Dutton (1993) presents a further HEAPSORT variant called WEAK-HEAPSORT, which also contains a new data structure for priority queues. The sorting algorithm and the underlying data structure are analyzed showing that WEAK-HEAPSORT is the best HEAPSORT variant and that it has a lot of nice properties.
It is shown that the worst case number of comparisons is n⌈log n⌉ — 2⌈log n⌉ + n − ⌈log n⌉ ≤ n log n + 0.1n and weak heaps can be generated with n − 1 comparisons. A double-ended priority queue based on weakheaps can be generated in n + ⌈n/2⌉ − 2 comparisons.
Moreover, examples for the worst and the best case of WEAK-HEAP-SORT are presented, the number of Weak-Heaps on 1, ... , n is determined, and experiments on the average case are reported.
Average Case Priority Queue Sorting Algorithm Kolmogorov Complexity Extra Space
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