GATE | GATE-CS-2003 | Question 62

In a permutation a1…..an of n distinct integers, an inversion is a pair (ai, aj) such that i aj. What would be the worst case time complexity of the Insertion Sort algorithm, if the inputs are restricted to permutations of 1…..n with at most n inversions?
(A) Θ (n²)
(B) Θ (n log n)
(C) Θ (n^1.5)
(D) Θ (n)


Answer: (D)

Explanation: Insertion sort runs in Θ(n + f(n)) time, where f(n) denotes the number of inversion initially present in the array being sorted.

Source: http://cs.xidian.edu.cn/jpkc/Algorithm/down/Solution%20to%202-4%20Inversions.pdf

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