From Introduction to Algorithms ISBN:978-0-262-03293-3 You are given a a sequenc

Question

From Introduction to Algorithms ISBN:978-0-262-03293-3 You are given a a sequence of elements to sort. The input sequence consists of n k subsequences, each containing k elements. The elements in a given subsequence are all smaller than the elements in the succeeding subsequence and larger than the elements in the preceeding subsequences. Thus, all that is needed to sort the whole sequence of length n is to sort the k elements in each of the n k subsequences. Show an ? (n log k) lower bound on the number of comparisons needed to solve this variant of the sorting problem.

Explanation / Answer

The algorithm to sort the entire list is given as follows:

The analysis of complexity is explained below:

Therefore, the complexity of the algorithm would be O (n lg k).

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