heapsort

In computer science, heapsort is an efficient, comparison-based sorting algorithm that reorganizes an input array into a heap (a data structure where each node is greater than its children) and then repeatedly removes the largest node from that heap, placing it at the end of the array in a similar manner to Selection sort.

Key facts

Algorithm.caption: A run of heapsort sorting an array of randomly permuted values. In the first stage of the algorithm the array elements are reordered to satisfy the heap property. Before the actual sorting takes place, the heap tree structure is shown briefly for illustration.
Algorithm.data: Array
Algorithm.time: O(n\log n)
Algorithm.average time: O(n\log n)
Algorithm.best time: O(n\log n) (distinct keys)or O(n) (equal keys)
Algorithm.space: O(n) total O(1) auxiliary
Algorithm.class: Sorting algorithm
Algorithm.image: File:Sorting heapsort anim.gif

via Wikipedia infobox

~20 min read

Encyclopedic overview

16 sections

Contents

Overview
Algorithm
Pseudocode
Standard implementation
Variations
Williams' heap construction
Bottom-up heapsort
Other variations
Comparison with other sorts
Example
Heap construction (Williams' algorithm)
Heap construction (Floyd's algorithm)
Heap extraction
Notes
References
External links

Although somewhat slower in practice on most machines than a well-implemented quicksort, it has the advantages of very simple implementation and a more favorable worst-case runtime. Most real-world quicksort variants include an implementation of heapsort as a fallback should they detect that quicksort is becoming degenerate. Heapsort is an in-place algorithm, but it is not a stable sort.

Excerpted from Wikipedia’s “heapsort” article, available under the CC BY-SA 4.0 licence.