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A machine needs a minimum of 200 sec to sort 1000 elements by Quick sort. The minimum time needed to sort 200 elements will be approximately __________

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in Data Structures & Algorithms II by (110k points)
A machine needs a minimum of 200 sec to sort 1000 elements by Quick sort. The minimum time needed to sort 200 elements will be approximately __________

(a) 60.2 sec

(b) 45.54 sec

(c) 31.11 sec

(d) 20 sec

The question was asked in unit test.

I need to ask this question from Quicksort topic in division Sorting of Data Structures & Algorithms II

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Right choice is (c) 31.11 sec

The best I can explain: The Quick sort requires nlog2n comparisons in best case, where n is size of input array. So, 1000 * log21000 ≈ 9000 comparisons are required to sort 1000 elements, which takes 200 sec. To sort 200 elements minimum of 200 * log2200 ≈ 1400 comparisons are required. This will take 200 * 1400 / 9000 ≈ 31.11 sec.

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