GATE CS 2014 Set 1 — Question 24
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Algorithms → Sorting → Quick Sort
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Question
Let be a quicksort program to sort numbers in ascending order using the first element as the pivot. Let and be the number of comparisons made by for the inputs [1 2 3 4 5] and [4 1 5 3 2] respectively. Which one of the following holds?
Correct answer
(C) t₁ t₂
Solution
We calculate the number of comparisons for each input. In Quicksort, the pivot is compared with every other element in the current sub-array to partition it.For input [1 2 3 4 5] ():
Therefore, .
1.Pivot = 1. Compare with 2, 3, 4, 5 (4 comparisons). Partition: Left=[], Right=[2, 3, 4, 5].
2.Recurse on [2, 3, 4, 5]. Pivot = 2. Compare with 3, 4, 5 (3 comparisons). Partition: Left=[], Right=[3, 4, 5].
3.Recurse on [3, 4, 5]. Pivot = 3. Compare with 4, 5 (2 comparisons). Partition: Left=[], Right=[4, 5].
4.Recurse on [4, 5]. Pivot = 4. Compare with 5 (1 comparison). Partition: Left=[], Right=[5].
Total .For input [4 1 5 3 2] ():1.Pivot = 4. Compare with 1, 5, 3, 2 (4 comparisons). Partition: Left=[1, 3, 2], Right=[5].
2.Recurse on [1, 3, 2]. Pivot = 1. Compare with 3, 2 (2 comparisons). Partition: Left=[], Right=[3, 2].
3.Recurse on [3, 2]. Pivot = 3. Compare with 2 (1 comparison). Partition: Left=[2], Right=[].
Total .Comparing and :Therefore, .
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