Question

I have an array of N numbers which are same.I am applying Quick sort on it.
What should be the time complexity of the sorting in this case.

I goggled around this question but did not get the exact explanation.

Any help would be appreciated.

Answer 1

This depends on the implementation of Quicksort. The traditional implementation which partitions into 2 (< and >=) sections will have O(n*n) on identical input. While no swaps will necessarily occur, it will cause n recursive calls to be made – each of which need to make a comparison with the pivot and n-recursionDepth elements. i.e. O(n*n) comparisons need to be made

However there is a simple variant which partitions into 3 sets (<, = and >). This variant has O(n) performance in this case – instead of choosing the pivot, swapping and then recursing on 0to pivotIndex-1 and pivotIndex+1 to n, it will put swap all things equal to the pivot to the ‘middle’ partition (which in the case of all identical inputs always means swapping with itself i.e. a no-op) meaning the call stack will only be 1 deep in this particular case n comparisons and no swaps occur. I believe this variant has made its way into the standard library on linux at least.