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Heap Sort

Heap Sort. Ameya Damle. The Algorithm. Elements can be sorted by placing the values into a heap and removing them one at a time Done using balanced binary tree Time is O( nlogn ) with the average case Worst case is O( nlogn ) Best case is O(n)

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Heap Sort

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  1. Heap Sort Ameya Damle

  2. The Algorithm • Elements can be sorted by placing the values into a heap and removing them one at a time • Done using balanced binary tree • Time is O(nlogn) with the average case • Worst case is O(nlogn) • Best case is O(n) • Each enter/leave is O(logn) called heapify, and doing n inserts/leaves takes O(nlogn)

  3. Example 1

  4. Special case • Worst Case for heapsort is when tree is complete • Move down to lowest level (height is h) the time it takes is O(h) but since the tree is balanced it is O(logn) • Then to build a heal it is O(n) thus resulting in O(nlogn) • Making it less efficient with a complete tree

  5. Step by Step run through

  6. Memory • Heapsort uses no extra memory except for a few local temporary • Quicksort also uses no extra memory and is O(nlogn) at worst but it runs faster than the heapsort

  7. References • http://www.stoimen.com/blog/2012/08/07/computer-algorithms-heap-and-heapsort-data-structure/ • http://www.math.ucla.edu/~wittman/10b.1.10w/Lectures/Lec21.pdf • http://pages.cs.wisc.edu/~hasti/cs367-common/readings/Old/fall01/HEAP-SORT.htm • http://www.cs.cmu.edu/~tcortina/15-121sp10/Unit07B.pdf

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