In computer science, sorting is a fundamental operation that involves arranging elements in a particular order. There are various sorting algorithms, each with its own pros and cons. One popular technique is the Sort]], an efficient comparison-based algorithm that uses the principle of divide and conquer.
Merge Sort is a algorithm that recursively divides a given array into two halves until the base case is reached, where the array size becomes 1 or 0. It then merges the sorted halves back together to obtain a sorted array. This process is performed by a , which takes two sorted arrays and merges them into a single sorted array.
for the Merge Sort algorithm:
left = Merge Sort(arr[0...mid])
right = Merge Sort(arr[mid+1...end])
merged = []
if left[0] ≤ right[0]
append left[0] to merged
remove left[0] from left
append right[0] to merged
remove right[0] from right
In Merge Sort, the is primarily dependent on the number of elements being sorted. In the , , and scenarios, Merge Sort exhibits a of O(n log n), making it highly efficient. This complexity arises due to the recursive nature of the algorithm and the merging of the sorted subarrays.
Moreover, Merge Sort is a , meaning elements with equal values maintain their relative order in the sorted output. Additionally, it is an since it requires extra space to store the merged subarrays. The of Merge Sort is O(n), where n represents the number of elements in the input array.
ing]] refers to algorithms that sort the input array by modifying the positions of its elements without requiring additional memory. Although Merge Sort is not inherently an in-place sort, it can be transformed into an variant by modifying the merge function to utilize the existing input array directly. However, this in-place variant entails more complex logic and increases the number of element , resulting in a higher time complexity.
Overall, Merge Sort is a well-known, efficient, and stable ing algorithm, widely used in scenarios where a reliable and fast sort is required. Its and ability to handle large input sizes make it popular in various applications.
Keywords
space complexity | time complexity | comparison-based sort | stable sort | recursive | [[in-place sort | average case | linearithmic time complexity | swaps | worst case | out-of-place sort | best case | pseudocode | logarithmic time complexity | merge function | [[merge | in-place merge sort |
