You are given two sorted arrays A = [1, 2, 3] B = [2, 5, 6, 7], o/p = [1, 2, 2, 3, 5, 6, 7] Write an algorithm to merge these sorted arrays. Mention the time and space complexity of your algorithm
You are given two sorted arrays
A = [1, 2, 3] B = [2, 5, 6, 7], o/p = [1, 2, 2, 3, 5, 6, 7]
Write an
Merge Sort is a widely-used, efficient, and stable comparison-based sorting algorithm. It follows the divide and conquer paradigm to sort a list or array of elements. The key idea behind Merge Sort is to divide the unsorted list into smaller sublists until each sublist consists of only one element, and then merge those sublists in a way that results in a sorted, merged list.
Here's a step-by-step explanation of the Merge Sort algorithm:
Divide: The unsorted list is divided into two sublists of roughly equal size. This step continues recursively until each sublist contains only one element.
Conquer: After the divide step, you have a collection of small sorted sublists. In the conquer step, these sublists are merged in pairs to create larger sorted sublists. This merging process continues until there's a single sorted list.
Merge: To merge two sublists, you compare the elements of both sublists and insert them into a new sublist in the correct order. This process continues recursively until all sublists are merged into a single, sorted list.
The merge step is crucial and is where the algorithm derives its name. It involves the comparison and combination of the sublists in a way that ensures the resulting list is sorted. The merge operation is typically implemented as an auxiliary function.
Merge Sort has the following characteristics:
It is a stable sorting algorithm, meaning it preserves the relative order of equal elements.
It has a time complexity of O(n log n) for the worst, average, and best cases, making it a very efficient sorting algorithm.
It requires additional space for the merge step, which can make it less memory-efficient than in-place sorting algorithms, but the additional space is typically less of a concern in most modern computing environments.
Merge Sort is widely used in practice and is often used as the standard comparison when evaluating the efficiency of other sorting algorithms due to its consistent performance.
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