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What is the average time complexity of bottom up merge sort?

(a) O(n log n)

(b) O(n^2)

(c) O(n^2 log n)

(d) O(n log n^2)

The question was asked by my college director while I was bunking the class.

My question is based upon Sorting in division Sorting of Data Structures & Algorithms II

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The correct answer is (a) O(n log n)

Explanation: The merge function in the bottom up merge sort takes O(n) time which is placed inside the for loop. The loop runs for O(log n) time, thus the overall time complexity of the code becomes O(n log n).

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