Introspective Sort

November 11, 2016

The sorting algorithm that we have been working up to in three previous exercises is introspective sort, or introsort, invented by David Musser in 1997 for the C++ Standard Library. Introsort is basically quicksort, with median-of-three partitioning and a switch to insertion sort when the partitions get small, but with a twist. The problem of quicksort is that some sequences have the property that most of the recursive calls don’t significantly reduce the size of the data to be sorted, causing a quadratic worst case. Introsort fixes that by switching to heapsort if the depth of recursion gets too large; since heapsort has guaranteed O(n log n) behavior, so does introsort. The changeover from quicksort to heapsort occurs after k * floor(log(length(A))) recursive calls to quicksort, where k is a tuning parameter, frequently set to 2, that can be used to adjust performance of the sorting algorithm.

Your task is to implement introsort. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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