GATE CS 2019 Set 1 — Question 47
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Algorithms → Searching → Selection (Order Statistics)
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Question
There are unsorted arrays: . Assume that is odd. Each of contains distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of is
Correct answer
(C) O(n²)
Solution
To find the median of each array (where each has size ), it takes time using a linear selection algorithm (like Median of Medians or QuickSelect). Since there are arrays, finding all medians takes .Let the medians be . We then need to find the median of these values. This takes time.The total time complexity is .
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