GATE CS 2019 Set 1 — Question 30
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Algorithms → Sorting → Quick Sort
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Question
An array of 25 distinct elements is to be sorted using quicksort. Assume that the pivot element is chosen uniformly at random. The probability that the pivot element gets placed in the worst possible location in the first round of partitioning (rounded off to 2 decimal places) is _______.
Correct answer
0.08 to 0.08
Solution
In the QuickSort algorithm, the worst-case partitioning occurs when the pivot element divides the array into a subarray of size 0 and a subarray of size . This happens when the pivot is either the smallest element or the largest element in the current subarray.Total number of elements .
The pivot is chosen uniformly at random from the 25 elements.
Total possible choices for pivot = 25.The "worst possible locations" correspond to the pivot being the smallest (rank 1) or the largest (rank 25) element.
Number of favorable outcomes (worst cases) = 2.Probability = .
The pivot is chosen uniformly at random from the 25 elements.
Total possible choices for pivot = 25.The "worst possible locations" correspond to the pivot being the smallest (rank 1) or the largest (rank 25) element.
Number of favorable outcomes (worst cases) = 2.Probability = .
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