BOTTOM-UP-HEAPSORT, a new variant of HEAPSORT beating, on an average, QUICKSORT (if n is not very small)

Abstract

A variant of HEAPSORT, called BOTTOM-UP-HEAPSORT, is presented. It is based on a new reheap procedure. This sequential sorting algorithm is easy to implement and beats, on an average, QUICKSORT if n⩾400 and a clever version of QUICKSORT (where the split object is the median of 3 randomly chosen objects) if n⩾16000. The worst-case number of comparisons is bounded by 1.5 n log n+O( n). Moreover, the new reheap procedure improves the delete procedure for the heap data structure for all n.