On the Performance of WEAK-HEAPSORT

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 ndlog ne 2 ne + n dlog ne 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+ dn=2e 2 comparisons. Moreover, examples for the worst and the best case of WEAK-HEAPSORT are presented, the number of Weak-Heaps on f1; : : : ; ng is determined, and experiments on the average case are reported.