranges the elements bringing the smallest element to the first position. - - -**Python - Heaps** - -Heap is a special tree structure in which each parent node is less than or equal to its child node. Then it is called a Min Heap. - -If each parent node is greater than or equal to its child node then it is called a max heap. - -It is very useful is implementing priority queues where the queue item with higher weightage is given more priority in processing. - -A detailed discussion on heaps is available in our website here. Please study it first if you are new to heap data structure. In this chapter we will see the implementation of heap data structure using python. - -**Example** -``` python -import heapq - -H = [21,1,45,78,3,5] -# Use heapify to rearrange the elements -heapq.heapify(H) -print(H) -``` - -## Output -When the above code is executed, it produces the following result − -``` python -[1, 3, 5, 78, 21, 45] -``` -## Inserting into heap - -Inserting a data element to a heap always adds the element at the last index. But you can apply heapify function again to bring the newly added element to the first index only if it smallest in value. In the below example we insert the number 8. - -**Example** - -``` python -import heapq - -H = [21,1,45,78,3,5] -# Covert to a heap -heapq.heapify(H) -print(H) - -# Add element -heapq.heappush(H,8) -print(H) -``` - -## Output - -When the above code is executed, it produces the following result − -```python -[1, 3, 5, 78, 21, 45] -[1, 3, 5, 78, 21, 45, 8] -``` -## Removing from heap - -You can remove the element at first index by using this function. In the below example the function will always remove the element at the index position 1. - -**Example** -```python -import heapq - -H = [21,1,45,78,3,5] -# Create the heap - -heapq.heapify(H) -print(H) - -# Remove element from the heap -heapq.heappop(H) - -print(H) -Output -When the above code is executed, it produces the following result − -```python -[1, 3, 5, 78, 21, 45] -[3, 21, 5, 78, 45] -``` -## Replacing in a Heap - -The heap replace function always removes the smallest element of the heap and inserts the new incoming element at some place not fixed by any order. - -**Example** -``` python -import heapq - -H = [21,1,45,78,3,5] -# Create the heap - -heapq.heapify(H) -print(H) - -# Replace an element -heapq.heapreplace(H,6) -print(H) -``` - -## Output -When the above code is executed, it produces the following result − -```python -[1, 3, 5, 78, 21, 45] -[3, 6, 5, 78, 21, 45] -``` \ No newline at end of file diff --git a/docs/dsa/Heaps/image.png b/docs/dsa/Heaps/image.png deleted 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It's a dynamic programming technique named after its creator, Jay Kadane." ---- -## Kadane's Algorithm: - -- **Purpose**: Finds the maximum sum of a contiguous subarray. -- **Time Complexity**: $O(n)$ -- **Space Complexity**: O(1) -- **Use Case**: Optimal for solving maximum subarray sum problems in linear time. -### Simple Explanation -Kadane's Algorithm: - -1. **Initialize**: - - Set `maxSum` to a very small number (e.g., negative infinity). - - Set `currentSum` to 0. - -2. **Iterate Through the Array**: - - For each element in the array: - - Add the element to `currentSum`. - - Update `maxSum` if `currentSum` is greater than `maxSum`. - - If `currentSum` becomes negative, reset it to 0. - -3. **Result**: - - The value of `maxSum` at the end of the iteration is the maximum sum of any contiguous subarray. -### Code - -Input: arr = {-2,-3,4,-1,-2,1,5,-3} - -Output: 7 - -Explanation: The subarray {4,-1, -2, 1, 5} has the largest sum 7. - -### Python -```py - - def max_sub_array(nums): - max_sum = float('-inf') - current_sum = 0 - - for num in nums: - # Add the current number to the current_sum - current_sum += num - # Update max_sum if current_sum is greater - max_sum = max(max_sum, current_sum) - # Reset current_sum to 0 if it drops below 0 - if current_sum < 0: - current_sum = 0 - - return max_sum -``` - -### C++ -```cpp - // Kadane's Algorithm to find the maximum sum of a contiguous subarray - - #include - #include - #include - #include - - int maxSubArray(const std::vector& nums) { - // Initialize max_sum to the lowest possible value and current_sum to 0 - int max_sum = INT_MIN; - int current_sum = 0; - - for (int num : nums) { - // Add the current number to the current_sum - current_sum += num; - // Update max_sum if current_sum is greater - max_sum = std::max(max_sum, current_sum); - // Reset current_sum to 0 if it drops below 0 - if (current_sum < 0) { - current_sum = 0; - } - } - - return max_sum; - } -``` - -### Explanation -Explanation: - -#### Initialization: - - -`max_sum` is initialized to `INT_MIN` to handle arrays with all negative numbers. - - -`current_sum` starts at `0`. - -#### Iteration: - - -Traverse through each number in the array: - - -Add the number to `current_sum`. - - -Update `max_sum` to be the maximum of `max_sum` and `current_sum`. - - -If `current_sum` becomes negative, reset it to `0` to start a new subarray. - - diff --git a/docs/dsa/Matrix/_category_.json b/docs/dsa/Matrix/_category_.json deleted file mode 100644 index d8a0abc0d..000000000 --- a/docs/dsa/Matrix/_category_.json +++ /dev/null @@ -1,9 +0,0 @@ -{ - "label": "Matrix", - "position": 9, - "link": { - "type": "generated-index", - "description": "In data structures and algorithms (DSA), a matrix is a two-dimensional array consisting of rows and columns. It is often used to represent a grid-like structure or a table of values. Matrices are commonly used in various algorithms and mathematical operations, such as matrix multiplication, graph algorithms, image processing, and more. 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It is commonly used in various fields, including mathematics, computer science, and data analysis, to represent and manipulate structured data. " -tags: [dsa, data-structures, Matrix] ---- - -**Matrix Data Structure** is a two-dimensional array arranged in rows and columns. It is commonly used to represent mathematical matrices and is fundamental in various fields like mathematics, computer graphics, and data processing. Matrices allow for efficient storage and manipulation of data in a structured format - -## Components of Matrix Data Structure -- Size: A matrix has a specific size, defined by its number of rows and columns. -- Element: A matrix’s row and column indices serve to identify each entry, which is referred to as an element. -- Operations: Scalar multiplication and the operations of addition, subtraction, and multiplication on matrices are also supported. -- Determinant: A square matrix’s determinant is a scalar number that may be used to solve systems of linear equations and carry out other linear algebraic operations. -- Inverse: If a square matrix has an inverse, it may be used to solve linear equation systems and carry out other linear algebraic operations. -- Transpose: By flipping a matrix along its main diagonal and switching the rows and columns, you may create the transpose of the matrix. -- Rank: In many applications, including the solution of linear equations and linear regression analysis, the rank of a matrix—a measure of its linearly independent rows or columns—is utilized - -## Applications of Matrix Data Structure -- Linear Algebra: Matrices are widely used in linear algebra, a branch of mathematics that deals with linear equations, vector spaces, and linear transformations. Matrices are used to represent linear equations and to solve systems of linear equations. -- Optimization: Matrices are used in optimization problems, such as linear programming, to represent the constraints and objective functions of the problem. -- Statistics: Matrices are used in statistics to represent data and to perform operations such as correlation and regression. -- Signal Processing: Matrices are used in signal processing to represent signals and to perform operations such as filtering and transformation. -- Network Analysis: Matrices are used in network analysis to represent graphs and to perform operations such as finding the shortest path between two nodes. -- Quantum Mechanics: Matrices are used in quantum mechanics to represent states and operations in quantum systems. - - - -## Representation of Matrix Data Structure: - -![alt text](image.png) - -As you can see from the above image, the elements are organized in rows and columns. As shown in the above image the cell x[0][0] is the first element of the first row and first column. The value in the first square bracket represents the row number and the value inside the second square bracket represents the column number. (i.e, x[row][column]). - -## Declaration of Matrix Data Structure : - -Declaration of a Matrix or two-dimensional array is very much similar to that of a one-dimensional array, given as follows. -``` python -# Defining number of rows and columns in matrix -number_of_rows = 3 -number_of_columns = 3 -# Declaring a matrix of size 3 X 3, and initializing it with value zero -rows, cols = (3, 3) -arr = [[0]*cols]*rows -print(arr) -``` - -## Initializing Matrix Data Structure: -In initialization, we assign some initial value to all the cells of the matrix. Below is the implementation to initialize a matrix in different languages: - -``` python -# Initializing a 2-D array with values -arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]; -``` - -## Operations on Matrix Data Structure: - -We can perform a variety of operations on the Matrix Data Structure. Some of the most common operations are: - -- Access elements of Matrix -- Traversal of a Matrix -- Searching in a Matrix -- Sorting a Matrix - -## 1. Access elements of Matrix Data Structure: - -Like one-dimensional arrays, matrices can be accessed randomly by using their indices to access the individual elements. A cell has two indices, one for its row number, and the other for its column number. We can use arr[i][j] to access the element which is at the ith row and jth column of the matrix. - -```python -# Initializing a 2-D array with values -arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] - -# Accessing elements of 2-D array -print("First element of first row:", arr[0][0]) -print("Third element of second row:", arr[1][2]) -print("Second element of third row:", arr[2][1]) -``` - -## 2. Traversal of a Matrix Data Structure: -We can traverse all the elements of a matrix or two-dimensional array by using two for-loops. - -``` python -arr = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]] -``` -```python -# Traversing over all the rows -for i in range(0, 3): - # Traversing over all the columns of each row - for j in range(0, 4): - print(arr[i][j], end=" ") - print("") -``` - -Output -``` python -1 2 3 4 -5 6 7 8 -9 10 11 12 -``` -## 3. Searching in a Matrix Data Structure: - -We can search an element in a matrix by traversing all the elements of the matrix. - -Below is the implementation to search an element in a matrix: - -```python -# Python code for above approach -def searchInMatrix(arr, x): - # m=4,n=5 - for i in range(0, 4): - for j in range(0, 5): - if(arr[i][j] == x): - return 1 - return - -x = 8 -arr = [[0, 6, 8, 9, 11], - [20, 22, 28, 29, 31], - [36, 38, 50, 61, 63], - [64, 66, 100, 122, 128]] -if(searchInMatrix(arr, x)): - print("YES") -else: - print("NO") - - # This code is contributed by dhairyagothi. -``` - -Output -```python -YES -``` - -## 4. Sorting Matrix Data Structure: -We can sort a matrix in two-ways: - -- Sort the matrix row-wise -- Sort the matrix column-wise - -## Advantages of Matrix Data Structure: -- It helps in 2D Visualization. -- It stores multiple elements of the same type using the same name. -- It enables access to items at random. -- Any form of data with a fixed size can be stored. -- It is easy to implement. - -## Disadvantages of Matrix Data Structure: -- Space inefficient when we need to store very few elements in the matrix. -- The matrix size should be needed beforehand. -- Insertion and deletion operations are costly if shifting occurs. -- Resizing a matrix is time-consuming. diff --git a/docs/dsa/Matrix/problems-matrix.md b/docs/dsa/Matrix/problems-matrix.md deleted file mode 100644 index 1801abef2..000000000 --- a/docs/dsa/Matrix/problems-matrix.md +++ /dev/null @@ -1,130 +0,0 @@ ---- -id: matrix-problems -title: Matrix Practice Problems -sidebar_label: Matrix Practice Problems -sidebar_position: 2 -description: "A matrix is a two-dimensional data structure consisting of rows and columns, where each element is identified by its row and column index. It is commonly used in various fields, including mathematics, computer science, and data analysis, to represent and manipulate structured data. " -tags: [dsa, data-structures, Matrix ] ---- - -## Sort the given matrix - -Given a n x n matrix. The problem is to sort the given matrix in strict order. Here strict order means that the matrix is sorted in a way such that all elements in a row are sorted in increasing order and for row ‘i’, where ```1 <= i <= n-1```, the first element of row ‘i’ is greater than or equal to the last element of row ‘i-1’. - -**Examples:** -``` -Input : mat[][] = { {5, 4, 7}, - {1, 3, 8}, - {2, 9, 6} } -Output : 1 2 3 - 4 5 6 - 7 8 9 -``` -## Solution -```python -# Python program for the above approach -# driver code -v = [[5,4,7], [1,3,8], [2,9,6]] -n = len(v) - -x = [] -for i in range(n): - for j in range(n): - x.append(v[i][j]) - -x.sort() -k = 0 -for i in range(n): - for j in range(n): - v[i][j] = x[k] - k += 1 - -print("Sorted Matrix will be: ") -for i in range(n): - for j in range(n): - print(v[i][j], end=" ") - print("") - -# THIS CODE IS CONTRIBUTED BY Dhairya Gothi(dhairyagothi) -``` - -## Output -Sorted Matrix Will be: -``` -1 2 3 -4 5 6 -7 8 9 -``` -**Time Complexity:** O(n2log2n), O(n*n) for traversing, and O(n2log2n) for sorting the vector x, which has a size of n2. So overall time complexity is O(n2log2n). -**Auxiliary Space:** O(n*n), For vector. - -## Program for scalar multiplication of a matrix - -Given a matrix and a scalar element k, our task is to find out the scalar product of that matrix. - -**Examples:** -``` -Input : mat[][] = {{2, 3} - {5, 4}} - k = 5 -Output : 10 15 - 25 20 -We multiply 5 with every element. - -Input : 1 2 3 - 4 5 6 - 7 8 9 - k = 4 -Output : 4 8 12 - 16 20 24 - 28 32 36 -The scalar multiplication of a number k(scalar), multiply it on every entry in the matrix. and a matrix A is the matrix kA. - ``` - -```python -# Python 3 program to find the scalar -# product of a matrix - -# Size of given matrix -N = 3 - -def scalarProductMat( mat, k): - - # scalar element is multiplied - # by the matrix - for i in range( N): - for j in range( N): - mat[i][j] = mat[i][j] * k - -# Driver code -if __name__ == "__main__": - - mat = [[ 1, 2, 3 ], - [ 4, 5, 6 ], - [ 7, 8, 9 ]] - k = 4 - - scalarProductMat(mat, k) - - # to display the resultant matrix - print("Scalar Product Matrix is : ") - for i in range(N): - for j in range(N): - print(mat[i][j], end = " ") - print() - -# This code is contributed by dhairya -``` -## Output: -``` -Scalar Product Matrix is : -4 8 12 -16 20 24 -28 32 36 -``` - - -**ime Complexity:** O(n2), - -**Auxiliary Space:** O(1), since no extra space has been taken. - diff --git a/docs/dsa/Queue/_category_.json b/docs/dsa/Queue/_category_.json deleted file mode 100644 index 667dc3fce..000000000 --- a/docs/dsa/Queue/_category_.json +++ /dev/null @@ -1,8 +0,0 @@ -{ - "label": "Queue", - "position": 11, - "link": { - "type": "generated-index", - "description": "A queue is a data structure that follows the First-In-First-Out (FIFO) principle. 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z(XXdmtdeb*7|(+$3L?Na1_8E$3-+mtyaUO7KEX6wKq#bg(N0RmirVIZW+oB=PQHc&Fx$5akf(k`CNBfP)`X9HdK8CV#BZkNtyH zt>=0!xaL_vtP%Ftvha7j;P0g3;OhkcA!O0A^2gDN$1w^7jG_t#qk@r@M59&E=%56@ hv;X4+FK -#include - -class Queue { -private: - std::vector elements; - -public: - void enqueue(int element) { - elements.push_back(element); - } - - int dequeue() { - if (is_empty()) { - std::cerr << "Queue Underflow" << std::endl; - return -1; - } - int front = elements.front(); - elements.erase(elements.begin()); - return front; - } - - int peek() { - if (is_empty()) { - std::cerr << "Queue is empty" << std::endl; - return -1; - } - return elements.front(); - } - - bool is_empty() { - return elements.empty(); - } - - int size() { - return elements.size(); - } -}; - -// Example usage -int main() { - Queue queue; - queue.enqueue(10); - queue.enqueue(20); - std::cout << queue.dequeue() << std::endl; // Output: 10 - std::cout << queue.peek() << std::endl; // Output: 20 - std::cout << std::boolalpha << queue.is_empty() << std::endl; // Output: false - std::cout << queue.size() << std::endl; // Output: 1 - return 0; -} -``` - -#### Java Implementation - -```java -import java.util.ArrayList; - -public class Queue { - private ArrayList elements; - - public Queue() { - elements = new ArrayList<>(); - } - - public void enqueue(int element) { - elements.add(element); - } - - public int dequeue() { - if (is_empty()) { - System.out.println("Queue Underflow"); - return -1; - } - return elements.remove(0); - } - - public int peek() { - if (is_empty()) { - System.out.println("Queue is empty"); - return -1; - } - return elements.get(0); - } - - public boolean is_empty() { - return elements.isEmpty(); - } - - public int size() { - return elements.size(); - } - - // Example usage - public static void main(String[] args) { - Queue queue = new Queue(); - queue.enqueue(10); - queue.enqueue(20); - System.out.println(queue.dequeue()); // Output: 10 - System.out.println(queue.peek()); // Output: 20 - System.out.println(queue.is_empty()); // Output: false - System.out.println(queue.size()); // Output: 1 - } -} -``` - -### Complexity - -- **Time Complexity**: - - - Enqueue: $O(1)$ - - Dequeue: $O(1)$ - - Peek: $O(1)$ - - isEmpty: $O(1)$ - - Size: $O(1)$ - -- **Space Complexity**: $O(n)$, where $n$ is the number of elements in the queue. - -### Example - -Consider a queue with the following operations: - -1. Enqueue 10 -2. Enqueue 20 -3. Dequeue -4. Peek -5. Check if empty -6. Get size - -**Operations**: - -- Enqueue 10: Queue becomes [10] -- Enqueue 20: Queue becomes [10, 20] -- Dequeue: Removes 10, Queue becomes [20] -- Peek: Returns 20, Queue remains [20] -- isEmpty: Returns false -- Size: Returns 1 - -### Conclusion - -A queue is a fundamental data structure used in computer science for various applications where the FIFO (First In First Out) principle is required. It is simple to implement and provides efficient operations for adding and removing elements. Understanding and using queues effectively can help solve many algorithmic problems. - diff --git a/docs/dsa/Trees/Trees.md b/docs/dsa/Trees/Trees.md deleted file mode 100644 index 289ac50a8..000000000 --- a/docs/dsa/Trees/Trees.md +++ /dev/null @@ -1,415 +0,0 @@ -# Trees in Data Structures and Algorithms - -A tree is a widely used data structure in computer science that represents a hierarchical structure. It consists of nodes connected by edges, where each node can have zero or more child nodes. Trees are used to represent various real-world scenarios and are essential in many algorithms and data manipulation operations. - -![alt text](image-1.png) - -**Here are some key concepts related to DSA trees:** - -1. **Node**: A node is a fundamental building block of a tree. It contains data and references to its child nodes, if any. In a binary tree, each node can have at most two child nodes, referred to as the left child and the right child. - -2. **Root**: The root is the topmost node of a tree. It serves as the starting point for traversing the tree and accessing its elements. - -3. **Parent and Child**: Nodes in a tree are connected in a parent-child relationship. A parent node is the immediate predecessor of its child node, and a child node is a direct descendant of its parent node. - -4. **Leaf**: A leaf node is a node that does not have any child nodes. It is located at the bottom of the tree. - -5. **Binary Tree**: A binary tree is a tree in which each node can have at most two child nodes, the left child and the right child. Binary trees are commonly used in search algorithms and binary tree traversals. - -6. **Binary Search Tree (BST)**: A binary search tree is a binary tree in which the left child of a node contains a value less than the node's value, and the right child contains a value greater than the node's value. BSTs are efficient for searching, insertion, and deletion operations. - -7. **Traversal**: Traversal refers to the process of visiting all the nodes in a tree in a specific order. Common traversal algorithms include in-order, pre-order, and post-order traversals. In-order traversal visits the left subtree, then the root, and finally the right subtree. Pre-order traversal visits the root, then the left subtree, and finally the right subtree. Post-order traversal visits the left subtree, then the right subtree, and finally the root. - -8. **Balanced Trees**: Balanced trees are trees that maintain a balance between the left and right subtrees of each node. Examples of balanced trees include AVL trees and red-black trees. Balanced trees provide faster search, insertion, and deletion operations compared to regular binary search trees. - -9. **B-Tree**: A B-tree is a self-balancing search tree that can have more than two children per node. It is commonly used in file systems and databases, as it provides efficient disk access and supports large amounts of data. - -These are just some of the key concepts related to DSA trees. Trees are a rich topic with many variations and algorithms associated with them. It's important to understand these concepts and their implementations in different programming languages to effectively use trees in your programs. - - -## Types of Trees - -![alt text](image.png) - -1. **Binary Tree**: A binary tree is a tree in which each node can have at most two child nodes, referred to as the left child and the right child. Binary trees are commonly used in search algorithms and binary tree traversals. - -2. **Binary Search Tree (BST)**: A binary search tree is a binary tree in which the left child of a node contains a value less than the node's value, and the right child contains a value greater than the node's value. BSTs are efficient for searching, insertion, and deletion operations. - -3. **AVL Tree**: An AVL tree is a self-balancing binary search tree. It ensures that the heights of the left and right subtrees of any node differ by at most one. AVL trees provide faster search, insertion, and deletion operations compared to regular binary search trees. - -4. **Red-Black Tree**: A red-black tree is another self-balancing binary search tree. It maintains balance by coloring the nodes red or black and applying specific rules during insertion and deletion operations. Red-black trees guarantee logarithmic time complexity for search, insertion, and deletion. - -5. **B-Tree**: A B-tree is a self-balancing search tree that can have more than two children per node. It is commonly used in file systems and databases, as it provides efficient disk access and supports large amounts of data. - -## Basic Operations on Trees - -1. **Insertion**: Adding a new node to the tree at the appropriate position based on its value. - -2. **Deletion**: Removing a node from the tree while maintaining the tree's structure and properties. - -3. **Search**: Finding a specific value or node in the tree. - -4. **Traversal**: Visiting all the nodes in the tree in a specific order. Common traversal algorithms include in-order, pre-order, and post-order traversals. - -## Implementation in Different Languages - -Trees can be implemented in various programming languages. Here are some examples: - -- **Java**: Java provides built-in classes like `TreeNode` and `BinarySearchTree` to implement trees. You can also create custom classes and use recursion for tree operations. - -- **Python**: Python offers flexibility in implementing trees using classes and objects. You can define a `TreeNode` class and implement tree operations using methods and recursion. - -- **C++**: C++ allows you to create tree structures using classes and pointers. You can define a `TreeNode` class and implement tree operations using pointers and recursive functions. - -- **JavaScript**: JavaScript provides the flexibility of implementing trees using objects and classes. You can define a `TreeNode` object and implement tree operations using object-oriented programming concepts. - -Remember to refer to the specific documentation and resources for each programming language to understand the syntax and details of implementing trees. - -## Implementation in Different Languages - -Trees can be implemented in various programming languages. Here are some examples: - -- **Java**: - -```java -class TreeNode { - int data; - TreeNode left; - TreeNode right; - - public TreeNode(int data) { - this.data = data; - this.left = null; - this.right = null; - } -} - -class BinaryTree { - TreeNode root; - - public BinaryTree(int data) { - this.root = new TreeNode(data); - } - - public void insert(int data) { - // Implementation of insertion - } - - public void delete(int data) { - // Implementation of deletion - } - - public TreeNode search(int data) { - // Implementation of search - return null; - } - - public void inOrderTraversal(TreeNode node) { - // Implementation of in-order traversal - } -} - -public class Main { - public static void main(String[] args) { - BinaryTree tree = new BinaryTree(5); - tree.insert(3); - tree.insert(7); - tree.insert(2); - tree.insert(4); - tree.insert(6); - tree.insert(8); - - tree.inOrderTraversal(tree.root); - } -} -``` - -Output: -``` -2 3 4 5 6 7 8 -``` - -- **Python**: - -```python -class TreeNode: - def __init__(self, data): - self.data = data - self.left = None - self.right = None - -class BinaryTree: - def __init__(self, data): - self.root = TreeNode(data) - - def insert(self, data): - # Implementation of insertion - - def delete(self, data): - # Implementation of deletion - - def search(self, data): - # Implementation of search - return None - - def in_order_traversal(self, node): - # Implementation of in-order traversal - -tree = BinaryTree(5) -tree.insert(3) -tree.insert(7) -tree.insert(2) -tree.insert(4) -tree.insert(6) -tree.insert(8) - -tree.in_order_traversal(tree.root) -``` - -Output: -``` -2 3 4 5 6 7 8 -``` - -- **C++**: - -```cpp -class TreeNode { -public: - int data; - TreeNode* left; - TreeNode* right; - - TreeNode(int data) { - this->data = data; - this->left = nullptr; - this->right = nullptr; - } -}; - -class BinaryTree { -public: - TreeNode* root; - - BinaryTree(int data) { - this->root = new TreeNode(data); - } - - void insert(int data) { - // Implementation of insertion - } - - void deleteNode(int data) { - // Implementation of deletion - } - - TreeNode* search(int data) { - // Implementation of search - return nullptr; - } - - void inOrderTraversal(TreeNode* node) { - // Implementation of in-order traversal - } -}; - -int main() { - BinaryTree tree(5); - tree.insert(3); - tree.insert(7); - tree.insert(2); - tree.insert(4); - tree.insert(6); - tree.insert(8); - - tree.inOrderTraversal(tree.root); - - return 0; -} -``` - -Output: -``` -2 3 4 5 6 7 8 -``` - -- **JavaScript**: - -```javascript -class TreeNode { - constructor(data) { - this.data = data; - this.left = null; - this.right = null; - } -} - -class BinaryTree { - constructor(data) { - this.root = new TreeNode(data); - } - - insert(data) { - // Implementation of insertion - } - - delete(data) { - // Implementation of deletion - } - - search(data) { - // Implementation of search - return null; - } - - inOrderTraversal(node) { - // Implementation of in-order traversal - } -} - -const tree = new BinaryTree(5); -tree.insert(3); -tree.insert(7); -tree.insert(2); -tree.insert(4); -tree.insert(6); -tree.insert(8); - -tree.inOrderTraversal(tree.root); -``` - -Output: -``` -2 3 4 5 6 7 8 -``` - -Remember to refer to the specific documentation and resources for each programming language to understand the syntax and details of implementing trees. - - -## Operations on Trees in Python - -Here are some examples of tree operations implemented in Python: - -1. **Insertion**: - -```python -class TreeNode: - def __init__(self, data): - self.data = data - self.left = None - self.right = None - -class BinaryTree: - def __init__(self, data): - self.root = TreeNode(data) - - def insert(self, data): - if self.root is None: - self.root = TreeNode(data) - else: - self._insert_recursive(self.root, data) - - def _insert_recursive(self, node, data): - if data < node.data: - if node.left is None: - node.left = TreeNode(data) - else: - self._insert_recursive(node.left, data) - else: - if node.right is None: - node.right = TreeNode(data) - else: - self._insert_recursive(node.right, data) -``` - -2. **Deletion**: - -```python -class BinaryTree: - # ... - - def delete(self, data): - self.root = self._delete_recursive(self.root, data) - - def _delete_recursive(self, node, data): - if node is None: - return node - - if data < node.data: - node.left = self._delete_recursive(node.left, data) - elif data > node.data: - node.right = self._delete_recursive(node.right, data) - else: - if node.left is None: - return node.right - elif node.right is None: - return node.left - else: - min_node = self._find_min(node.right) - node.data = min_node.data - node.right = self._delete_recursive(node.right, min_node.data) - - return node - - def _find_min(self, node): - current = node - while current.left is not None: - current = current.left - return current -``` - -3. **Search**: - -```python -class BinaryTree: - # ... - - def search(self, data): - return self._search_recursive(self.root, data) - - def _search_recursive(self, node, data): - if node is None or node.data == data: - return node - - if data < node.data: - return self._search_recursive(node.left, data) - else: - return self._search_recursive(node.right, data) -``` - -4. **Traversal**: - -```python -class BinaryTree: - # ... - - def in_order_traversal(self, node): - if node is not None: - self.in_order_traversal(node.left) - print(node.data, end=" ") - self.in_order_traversal(node.right) -``` - -Example usage: - -```python -tree = BinaryTree(5) -tree.insert(3) -tree.insert(7) -tree.insert(2) -tree.insert(4) -tree.insert(6) -tree.insert(8) - -tree.in_order_traversal(tree.root) -``` - -Output: -``` -2 3 4 5 6 7 8 -``` - -Remember to refer to the specific documentation and resources for Python to understand the syntax and details of implementing trees. - -Practise more and more ........... - diff --git a/docs/dsa/Trees/_category_.json b/docs/dsa/Trees/_category_.json deleted file mode 100644 index 90071153a..000000000 --- a/docs/dsa/Trees/_category_.json +++ /dev/null @@ -1,8 +0,0 @@ -{ - "label": "Trees", - "position": 13, - "link": { - "type": "generated-index", - "description": "In data structures and algorithms (DSA), a tree is a hierarchical data structure consisting of nodes connected by edges. 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zQaR=*8DgL1YxLoY+s;BmI|-#4W6K38DN*nB93+TzeL|sim^*ywRvA2DjagzB&jUt5 z%DQs1va}LOanScEOEnI{n)8N=V1wh_Ht^x=Tf~`?_rMDYI#RHNo2#pcFm6o-4Q=gF zql9I?m5=tDrhW@vZag6CyW?Qku&y{nk4#0JdRP|*5!Gt(ZEyb=L^) zE+z10!fEISED#bRjcFyKf3h2!uAFh1gEtjMOKSK?%slGv`d*r(So4G(1s(v<1r{IH zHG~+Fst8l}=o;#ehgVE^_IXrzRQk_S;x^!sNQNx`Z&NYI%Qkb+%aJ0+cUuyZqUg91}>YoBm|WBw^~TyivGUzE@0a9nQvrNXm04O~hBpE;ND_6bExFFlmm_4bQai zS)x2Dk(oO|^Z2v|as!Kezp$_s0=YQ0z0|cLJ&&qfoGyCYY9mx*rGJN}GTNDB%-Doy zV#72|YE^#G>-vp}|6+@X+daRU!K=q+zvrF&S~4Z#8-v46K?+QCN)$eGF|nr?*jMwK z_T3MQux+aYXTs;_a9y+%w z{|0KZdHr8ndF_|C_5WMse}KPG|0?-!nw!VQ(tnQrsgYH66ISH>tB=C_vJn6P@IX~w zLhWs!4l;JW4!8$E1S}#Z2$m2OmM{ - -```Python showLineNumbers -def knapsack_greedy(values, weights, capacity): - # Create a list of items with their values and weights - items = list(zip(values, weights)) - - # Sort the items based on their value-to-weight ratio in descending order - items.sort(key=lambda x: x[0] / x[1], reverse=True) - - # Initialize the total value and total weight - total_value = 0 - total_weight = 0 - - # Iterate through the sorted items - for value, weight in items: - # Check if adding the current item exceeds the capacity - if total_weight + weight <= capacity: - # Add the item to the knapsack - total_value += value - total_weight += weight - - return total_value - -# Example usage -values = [60, 100, 120] -weights = [10, 20, 30] -capacity = 50 - -max_value = knapsack_greedy(values, weights, capacity) -print("Maximum value:", max_value) - -``` - - - ```cpp - #include -#include -#include -using namespace std; - -struct Item { - int value; - int weight; -}; - -bool compare(Item a, Item b) { - double r1 = (double)a.value / a.weight; - double r2 = (double)b.value / b.weight; - return r1 > r2; -} - -int knapsack_greedy(vector& values, vector& weights, int capacity) { - vector items(values.size()); - for (size_t i = 0; i < values.size(); ++i) { - items[i] = {values[i], weights[i]}; - } - - sort(items.begin(), items.end(), compare); - - int total_value = 0; - int total_weight = 0; - - for (auto& item : items) { - if (total_weight + item.weight <= capacity) { - total_value += item.value; - total_weight += item.weight; - } - } - - return total_value; -} - -int main() { - vector values = {60, 100, 120}; - vector weights = {10, 20, 30}; - int capacity = 50; - - int max_value = knapsack_greedy(values, weights, capacity); - cout << "Maximum value: " << max_value << endl; - - return 0; -} - - ``` - - -``` jsx showLineNumbers -import java.util.ArrayList; -import java.util.Collections; -import java.util.Comparator; -import java.util.List; - -class Item { - int value; - int weight; - - Item(int value, int weight) { - this.value = value; - this.weight = weight; - } -} - -public class KnapsackGreedy { - - public static int knapsackGreedy(int[] values, int[] weights, int capacity) { - List items = new ArrayList<>(); - for (int i = 0; i < values.length; i++) { - items.add(new Item(values[i], weights[i])); - } - - Collections.sort(items, new Comparator() { - public int compare(Item a, Item b) { - double r1 = (double) a.value / a.weight; - double r2 = (double) b.value / b.weight; - return Double.compare(r2, r1); - } - }); - - int totalValue = 0; - int totalWeight = 0; - - for (Item item : items) { - if (totalWeight + item.weight <= capacity) { - totalValue += item.value; - totalWeight += item.weight; - } - } - - return totalValue; - } - - public static void main(String[] args) { - int[] values = {60, 100, 120}; - int[] weights = {10, 20, 30}; - int capacity = 50; - - int maxValue = knapsackGreedy(values, weights, capacity); - System.out.println("Maximum value: " + maxValue); - } -} - -``` - - - -``` jsx showLineNumbers -function knapsackGreedy(values, weights, capacity) { - let items = []; - for (let i = 0; i < values.length; i++) { - items.push({ value: values[i], weight: weights[i] }); - } - - items.sort((a, b) => (b.value / b.weight) - (a.value / a.weight)); - - let totalValue = 0; - let totalWeight = 0; - - for (let item of items) { - if (totalWeight + item.weight <= capacity) { - totalValue += item.value; - totalWeight += item.weight; - } - } - - return totalValue; -} - -// Example usage -let values = [60, 100, 120]; -let weights = [10, 20, 30]; -let capacity = 50; - -let maxValue = knapsackGreedy(values, weights, capacity); -console.log("Maximum value:", maxValue); - - -``` - - - - - -This code demonstrates the Greedy algorithm in action by solving the Knapsack problem. The goal is to maximize the total value of items that can be put into a knapsack with a given capacity. The algorithm selects items based on their value-to-weight ratio, choosing the most valuable items first until the knapsack is full. - -### Conclusion - -The Greedy algorithm is a powerful and intuitive approach for solving optimization problems. It follows the principle of making locally optimal choices at each step to find a global optimum solution. - -The advantages of the Greedy algorithm include its simplicity, efficiency, and intuitive thought process. It is easy to understand and implement compared to complex algorithms, provides fast and efficient solutions in many cases, and follows a natural thought process. - -However, the Greedy algorithm also has its limitations. Locally optimal choices may not always lead to the globally optimal solution, resulting in suboptimal choices. It is not suitable for all problems, especially those requiring a comprehensive approach. - -In conclusion, the Greedy algorithm is a valuable tool in solving optimization problems, but it is important to analyze the problem and consider other approaches for the most efficient solution. \ No newline at end of file diff --git a/docs/dsa/algorithms/_category_.json b/docs/dsa/algorithms/_category_.json deleted file mode 100644 index 3055c678d..000000000 --- a/docs/dsa/algorithms/_category_.json +++ /dev/null @@ -1,8 +0,0 @@ -{ - "label": "Algorithms", - "position": 14, - "link": { - "type": "generated-index", - "description": "Searching algorithms are a set of techniques used to find a specific element or value in a collection of data. They are commonly used in computer science and data analysis to efficiently locate desired information." - } - } \ No newline at end of file diff --git a/docs/dsa/algorithms/backtracking.md b/docs/dsa/algorithms/backtracking.md deleted file mode 100644 index 9d15acdfd..000000000 --- a/docs/dsa/algorithms/backtracking.md +++ /dev/null @@ -1,223 +0,0 @@ ---- -id: backtracking-in-dsa -title: Backtracking in Data Structures and Algorithms -sidebar_label: Backtracking Algorithm -sidebar_position: 1 -description: "Backtracking is a technique used to solve problems by exploring all possible solutions." -tags : [dsa,data-algorithms , backtracking] ---- - - -## Backtracking in Python - -Backtracking is a technique used to solve problems by exploring all possible solutions. It is especially useful when the problem can be broken down into a series of decisions or choices. -![alt text](image-3.png) - -To implement backtracking in Python, you can follow these steps: - -1. Define a function that takes the problem and a partial solution as input. -2. Check if the solution is complete. If it is, return the solution. -3. Generate possible candidates for the next step. -4. Iterate through the candidates. -5. Make a choice and update the solution. -6. Recursively call the function with the updated solution. -7. If a valid solution is found, return it. -8. Undo the choice and continue with the next candidate. -9. If no valid solution is found, return None. - -Here's an example implementation of the backtracking algorithm in Python: - -```python -def backtrack(problem, solution): - # Base case: if the solution is complete, return it - if is_solution(problem, solution): - return solution - - # Generate possible candidates for the next step - candidates = generate_candidates(problem, solution) - - # Iterate through the candidates - for candidate in candidates: - # Make a choice and update the solution - make_choice(problem, solution, candidate) - - # Recursively backtrack with the updated solution - result = backtrack(problem, solution) - - # If a valid solution is found, return it - if result is not None: - return result - - # Undo the choice and continue with the next candidate - undo_choice(problem, solution, candidate) - - # If no valid solution is found, return None - return None -``` - -You can customize the `is_solution`, `generate_candidates`, `make_choice`, and `undo_choice` functions to fit your specific problem. - -Remember, backtracking explores all possible solutions, so it can be computationally expensive for large problem spaces. However, it is a powerful technique for solving problems that can be represented as a series of choices or decisions. - - -### Example: Permutations of Letters - -The task is to find all possible arrangements (permutations) of a given set of letters. - -### Explanation: - -**Function Definition:** - -We define a function permute(letters, current_perm, all_permutations). -letters is the original set of letters. -current_perm is a list to hold the current permutation being built. -all_permutations is a list to store all the final permutations. -Base Case: - -If all letters have been used (i.e., len(current_perm) == len(letters)), we've found a complete permutation. -Append the current_perm to the all_permutations list. -Recursive Exploration: - -Iterate through the remaining letters in letters. -For each letter: -Add the letter to the current_perm. -Make a recursive call to permute with the updated current_perm and the remaining letters (excluding the chosen letter). -After the recursive call (exploring possibilities with the chosen letter), remove the letter from current_perm to backtrack and explore other options (avoiding duplicates). -#### Codes in Different Languages - - - - - - ```cpp -#include -#include -using namespace std; -void permute(vector& letters, vector& current_perm, vector>& all_permutations) { - if (current_perm.size() == letters.size()) { - all_permutations.push_back(current_perm); - return; - } - - for (size_t i = 0; i < letters.size(); ++i) { - if (find(current_perm.begin(), current_perm.end(), letters[i]) == current_perm.end()) { - current_perm.push_back(letters[i]); - permute(letters, current_perm, all_permutations); - current_perm.pop_back(); - } - } -} - -int main() { - vector letters = {'a', 'b', 'c'}; - vector current_perm; - vector> all_permutations; - - permute(letters, current_perm, all_permutations); - - cout << "All permutations:\n"; - for (const auto& perm : all_permutations) { - for (char c : perm) { - cout << c << ' '; - } - cout << '\n'; - } - - return 0; -} - - ``` - - -```Python showLineNumbers -def permute(letters, current_perm=[], all_permutations=[]): - """Finds all permutations (arrangements) of the given letters.""" - if len(current_perm) == len(letters): - all_permutations.append(current_perm.copy()) # Append a copy to avoid modification - return - - for i in range(len(letters)): - if letters[i] not in current_perm: # Avoid duplicates - current_perm.append(letters[i]) - permute(letters, current_perm, all_permutations) - current_perm.pop() # Backtrack - -# Example usage -letters = ['a', 'b', 'c'] -permute(letters, all_permutations=[]) -print("All permutations:", all_permutations) - - -``` - - -``` jsx showLineNumbers -import java.util.ArrayList; -import java.util.List; - -public class Permutations { - public static void permute(char[] letters, List currentPerm, List> allPermutations) { - if (currentPerm.size() == letters.length) { - allPermutations.add(new ArrayList<>(currentPerm)); - return; - } - - for (char letter : letters) { - if (!currentPerm.contains(letter)) { - currentPerm.add(letter); - permute(letters, currentPerm, allPermutations); - currentPerm.remove(currentPerm.size() - 1); - } - } - } - - public static void main(String[] args) { - char[] letters = {'a', 'b', 'c'}; - List currentPerm = new ArrayList<>(); - List> allPermutations = new ArrayList<>(); - - permute(letters, currentPerm, allPermutations); - - System.out.println("All permutations:"); - for (List perm : allPermutations) { - for (char c : perm) { - System.out.print(c + " "); - } - System.out.println(); - } - } -} - - -``` - - - -``` jsx showLineNumbers -function permute(letters, currentPerm = [], allPermutations = []) { - if (currentPerm.length === letters.length) { - allPermutations.push([...currentPerm]); // Append a copy - return; - } - - for (let i = 0; i < letters.length; i++) { - if (!currentPerm.includes(letters[i])) { - currentPerm.push(letters[i]); - permute(letters, currentPerm, allPermutations); - currentPerm.pop(); // Backtrack - } - } -} - -// Example usage -let letters = ['a', 'b', 'c']; -let allPermutations = []; -permute(letters, [], allPermutations); -console.log("All permutations:", allPermutations); - - -``` - - - - \ No newline at end of file diff --git a/docs/dsa/algorithms/bitwise.md b/docs/dsa/algorithms/bitwise.md deleted file mode 100644 index f1b6884d9..000000000 --- a/docs/dsa/algorithms/bitwise.md +++ /dev/null @@ -1,55 +0,0 @@ ---- -id: bitwise-in-dsa -title: Bitwise Algorithm in Data Structures and Algorithms -sidebar_label: Bitwise Algorithm -sidebar_position: 1 -description: "" -tags: - [dsa,data-algorithms , bitwise - ] ---- - -Bitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits within an integer's binary representation to solve problems efficiently. These algorithms use bitwise operators like AND, OR, XOR, NOT, LEFT SHIFT, and RIGHT SHIFT. They are fundamental in low-level programming, encryption, compression, and optimization tasks due to their direct manipulation of data at the bit level. -![bitwise](image-7.png) - -### Explanation -Bitwise algorithms operate directly on the binary representation of numbers. For example, the bitwise AND operator (&) compares each bit of two numbers and returns a new number whose bits are set to 1 only if both compared bits are 1. Other operators work similarly, manipulating bits to achieve various outcomes. - -## Advantages -- Efficiency: Bitwise operations are extremely fast, as they are directly supported by the processor. -- Low-level control: They provide granular control over data, allowing for optimizations not possible with higher-level abstractions. -- Space-saving: Bitwise operations can be used to compactly store and manipulate data, reducing memory usage. - -## Disadvantages -- Readability: Code using bitwise operations can be hard to read and understand, especially for those not familiar with these operations. -- Error-prone: Small mistakes in bitwise operations can lead to significant bugs, as the operations are very low-level. -- Limited applicability: Not all problems benefit from bitwise optimizations; their use is somewhat niche. - -## Application in a Problem -Consider the problem of finding the unique number in an array where all numbers except one are repeated twice. A bitwise XOR operation can solve this efficiently. - -**Example** -Given an array: [4, 1, 2, 1, 2], find the unique number. - -## Step-by-step: - -- XOR all the numbers in the array. -- Repeated numbers will cancel each other out because n XOR n = 0. -- The result will be the unique number, as n XOR 0 = n. - -## Implementation: -```python -def findUnique(arr): - unique = 0 - for num in arr: - unique ^= num - return unique - -arr = [4, 1, 2, 1, 2] -print(findUnique(arr)) # Output: 4 -``` - -In this example, the XOR operation is used to find the unique number efficiently. This showcases the power of bitwise operations in solving specific types of problems with minimal code and high performance. - - -Bitwise algorithms leverage the fundamental operations of bitwise logic to perform calculations directly on the binary representations of numbers. This approach offers a unique blend of efficiency, precision, and low-level data manipulation capabilities that are unmatched by higher-level algorithmic strategies. 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