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 < j and ai > 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 inversions 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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