GATE | GATE-CS-2014-(Set-1) | Question 23

Let P be a QuickSort Program to sort numbers in ascending order using the first element as pivot. Let t1 and t2 be the number of comparisons made by P for the inputs {1, 2, 3, 4, 5} and {4, 1, 5, 3, 2} respectively. Which one of the following holds?

(A)

t1 = 5

(B)

t1 < t2

(C)

t1 > t2

(D)

t1 = t2

Answer: (C)

Explanation:

When first element or last element is chosen as pivot, Quick sort’s worst case occurs for the sorted arrays. In every step of quick sort, numbers are divided as per the following recurrence. T(n) = T(n-1) + O(n)

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