GATE DA 2024 Set 1 — Question 30
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Programming, Data Structures & Algorithms → Divide & Conquer → Quick Sort
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Question
Consider sorting the following array of integers in ascending order using an in-place Quicksort algorithm that uses the last element as the pivot.
The minimum number of swaps performed during this Quicksort is ______.
Correct answer
0 to 0
Solution
The array is already sorted: . The pivot is the last element, .In an in-place Quicksort (e.g., using the Lomuto partition scheme), we iterate through the array. Since every element is less than or equal to the pivot (), the partition index increments with the loop index.
- If the algorithm is optimized to avoid self-swaps (swapping an element with itself) or uses Hoare's partition scheme (which handles sorted arrays efficiently), the number of swaps is 0.
- Even in a standard unoptimized Lomuto partition, the operations would be self-swaps (e.g., swapping 60 with 60), which logically result in 0 changes to the array structure. The question asks for the "minimum" number of swaps, implying the most efficient execution path for this specific input.
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