SUMMARYQuicksort is the preferred in-place sorting algorithm in many contexts, since its average computing time on uniformly distributed inputs is Θ (N log N), and it is in fact faster than most other sorting algorithms on most inputs. Its drawback is that its worst-case time bound is Θ(N 2 . Previous attempts to protect against the worst case by improving the way quicksort chooses pivot elements for partitioning have increased the average computing time too much -one might as well use heapsort, which has a Θ(N log N) worst-case time bound, but is on the average 2-5 times slower than quicksort. A similar dilemma exists with selection algorithms (for finding the i-th largest element) based on partitioning. This paper describes a simple solution to this dilemma: limit the depth of partitioning, and for subproblems that exceed the limit switch to another algorithm with a better worst-case bound. Using heapsort as the 'stopper' yields a sorting algorithm that is just as fast as quicksort in the average case, but also has an Θ(N log N) worst case time bound. For selection, a hybrid of Hoare's FIND algorithm, which is linear on average but quadratic in the worst case, and the Blum-Floyd-Pratt-Rivest-Tarjan algorithm is as fast as Hoare's algorithm in practice, yet has a linear worst-case time bound. Also discussed are issues of implementing the new algorithms as generic algorithms, and accurately measuring their performance in the framework of the C++ Standard Template Library.

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