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Algorithms | Sorting | Question 2

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  • Difficulty Level : Medium
  • Last Updated : 28 Jun, 2021
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Suppose we have a O(n) time algorithm that finds median of an unsorted array.

Now consider a QuickSort implementation where we first find median using the above algorithm, then use median as pivot. What will be the worst case time complexity of this modified QuickSort.
(A) O(n^2 Logn)
(B) O(n^2)
(C) O(n Logn Logn)
(D) O(nLogn)

Answer: (D)

Explanation: If we use median as a pivot element, then for each iteration it takes O(n) time to find median from given function and every time the array partitions in 2 subparts.
so the recurrence equation becomes.

T(n) = 2T(n/2) + O(n)

The above recurrence can be solved using Master Method. It falls in case 2 of master method
which results in complexity O(nlogn).

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