Design and Analysis of Algorithms - Mergesort Algorithm (Part-3) | Time and Space Complexity | Sorting Algorithm | GATECSE | DAA

#mergesorttimecomplexity, #mergesort, #thegatehub merge sort timecomplexity || merge sort algorithm timecomplexity || sorting algorithms timecomplexity || merge sort time complexity || gate computer science || how merge sort works || merge sort in daa || data structure and algorithms || divide and conquer || merge sort questions || merge sort in divide and conquer || merge sort using divide and conquer || recursive merge sort || recursive mergesort || analysis of mergesort || performance of merge sort || How Merge Sort Works? || How Merge Sort algorithms Works? || How 2 way Mergesort Works? || How 2 way Mergesort algorithm Works? || Algorithm for merging two arrays || Algorithm for merging two sorted subarrays || Algorithm for merging two list || Algorithm for merging two arrays in data structure || Algorithm for merging two arrays in algorithms In this vedio i have Discussed merging algorithm with an example. Step by step instructions on how merging is to be done with the code of merge function. Merge sort is the first algorithm we are going to study in Divide and Conquer. According to Divide and Conquer, it first divides an array into smaller subarrays and then merges them together to get a sorted array. Divide: Divide the unsorted array into two subarray of about half the size. Conquer: Sort each of the two subarray recursively until we have list sizes of length 1, in which case the array items are returned. Combine: Merge the two sorted Subarray back into one sorted array. Mergesort Algorithm, Merge Procedure, Merging, Divide and Conquer Megesort full explanation in hindi Megesort detailed explanation in hindi How Merge Sort Works? How Merge Sort algorithms Works? How 2 way Mergesort Works? How 2 way Mergesort algorithm Works? How merge procedure Works? How merge function Works? How 2 way Mergesort Works? How 2 way merging algorithm Works? Mergesort time complexity How to calculate Mergesort time complexity How to analyze Mergesort time complexity How to calculate Merge procedure time complexity How to analyze Merge procedure time complexity How to calculate Mergesort space complexity How to analyze Mergesort space complexity How to analyze Merge procedure space complexity Analysis of merge procedure Algorithm for merging two arrays Algorithm for merging two sorted subarrays Algorithm for merging two list Algorithm for merging two arrays in data structure Algorithm for merging two arrays in algorithms merge sort in divide and conquer merge sort algorithm in divide and conquer merging of two arrays in data structure merging of two arrays in algorithm Merging Two Sorted Sequences Merge sort full explanation with example Merge sort full explanation with gate example most expected question gate on mergesort most frequently asked question gate on mergesort merging algorithm with code Top-down implementation mergesort Bottom-up implementation mergesort Top-down implementation merge procedure Bottom-up implementation merge procedure Worst-case performance of mergesort O(n log n) Best-case performance of mergesort O(n log n) Average performance of mergesort O(n log n) Worst-case space complexity of mergesort О(n) space complexity of mergeprocedure О(n) We study the mergesort algorithm and show that it guarantees to sort any array of n items with at most n log n compares. We also consider a nonrecursive, bottom-up version. We prove that any compare-based sorting algorithm must make at least n lg n compares in the worst case. We discuss using different orderings for the objects that we are sorting and the related concept of stability. Mergesort has two steps: merging and sorting. The algorithm uses a divide-and-conquer approach to merge and sort a list. Divide and conquer is a technique used for breaking algorithms down into subproblems, solving the subproblems, and then combining the results back together to solve the original problem. It can be helpful to think of this method as divide, conquer, and combine. The mergesort algorithm focuses on how to merge together two pre-sorted arrays such that the resulting array is also sorted. Mergesort can be implemented either recursively or iteratively. Here is the recursive mergesort algorithm: If the list has only one element, return the list and terminate. (Base case) Split the list into two halves that are as equal in length as possible. (Divide) Using recursion, sort both lists using mergesort. (Conquer) Merge the two sorted lists and return the result. (Combine) Complexity of Mergesort Division: It takes O(1) time to divide the problem into two parts. To divide the problem, the algorithm computes the middle of the list by taking the length of the list and dividing by two, which takes constant time.