The heapsortMathworldPlanetmath algorithmMathworldPlanetmath is an elegant application of the heap data structure to the sorting problem. It consists of building a heap out of some list of n elements, and the removing a maximal value one at a time.

The Algorithm

The following pseudocode illustrates the heapsort algorithm. It builds upon the heap insertion and heap removal algorithms.

Algorithm HeapSort((A,,n))
Input: List A of n elements
Output: A sorted, such that is a total orderMathworldPlanetmath over A

          for i2𝐭𝐨𝐧 do


for in𝐝𝐨𝐰𝐧𝐭𝐨𝟐 do




Note that the algorithm given is based on a top-down heap insertion algorithm. It is possible to get better results through bottom-up heap construction.

Each step of each of the two for loops in this algorithm has a runtime complexity of 𝒪(logi). Thus overall the heapsort algorithm is 𝒪(nlogn).

Heapsort is not quite as fast as quicksortMathworldPlanetmath in general, but it is not much slower, either. Also, like quicksort, heapsort is an in-place sorting algorithm, but not a stable sorting algorithm. Unlike quicksort, its performance is guaranteed, so despite the orderingMathworldPlanetmath of its input its worst-case complexity is 𝒪(nlogn). Given its simple implementation and reasonable performance, heapsort is ideal for quickly implementing a decent sorting algorithm.

Title heapsort
Canonical name Heapsort
Date of creation 2013-03-22 12:31:02
Last modified on 2013-03-22 12:31:02
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 9
Author mathcam (2727)
Entry type Algorithm
Classification msc 68P10
Related topic HeapInsertionAlgorithm
Related topic HeapRemovalAlgorithm
Related topic Heap
Related topic SortingProblem