Download presentation

Presentation is loading. Please wait.

Published byCarli Kindall Modified over 3 years ago

1
Design and Analysis of Algorithms Heapsort Haidong Xue Summer 2012, at GSU

2
Max-Heap A complete binary tree, and … Yes No every level is completely filled, except possibly the last, which is filled from left to right

3
Max-Heap Satisfy max-heap property: parent >= children 16 1410 8793 2 Since it is a complete tree, it can be put into an array without lose its structure information.

4
Max-Heap 16 1410 8793 2 123 4 5 6 78

5
Max-Heap Use an array as a heap 16 1410 8793 2 123 4 5 6 78 16 14 10 8 7932 1 23 456 7 8 For element at i: Parent index =parent(i)= floor(i/2); Left child index = left(i)=2*i; Right child index =right(i)=2*i +1 Last non-leaf node = floor(length/2) i=3 2*i = 6 2*i+1=7 floor(i/2)=floor(1.5)=1 floor(length/2)=4

6
Max-Heapify Input: A compete binary tree rooted at i, whose left and right sub trees are max-heaps; last node index Output: A max-heap rooted at i. Algorithm: 1. Choose the largest node among node i, left(i), right(i). 2. if(the largest node is not i){ – Exchange i with the largest node – Max-Heapify the affected subtree }

7
Max-Heapify Example 2 1610 14793 8

8
Heapsort for a heap Input: a heap A Output: a sorted array A Algorithm: 1. Last node index l = A’s last node index 2. From the last element to the second{ exchange (current, root); l--; Max-Heapify(A, root, l); }

9
Heapsort example 16 1410 87 9 3 2

10
Heapsort example 14 810 27 9 3 16

11
Heapsort example 10 89 27 3 14 16

12
Heapsort example 9 83 27 10 14 16

13
Heapsort example 8 73 29 10 14 16

14
Heapsort example 7 23 89 10 14 16

15
Heapsort example 3 27 89 10 14 16

16
Array -> Max-Heap Input: a array A Output: a Max-Heap A Algorithm: Considering A as a complete binary tree, from the last non-leaf node to the first one{ Max-Heapify(A, current index, last index); }

17
Build Heap Example 16 14 10 8 7 14 8 16 107

18
Heapsort Input: array A Output: sorted array A Algorithm: 1. Build-Max-Heap(A) 2. Last node index l = A’s last node index 3. From the last element to the second{ exchange (current, root); l--; Max-Heapify(A, root, l); } Let’s try it

19
Analysis of Heapsort Input: array A Output: sorted array A Algorithm: 1. Build-Max-Heap(A) 2. Last node index l = A’s last node index 3. From the last element to the second{ exchange (current, root); l--; Max-Heapify(A, root, l); } O(n) or O(nlgn) O(nlgn) O(n)

Similar presentations

OK

Priority Queues and Heaps Data Structures and Algorithms CS 244 Brent M. Dingle, Ph.D. Department of Mathematics, Statistics, and Computer Science University.

Priority Queues and Heaps Data Structures and Algorithms CS 244 Brent M. Dingle, Ph.D. Department of Mathematics, Statistics, and Computer Science University.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on power diode Ppt on road accidents essay Ppt on latest technology in electronics and instrumentation Ppt on condition monitoring of transformers Ppt on new technology in electrical Ppt on summary writing worksheets Hindi ppt on pollution Ppt on nazism and hitler in germany Ppt on power grid failure Ppt on new technology in electronics