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Add Median of Medians fallback to introselect Fixes #102451. This PR is a follow up to #106997. It adds a Fast Deterministic Selection implementation as a fallback to the introselect algorithm used by `select_nth_unstable`. This allows it to guarantee O(n) worst case running time, while maintaining good performance in all cases. This would fix #102451, which was opened because the `select_nth_unstable` docs falsely claimed that it had O(n) worst case performance, even though it was actually quadratic in the worst case. #106997 improved the worst case complexity to O(n log n) by using heapsort as a fallback, and this PR further improves it to O(n) (this would also make #106933 unnecessary). It also improves the actual runtime if the fallback gets called: Using a pathological input of size `1 << 19` (see the playground link in #102451), calculating the median is roughly 3x faster using fast deterministic selection as a fallback than it is using heapsort. The downside to this is less code reuse between the sorting and selection algorithms, but I don't think it's that bad. The additional algorithms are ~250 LOC with no `unsafe` blocks (I tried using unsafe to avoid bounds checks but it didn't noticeably improve the performance). I also let it fuzz for a while against the current `select_nth_unstable` implementation to ensure correctness, and it seems to still fulfill all the necessary postconditions. cc `@scottmcm` who reviewed #106997 |
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