Complexity of quick sort, Data Structure & Algorithms

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Q. What do you mean by the best case complexity of quick sort and outline why it is so. How would its worst case behaviour arise?                                                                                                 

Ans:

In the best case complexity, pivot is in the middle. To simplify the calculation, we assume that the two sub-files are both  exactly half  of the size of the original file, and although this gives a minor overestimate, this is except able because we are only interested in a Big-Oh answer.

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

which yields

T(n) = cn log n + n = O(n log n)

In the worst case the pivot is the smallest element, all the time. Then i = 0 and if we ignore  T(0) = 1, which is not important, the recurrence is T(n) = T(n - 1) + cn, n > 1 which yields

1908_Quick Sort1.png


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