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Counting sort is a sorting technique based on keys between a specific range. It works by counting the number of objects having distinct key values (kind of hashing). Then do some arithmetic to calculate the position of each object in the output sequence.&nbsp;Counting sort makes assumptions about the data, for example, it assumes that values are going to be in the range of 0 to 10 or 10 – 99 etc, Some other assumptions counting sort makes are input data will be all real numbers. Like other algorithms this sorting algorithm is not a comparison-based algorithm, it hashes the value in a temporary count array and uses them for sorting. It uses a temporary array making it a non In Place algorithm.Counting Sort : <a href="https://www.geeksforgeeks.org/counting-sort/">https://www.geeksforgeeks.org/counting-sort/</a>

Counting Sort

<h2>Heap Sort | Comprehensive Guide</h2>Heap Sort is a popular and efficient comparison-based sorting algorithm that uses a binary heap data structure to sort elements. It is known for its efficiency in handling large datasets and provides a time complexity of O(n log n), making it one of the most widely used algorithms for sorting.<h3>What is Heap Sort?</h3>Heap Sort is a sorting algorithm that organizes data by leveraging the properties of a binary heap. A binary heap is a complete binary tree where the elements are arranged either in increasing order (min-heap) or decreasing order (max-heap). Heap sort typically uses a max-heap to repeatedly remove the largest element and place it at the end of the list until the entire list is sorted.<h3>How Heap Sort Works</h3>Heap sort operates in two main phases:Building the Heap:<ul><li>First, the input data is converted into a binary heap structure. This is done using a process called heapify, where each element of the array is rearranged to satisfy the heap property (i.e., for a max-heap, the parent node is greater than its children).</li></ul>Extracting Elements:<ul><li>Once the heap is built, the largest element (root of the max-heap) is removed and swapped with the last element of the heap. The heap is then adjusted (heapified) to maintain the heap structure, and this process is repeated until all elements are sorted.</li></ul><h3>Steps of Heap Sort Algorithm</h3>Build a Max-Heap:<ul><li>Rearrange the elements of the array to form a max-heap. In a max-heap, each parent node is greater than or equal to its child nodes.</li></ul>Swap the Root with the Last Element:<ul><li>After building the max-heap, swap the root element (the largest value) with the last element of the heap.</li></ul>Reduce Heap Size and Heapify:<ul><li>Reduce the heap size by 1 (since the last element is now sorted) and call the heapify function to maintain the max-heap property. Repeat this process until all elements are sorted.</li></ul><h3>Time Complexity of Heap Sort</h3>The time complexity of Heap Sort is O(n log n). Here's why:<ul><li>Building the Heap: It takes O(n) time to build a max-heap from the input array.</li><li>Heapify Process: Heapifying an element takes O(log n) time, and it is performed n times during the extraction phase, resulting in a total of O(n log n) for the sorting phase.</li></ul>Thus, the overall time complexity is O(n log n), making Heap Sort efficient for large datasets.<h3>Space Complexity of Heap Sort</h3>The space complexity of Heap Sort is O(1), as it is an in-place sorting algorithm. This means that Heap Sort does not require any additional memory beyond the input array itself, making it space-efficient.<h3>Applications of Heap Sort</h3>Sorting Large Datasets:<ul><li>Heap Sort is often used for sorting large datasets because of its O(n log n) time complexity and efficient memory usage.</li></ul>Priority Queues:<ul><li>Since a max-heap (or min-heap) is used to implement priority queues, Heap Sort can be utilized to manage and organize priority queues efficiently.</li></ul>Selection Algorithms:<ul><li>Heap Sort is also used in selection algorithms where finding the largest or smallest elements from a list is required.</li></ul><h3>Advantages of Heap Sort</h3>Efficiency:<ul><li>Heap Sort has a time complexity of O(n log n), making it highly efficient for large datasets.</li></ul>In-Place Sorting:<ul><li>Heap Sort is an in-place algorithm, meaning it requires no additional memory beyond the input array.</li></ul>No Worst-Case Degradation:<ul><li>Unlike algorithms like Quick Sort, which can degrade to O(n²) in the worst case, Heap Sort maintains its O(n log n) complexity for all cases.</li></ul><h3>Disadvantages of Heap Sort</h3>Not Stable:<ul><li>Heap Sort is not a stable sorting algorithm, meaning that the relative order of equal elements is not preserved during the sorting process.</li></ul>More Comparisons:<ul><li>Heap Sort generally performs more comparisons compared to Quick Sort or Merge Sort, making it less efficient in some scenarios.</li></ul><h3>Why Learn Heap Sort?</h3>Heap Sort is an important algorithm to learn because of its efficiency, memory usage, and versatility. It’s used in scenarios where sorting large datasets in O(n log n) time is required, and its use of the heap data structure makes it valuable in understanding priority queues and other advanced topics in computer science.Topics Covered:Definition of Heap Sort: What Heap Sort is and how it works.Steps of the Algorithm: Building the heap and extracting elements.Applications: Common uses of Heap Sort in real-world scenarios.For more details and further examples, check out the full article on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/heap-sort/">https://www.geeksforgeeks.org/heap-sort/</a>.

Heap Sort - Data Structures and Algorithms

<h2>Bipartite Graph | A Comprehensive Guide</h2>In this guide, we’ll explore the concept of a bipartite graph, a fundamental structure in graph theory used in various real-world applications such as matching problems, scheduling, and network flow. Bipartite graphs can be easily recognized by their unique properties and are widely used in algorithms to optimize different types of computations. By the end of this guide, you’ll understand what a bipartite graph is, its key properties, how to identify it, and its applications.<h2>What is a Bipartite Graph?</h2>A bipartite graph is a graph in which the set of vertices can be divided into two disjoint sets, such that no two vertices within the same set are adjacent. In other words, edges only connect vertices from one set to the other set, and there are no edges between vertices within the same set.<h3>Formal Definition:</h3>A graph G=(V,E)G = (V, E)G=(V,E) is bipartite if its vertex set VVV can be divided into two disjoint sets UUU and WWW, such that every edge in EEE connects a vertex in UUU with a vertex in WWW.<h3>Example:</h3>Consider the following bipartite graph:mathematicaCopy codeSet U = {1, 2, 3}
Set W = {A, B, C}
Edges: (1, A), (2, B), (3, C)
In this graph, vertices in Set UUU only connect to vertices in Set WWW, with no edges between vertices in Set UUU or Set WWW.<h2>Key Properties of Bipartite Graphs:</h2>Two Disjoint Sets:<ul><li>The vertices are divided into two disjoint sets UUU and WWW, with edges only between these sets.</li></ul>No Odd-Length Cycles:<ul><li>A graph is bipartite if and only if it contains no odd-length cycles. If a graph has an odd-length cycle, it cannot be bipartite.</li></ul>2-Colorability:<ul><li>Bipartite graphs can be colored with two colors such that no two adjacent vertices share the same color. This property is a result of the two-set structure of bipartite graphs, where one color can be assigned to vertices in one set and the other color to the vertices in the second set.</li></ul>Maximum Matching:<ul><li>Bipartite graphs are particularly useful in solving maximum matching problems, where you aim to find the largest possible set of edges that match vertices between the two sets.</li></ul><h2>How to Check if a Graph is Bipartite:</h2>There are multiple ways to determine whether a given graph is bipartite:<h3>1. Breadth-First Search (BFS) or Depth-First Search (DFS):</h3><ul><li>To check if a graph is bipartite, you can use BFS or DFS to try and 2-color the graph. Start from any vertex, assign it one color, and assign its adjacent vertices the opposite color. Continue this process, and if any two adjacent vertices end up with the same color, the graph is not bipartite.</li></ul><h3>2. Cycle Detection:</h3><ul><li>As bipartite graphs do not contain odd-length cycles, checking whether a graph contains any odd-length cycles is another method to determine if the graph is bipartite. If such a cycle is found, the graph is not bipartite.</li></ul><h2>Applications of Bipartite Graphs:</h2>Matching Problems:<ul><li>Bipartite graphs are used in job assignment problems, where one set of vertices represents workers and the other set represents jobs. Edges connect workers to jobs they are qualified for, and the goal is to maximize the number of jobs assigned.</li></ul>Scheduling and Task Assignment:<ul><li>In scheduling tasks or assigning resources, bipartite graphs help model the relationship between tasks and available resources, ensuring optimal assignments.</li></ul>Recommendation Systems:<ul><li>In recommendation systems, bipartite graphs model relationships between users and items (e.g., movies, books). An edge represents an interaction (e.g., a user rating a movie), and recommendations are generated based on these connections.</li></ul>Network Flow Problems:<ul><li>Bipartite graphs are also used in network flow algorithms, particularly in solving problems like the maximum flow problem, where the goal is to maximize the flow through a network by finding the best matching.</li></ul><h3>Real-World Example:</h3>One of the most common uses of bipartite graphs is in job assignment:<ul><li>One set of vertices represents workers, and the other set represents jobs.</li><li>An edge between a worker and a job indicates that the worker is qualified for that job.</li><li>The problem becomes finding the optimal way to assign workers to jobs, such that the maximum number of jobs is filled, without assigning more than one job to a worker.</li></ul><h2>Why Learn About Bipartite Graphs?</h2>Bipartite graphs are essential in solving a variety of problems, from matching jobs to workers to generating recommendations in e-commerce systems. They form the backbone of several important algorithms used in both theoretical computer science and real-world applications. Understanding bipartite graphs and how to check for them helps you approach and solve problems related to optimization, matching, and flow more efficiently.Topics Covered:Definition and Properties of Bipartite Graphs: Learn the characteristics that make a graph bipartite, including 2-colorability and the absence of odd-length cycles.Checking for Bipartiteness: Understand how to use BFS or DFS to determine if a graph is bipartite and why detecting odd-length cycles is important.Applications: Discover real-world problems and use cases where bipartite graphs are essential, such as in job assignments, recommendation systems, and network flow.For more details and a deeper understanding, check out the full article on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/bipartite-graph/">https://www.geeksforgeeks.org/bipartite-graph/</a>.

Algorithm and Code for Bipartite Graph 

Welcome to the daily solving of our PROBLEM OF THE DAY with Karan Mashru We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Sorting but also build up problem-solving skills. Given two positive integer arrays arr and brr, find the number of pairs such that&nbsp;xy &gt; yx&nbsp;(raised to power of) where x is an element from arr and y is an element from brr. Examples :Input: arr[] = [2, 1, 6], brr[] = [1, 5]
Output: 3
Explanation: The pairs which follow xy &gt; yx are: 21 &gt; 12,&nbsp; 25 &gt; 52 and 61 &gt; 16 .Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/number-of-pairs-1587115620/1">https://practice.geeksforgeeks.org/problems/number-of-pairs-1587115620/1</a>

PROBLEM OF THE DAY : 25/08/2024 | Number of pairs

Welcome to the daily solving of our PROBLEM OF THE DAY with Nitin Kaplas We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Graph but also build up problem-solving skills. You are given an Undirected Graph having unit weight of the edges, find the shortest path from src to all the vertex and if it is unreachable to reach any vertex, then return -1 for that vertex.Examples :Input:
n = 9, m = 10
edges=[[0,1],[0,3],[3,4],[4,5],[5,6],[1,2],[2,6],[6,7],[7,8],[6,8]] 
src=0
Output:
0 1 2 1 2 3 3 4 4Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/shortest-path-in-undirected-graph-having-unit-distance/1">https://practice.geeksforgeeks.org/problems/shortest-path-in-undirected-graph-having-unit-distance/1</a>

PROBLEM OF THE DAY : 21/08/2024 | Shortest Path in Undirected Graph

Welcome to the daily solving of our PROBLEM OF THE DAY with Devashish Khare. We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of&nbsp; but also build Backtracking up problem-solving skills. Consider a rat placed at (0, 0) in a square matrix mat of order n* n. It has to reach the destination at (n - 1, n - 1). Find all possible paths that the rat can take to reach from source to destination. The directions in which the rat can move are 'U'(up), 'D'(down), 'L' (left), 'R' (right). Value 0 at a cell in the matrix represents that it is blocked and rat cannot move to it while value 1 at a cell in the matrix represents that&nbsp;rat&nbsp;can be travel&nbsp;through it. Note: In a path, no cell can be visited more than one time.&nbsp;If the source cell is 0, the rat cannot move to any other cell. In case of no path, return an empty list. The driver will output "-1" automatically.Examples:Input: mat[][] = {{1, 0, 0, 0},
 &nbsp; &nbsp; &nbsp; &nbsp; {1, 1, 0, 1}, 
 &nbsp; &nbsp; &nbsp; &nbsp; {1, 1, 0, 0},
 &nbsp; &nbsp; &nbsp; &nbsp; {0, 1, 1, 1}}
 Output:
DDRDRR DRDDRR
 Explanation:
The rat can reach the destination at 
(3, 3) from (0, 0) by two paths - DRDDRR 
and DDRDRR, when printed in sorted order 
we get DDRDRR DRDDRR. Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems-preview/rat-in-a-maze-problem/1">https://practice.geeksforgeeks.org/problems/rat-in-a-maze-problem/1</a>

PROBLEM OF THE DAY : 30/07/2024 | Rat in a Maze Problem - I

Welcome to the daily solving of our PROBLEM OF THE DAY with Nitin Kaplas We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Arrays but also build up problem-solving skills. Given two sorted arrays arr1 and arr2 and an element k. The task is to find the element that would be at the kth position of the combined sorted array.Examples :Input: k = 5, arr1[] = [2, 3, 6, 7, 9], arr2[] = [1, 4, 8, 10]
 Output: 6
 Explanation: The final combined sorted array would be - 1, 2, 3, 4, 6, 7, 8, 9, 10. The 5th element of this array is 6. &nbsp;Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/k-th-element-of-two-sorted-array1317/1">https://practice.geeksforgeeks.org/problems/k-th-element-of-two-sorted-array1317/1</a>

PROBLEM OF THE DAY : 07/08/2024 | K-th element of two Arrays

Unlock the secrets of the Binary Search Algorithm with this comprehensive tutorial! Whether you’re a beginner or an experienced programmer, this video will guide you through both iterative and recursive implementations of binary search in Python, helping you understand their differences and applications.<h2>What You'll Learn in this Video</h2><ol><li>Introduction to Binary Search Trees: Understand the fundamentals of BST and its importance in computer science.</li><li>Iterative vs. Recursive BST: Learn the key differences and advantages of using iterative methods.</li><li>Implementing Iterative BST in Python: Step-by-step coding guide to implementing an iterative binary search tree.</li><li>Insertion and Deletion: Master the techniques for inserting and deleting nodes in an iterative BST.</li><li>Search Operations: Efficiently perform search operations within your BST.</li><li>Tree Traversal: Learn various tree traversal methods including in-order, pre-order, and post-order traversal.</li></ol><h2>Why Watch?</h2><ul><li>Optimize Your Code: Learn how to make your search operations faster and more efficient.</li><li>Enhance Problem-Solving Skills: Mastering both iterative and recursive techniques will broaden your algorithm toolkit.</li><li>Interview Prep: Perfect for acing coding interviews and technical assessments.</li></ul><h2>Resources</h2>Read the Full Article <a href="https://www.geeksforgeeks.org/binary-search/">Here</a>

Iterative Binary Search Tree

Welcome to the daily solving of our PROBLEM OF THE DAY with Yash Dwivedi. We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Tree but also build up problem-solving skills. Given a binary tree, your task is to find all duplicate subtrees from the given binary tree.Duplicate Subtree : Two trees are duplicates if they have the same structure with the same node values.Note:&nbsp; Return the root of each tree in the form of a list array &amp; the driver code will print the tree in pre-order tree traversal in lexicographically increasing order.Examples: Input :&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;1 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; / &nbsp;\ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 2 &nbsp; &nbsp; 3 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; / &nbsp; &nbsp; &nbsp;/ &nbsp;\ &nbsp; &nbsp; &nbsp; &nbsp; 4 &nbsp; &nbsp; 2 &nbsp; &nbsp; &nbsp;4 &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;/ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; 4 Output: 2 &nbsp;4 &nbsp;&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;4 Explanation: The above tree have two duplicate subtrees.i.e&nbsp; &nbsp; 2 &nbsp;/ 4 &nbsp;and 4. Therefore, you need to return the above tree root in the form of a list.Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/duplicate-subtrees/1">https://practice.geeksforgeeks.org/problems/duplicate-subtrees/1</a>

PROBLEM OF THE DAY : 04/07/2024 | Duplicate Subtrees

Welcome to the daily solving of our PROBLEM OF THE DAY with Ayush Tripathi. We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Matrix but also build up problem-solving skills. Given a binary matrix contains 0s and 1s only, we need to find the sum of coverage of all zeros of the matrix where coverage for a particular 0 is defined as a total number of ones around a zero in left, right, up and bottom directions.Examples:Input: matrix = [[0, 1, 0], &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [0, 1, 1], &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;[0, 0, 0]] Output: 6 Explanation: There are a total of 6 coverage are there.Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/coverage-of-all-zeros-in-a-binary-matrix4024/1">https://practice.geeksforgeeks.org/problems/coverage-of-all-zeros-in-a-binary-matrix4024/1</a>

PROBLEM OF THE DAY : 26/06/2024 | Coverage of all Zeros in a Binary Matrix

Welcome to the daily solving of our PROBLEM OF THE DAY with Nitin Kaplas. We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Matrix but also build up problem-solving skills. You are given an integer k and matrix&nbsp;mat.&nbsp;Rotate the elements of the given matrix to the left k times and return the resulting matrix.Examples:Input: k=1, mat=[[1,2,3],[4,5,6],[7,8,9]]
 Output: 2 3 1 5 6 4
8 9 7
 Explanation: Rotate the matrix by one 1 2 3 &nbsp; &nbsp; &nbsp; 2 3 1 4 5 6 &nbsp;=&gt; &nbsp;5 6 4 7 8 9 &nbsp; &nbsp; &nbsp; 8 9 7Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/left-rotate-matrix-k-times2351/1">https://practice.geeksforgeeks.org/problems/left-rotate-matrix-k-times2351/1</a>

PROBLEM OF THE DAY : 25/06/2024 | Left Rotate Matrix K times

Welcome to the daily solving of our PROBLEM OF THE DAY with Ayush Tripathi. We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Matrix but also build up problem-solving skills. A matrix is constructed of size n*n and given an integer ‘q’. The value at every cell of the matrix is given as, M(i,j) = i+j, where ‘M(i,j)' is the value of a cell, ‘i’ is the row number, and ‘j’ is the column number. Return the number of cells having value ‘q’.Note: Assume, the array is in 1-based indexing.Examples:Input: n = 4, q = 7
 Output: 2
 Explanation: Matrix becomes
2 3 4 5 
3 4 5 6 
4 5 6 7
5 6 7 8
The count of 7 is 2.Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/summed-matrix5834/1">https://practice.geeksforgeeks.org/problems/summed-matrix5834/1</a>

PROBLEM OF THE DAY : 24/06/2024 | Summed Matrix