Merge sort achieves time complexity log the average and worst cases
To analyze the number of comparisons required by Merge Sort to sort an array, let's consider the example given: [38, 27, 43, 3, 9, 82, 10].
In the first level, we have two sub-arrays: [38] and [27]. Since there is only one element in each sub-array, no comparison is needed.
27 - 9
27 - 10
It's important to note that the number of comparisons in Merge Sort is directly related to the number of elements in the input array. As Merge Sort follows a divide-and-conquer approach, it splits the array into smaller sub-arrays recursively until reaching single-element sub-arrays. The number of comparisons increases with the depth of the recursion and the number of elements to be merged.
By utilizing the divide-and-conquer strategy efficiently, Merge Sort achieves a time complexity of O(n log n) in the average and worst cases, making it a highly efficient sorting algorithm for large datasets.
