IGNOU BMTC 103 2026 - Compute the time complexity of the merge sort algorithm.

Question

Compute the time complexity of the merge sort algorithm.

20 Jan 2026

Answer :

Word Count : 239

Merge sort is a classic divide-and-conquer algorithm that recursively divides an array into two halves, sorts each half, and then merges the sorted halves. To compute its time complexity, let us denote the number of elements in the array by (n) and the time taken to sort (n) elements by (T(n)). The algorithm divides the array into two halves of size (n/2) each and recursively sorts them. The merging step requires comparing and combining all elements from both halves, which takes linear time (O(n)). Therefore, the recurrence relation for the time complexity is:

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