MS_1
Below is the Merge Sort discussed in lectures.
What is the time complexity of the provided merge sort algorithm in the average case?

Question

BlackTom AI · Accepted Answer

First, restating the context: the question asks for the average-case time complexity of the provided merge sort algorithm.
Option 1: O(n^2). This would imply quadratic growth, which is characteristic of inefficient algorithms like simple bubble sort in the worst case, not merge sort. Merge sort divides the problem and performs linear-time merging, so quadratic time is not appropriate here.
Option 2: O(log n). logarithmic time would be typical for binary search or certain divide-and-conquer steps that don’t involve processing all elements. In merge sort, elements are moved and copied multiple times during merging, so the total work cannot be just logarithmic.
Option 3: O(n). Linear time would indicate that each element is processed a constant number of times overall. However, in merge sort, each merge step processes all elements, and there are log n levels of these merges, so the total is more than linear.
Option 4: O(n log n). This reflects the standard behavior of merge sort: at each of the log n levels of recursion, all n elements are involved in the merging process, yielding the product n * log n, which is the typical average (and worst) case for merge sort.
In summary, the algorithm’s structure—dividing the input recursively and merging sorted halves—produces a complexity that scales with n times the height of the recursion tree, i.e., n log n, while the incorrect options mischaracterize how work scales with input size.

MS_1 Below is the Merge Sort discussed in lectures. What is the time complexity of the provided merge sort algorithm in the average case?

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