A faster sorting algorithm given a magic data structure?

Counting sort is of O(n) complexity en.wikipedia.org/wiki/Counting_sort . However, it is not always convenient to use, because temporary array that is created by the algorithm has size of maximum integer value of sorted array.

Any comparison based sort requires O(n log(n)) comparisons in the average case, let alone the worst one. See en.wikipedia.org/wiki/Comparison_sort#Nu... for details of why. Therefore no comparison based sort can beat that lower limit even with your magic data structure.

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