Heapsort: In-Place Sorting with Guaranteed N Log N Runtime

Summary

This document explains heapsort, a comparison-based sorting method that builds a binary heap, repeatedly moves the largest or smallest remaining item into its final position, and restores the heap. The data structure makes each next-extreme lookup efficient, giving the algorithm N log N time in its best, average, and worst cases. It also uses constant auxiliary memory, but does not preserve the relative order of equal keys.

The discussion compares heapsort with quicksort and merge sort. Quicksort is often faster in practice, though its worst case can reach quadratic time; merge sort offers stable ordering and good memory locality but generally needs additional space for arrays. Heapsort may suit environments that value a firm runtime bound and low extra memory, while its scattered accesses can hurt cache performance and it is not naturally parallel. An included MetaTrader example sorts symbols by a color key, illustrating a generic sorting use rather than a trading signal or strategy. The document provides complexity and design tradeoffs, not benchmark results for trading workloads.

Key ideas

• Heapsort organizes data as a binary heap and repeatedly extracts the root element to produce sorted order.
• Its best, average, and worst case runtimes are all N log N, with constant auxiliary memory.
• Heapsort is in-place but unstable, so equal keys may change relative order.
• Quicksort may be faster in practice, while merge sort offers stability and stronger memory locality.
• The included example sorts trading symbols by a color key and does not define a market strategy.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.