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Welcome to the daily solving of our PROBLEM OF THE DAY with Jay Dalsaniya 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 2 sorted integer arrays arr1 and arr2. Find the sum of the middle elements of two sorted arrays arr1 and arr2.Examples:Input: arr1 = [1, 2, 4, 6, 10], arr2 = [4, 5, 6, 9, 12]
Output: 11
Explanation: The merged array looks like [1, 2, 4, 4, 5, 6, 6, 9, 10, 12]. Sum of middle elements is 11 (5 + 6). &nbsp;Give the problem a try before going through the video. All the best!!! Problem Link: <a href="https://practice.geeksforgeeks.org/problems/sum-of-middle-elements-of-two-sorted-arrays2305/1'">https://practice.geeksforgeeks.org/problems/sum-of-middle-elements-of-two-sorted-arrays2305/1</a>

PROBLEM OF THE DAY : 12/08/2024 | Median of Two Sorted Arrays

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

Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:Only one disk can be moved at a time. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e. a disk can only be moved if it is the uppermost disk on a stack. No disk may be placed on top of a smaller disk. Approach :Let rod 1 = 'A', rod 2 = 'B', rod 3 = 'C'. An example with 2 disks : Step 1 : Shift first disk from 'A' to 'B'.Tower of Hanoi &nbsp;: <a href="https://www.geeksforgeeks.org/c-program-for-tower-of-hanoi/">https://www.geeksforgeeks.org/c-program-for-tower-of-hanoi/</a>

Tower of Hanoi

Like QuickSort, Merge Sort is a Divide and Conquer algorithm. It divides the input array into two halves, calls itself for the two halves, and then it merges the two sorted halves. The merge() function is used for merging two halves. The merge(arr, l, m, r) is a key process that assumes that arr[l..m] and arr[m+1..r] are sorted and merges the two sorted sub-arrays into one.Pseudocode :• &nbsp; &nbsp;Declare left variable to 0 and right variable to n-1&nbsp; • &nbsp; &nbsp;Find mid by medium formula. mid = (left+right)/2 • &nbsp; &nbsp;Call merge sort on (left,mid) • &nbsp; &nbsp;Call merge sort on (mid+1,rear) • &nbsp; &nbsp;Continue till left is less than right • &nbsp; &nbsp;Then call merge function to perform merge sort.Merge Sort : <a href="https://www.geeksforgeeks.org/merge-sort/">https://www.geeksforgeeks.org/merge-sort/</a>&nbsp;

Merge Sort

Welcome to the daily solving of our PROBLEM OF THE DAY with Soham Mukherjee. 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 Divide and Conquer but also build up problem-solving skills. Given a sorted and rotated array arr of n distinct elements which may be rotated at some point, and given an element key, the task is to find the index of the given element key in the array arr. The whole array arr is given as the range to search.Rotation shifts elements of the array by a certain number of positions, with elements that fall off one end reappearing at the other end.Note:- 0-based index is followed &amp; return -1 if the key is not present.Examples :Input: arr[] = {5, 6, 7, 8, 9, 10, 1, 2, 3}, key = 10
 Output: 5
 Explanation: 10 is found at index 5. Problem Link: <a href="https://practice.geeksforgeeks.org/problems/search-in-a-rotated-array4618/1">https://practice.geeksforgeeks.org/problems/search-in-a-rotated-array4618/1</a>

PROBLEM OF THE DAY : 08/07/2024 | Search in a Rotated Array

Dive into the fascinating world of counting inversions with our comprehensive tutorial designed for both novice learners and experienced programmers. Explore the intricacies of this fundamental problem in computer science and gain valuable insights into efficient algorithms and techniques for its solution.Here's what you'll uncover:<ul><li>Problem Overview: Gain a clear understanding of the concept of inversions and their significance in various applications such as sorting algorithms, array manipulation, and computational geometry.</li><li>Key Concepts: Familiarize yourself with essential concepts such as inversion pairs, divide and conquer algorithms, and merge sort, laying the groundwork for effective problem-solving strategies.</li><li>Solution Approaches: Explore different approaches and algorithms for counting inversions, including brute-force methods, divide and conquer techniques, and optimized algorithms leveraging data structures such as segment trees or Fenwick trees.</li><li>Code Implementation: Delve into detailed code examples in popular programming languages like Python, Java, or C++, accompanied by explanations and optimizations to ensure clarity and efficiency.</li><li>Optimization Techniques: Learn how to optimize your solution by reducing redundant computations and leveraging algorithmic insights to achieve optimal time and space complexity.</li><li>Validation and Testing: Discover strategies for validating your implementation using test cases to ensure correctness and robustness across a variety of scenarios and input sizes.</li><li>Extensions and Applications: Explore extensions of the problem and its applications in real-world scenarios such as array manipulation, optimization problems, and computational biology.</li></ul>By the end of this tutorial, you'll have a comprehensive understanding of counting inversions, equipping you with the skills to tackle similar problems effectively and efficiently.For a detailed exploration of this topic, including code examples and in-depth explanations, visit our full article at <a href="https://www.geeksforgeeks.org/counting-inversions/">https://www.geeksforgeeks.org/counting-inversions/</a>. Whether you're a novice programmer or an experienced algorithmist, this tutorial provides invaluable insights to enhance your problem-solving abilities and broaden your computational toolkit.

Count Inversions | DSA Problem

Delve into the world of binary matrices and dynamic programming with GeeksforGeeks! Our comprehensive guide on finding the largest square in a binary matrix with at most K 1s for multiple queries will equip you with the skills to tackle complex problems efficiently.Here's what you can expect from this tutorial:<ul><li style="margin-left:0px;">Understanding the Problem: We'll break down the problem statement and explain the constraints involved in finding the largest square in a binary matrix with limited 1s.</li><li style="margin-left:0px;">Dynamic Programming Approach: Explore the dynamic programming approach used to solve this problem, including the formulation of recurrence relations and implementation strategies.</li><li style="margin-left:0px;">Handling Multiple Queries: Learn how to optimize the solution to handle multiple queries efficiently, ensuring optimal time and space complexity.</li></ul>Whether you're a beginner in dynamic programming or an experienced programmer seeking to sharpen your problem-solving skills, this tutorial offers valuable insights and techniques.Ready to unravel the mysteries of binary matrices and dynamic programming? Dive into the ultimate guide on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/largest-square-in-a-binary-matrix-with-at-most-k-1s-for-multiple-queries/">https://www.geeksforgeeks.org/largest-square-in-a-binary-matrix-with-at-most-k-1s-for-multiple-queries/</a>. Let's embark on this enlightening journey together!

Binary Matrix with at most K 1s | DSA Problem

Embark on a journey through optimization algorithms with this insightful guide from GeeksforGeeks on allocating the minimum number of pages. In this illuminating article, you'll explore essential concepts and algorithms for efficiently distributing pages of a book among students to minimize the maximum number of pages assigned, a critical skill for various applications such as education planning, resource allocation, and algorithmic problem-solving.Discover the principles behind optimization techniques as you delve into algorithms and methods for finding the optimal allocation of pages. Whether you're a coding enthusiast or a seasoned developer, mastering the art of efficiently allocating pages is essential for optimizing resources and solving real-world problems.Prepare to elevate your problem-solving skills and algorithmic proficiency as you explore detailed explanations and practical examples for allocating the minimum number of pages. Unlock the full potential of optimization algorithms in your projects by delving into the accompanying article on GeeksforGeeks: <a href="https://www.geeksforgeeks.org/allocate-minimum-number-pages/">https://www.geeksforgeeks.org/allocate-minimum-number-pages/</a>

Allocate minimum number of pages | DSA Problem

Given two integers x and n, write a function to compute xn. We may assume that x and n are small and overflow doesn’t happen. Input : x = 2, n = 3 Output : 8Input : x = 7, n = 2 Output : 49 Calculate power (x,y) using recursion : <a href="https://www.geeksforgeeks.org/write-a-c-program-to-calculate-powxn/">https://www.geeksforgeeks.org/write-a-c-program-to-calculate-powxn/</a>

Calculate power (x,y) using recursion

A Simple Solution is to linearly traverse the array and find the missing number. Time complexity of this solution is O(n). Below is the implementation From Mathematical formulae we know that in an AP, Sum of the n elements = (n/2)(a+l) n is the number of elements, a is the first element and l is the last elementIf we apply this formulae and keep it in a variable s, And take the sum of all elements and keep them in sum. We will get the missing number by s-sum(As sum doesnt includes the missing number) Find the missing element in the Arithmetic Progression : <a href="https://www.geeksforgeeks.org/find-missing-number-arithmetic-progression/">https://www.geeksforgeeks.org/find-missing-number-arithmetic-progression/</a>

Find the missing element in the Arithmetic Progression

here are 2 sorted arrays A and B of size n each. Write an algorithm to find the median of the array obtained after merging the above 2 arrays(i.e. array of length 2n). The complexity should be O(log(n)).&nbsp; Since the size of the set for which we are looking for the median is even (2n), we need to take the average of the middle two numbers and return the floor of the average. Use the merge procedure of merge sort. Keep track of count while comparing elements of two arrays. If count becomes n(For 2n elements), we have reached the median. Take the average of the elements at indexes n-1 and n in the merged array. Median of two sorted arrays of same size : <a href="https://www.geeksforgeeks.org/median-of-two-sorted-arrays/">https://www.geeksforgeeks.org/median-of-two-sorted-arrays/</a>

Median of two sorted arrays of same size

We are given an array of n points in the plane, and the problem is to find out the closest pair of points in the array. This problem arises in a number of applications. For example, in air-traffic control, you may want to monitor planes that come too close together, since this may indicate a possible collision. Recall the following formula for distance between two points p and q. \left \|pq \right \| = \sqrt{(p_{x}-q_{x})^{2}+ (p_{y}-q_{y})^{2}} &nbsp; &nbsp; &nbsp;&nbsp; The Brute force solution is O(n^2), compute the distance between each pair and return the smallest. We can calculate the smallest distance in O(nLogn) time using Divide and Conquer strategy. In this post, a O(n x (Logn)^2) approach is discussed. We will be discussing a O(nLogn) approach in a separate post.&nbsp;Closest Pair of Points : <a href="https://www.geeksforgeeks.org/closest-pair-of-points-using-divide-and-conquer-algorithm/">https://www.geeksforgeeks.org/closest-pair-of-points-using-divide-and-conquer-algorithm/</a>

Closest Pair of Points

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