GATE | GATE CS 2019 | Question 46

There are n unsorted arrays: A₁, A₂, ….,A_n. Assume that n is odd. Each of A₁, A₂, …., A_n contains n distinct elements. There are no common elements between any two arrays. The worst-case time complexity of computing the median of the medians of A₁, A₂, ….,A_n is ________ . 

(A)

Ο(n log n)

(B)

Ο(n²)

(C)

Ο(n)

(D)

Ω(n²log n)

Answer: (B)
Explanation:

Since given arrays are not sorted, so the time complexity to find median is O(n) in an unsorted array. You need to apply this algorithm n time to find all medians and again once to find the median of all these medians, so total time complexity is, 

= O(n)*O(n) + O(n)
= O(n2) + O(n)
≈ O(n2) 

So, option (B) is correct. 

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