Introselect
| Class | Selection algorithm |
|---|---|
| Data structure | Array |
| Worst-case performance | O(n) |
| Best-case performance | O(n) |
In computer science, introselect (short for "introspective selection") is a selection algorithm that is a hybrid of quickselect and median of medians which has fast average performance and optimal worst-case performance. Introselect is related to the introsort sorting algorithm: these are analogous refinements of the basic quickselect and quicksort algorithms, in that they both start with the quick algorithm, which has good average performance and low overhead, but fall back to an optimal worst-case algorithm (with higher overhead) if the quick algorithm does not progress rapidly enough. Both algorithms were introduced by David Musser in (Musser 1997), with the purpose of providing generic algorithms for the C++ Standard Library which had both fast average performance and optimal worst-case performance, thus allowing the performance requirements to be tightened.
Introsort achieves practical performance comparable to quicksort while preserving O(n log n) worst-case behavior by creating a hybrid of quicksort and heapsort. Introsort starts with quicksort, so it achieves performance similar to quicksort if quicksort works, and falls back to heapsort (which has optimal worst-case performance) if quicksort does not progress quickly enough. Similarly, introselect combines quickselect with median of medians to achieve worst-case linear selection with performance similar to quickselect.
Introselect works by optimistically starting out with quickselect and only switching to a worst-case linear-time selection algorithm (the Blum-Floyd-Pratt-Rivest-Tarjan median of medians algorithm) if it recurses too many times without making sufficient progress. The switching strategy is the main technical content of the algorithm. Simply limiting the recursion to constant depth is not good enough, since this would make the algorithm switch on all sufficiently large lists. Musser discusses a couple of simple approaches:
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