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.
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