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 (n1.5)
(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
Quiz of this Question
Please comment below if you find anything wrong in the above post