1. A Heap Implementation Chapter 26 Copyright ©2012 by Pearson Education, Inc. All rights reserved

2. Contents Reprise: The ADT Heap Using an Array to Represent a Heap Adding an Entry Removing the Root Creating a Heap Heap Sort Copyright ©2012 by Pearson Education, Inc. All rights reserved

3. Objectives Use an array to represent a heap Add an entry to an array-based heap Remove the root of an array-based heap Create a heap from given entries Sort an array by using a heap sort Copyright ©2012 by Pearson Education, Inc. All rights reserved

4. Reprise: The ADT Heap A heap:  Complete binary tree  Nodes contain Comparable objects A maxheap:  Object in each node greater than or equal to the objects in node’s descendants Copyright ©2012 by Pearson Education, Inc. All rights reserved

5. Reprise: The ADT Heap Interface considered in Chapter 23 Copyright ©2012 by Pearson Education, Inc. All rights reserved

6. Array to Represent a Heap Begin by using array to represent complete binary tree.  Complete tree is full to its next-to-last level  Leaves on last level are filled from left to right Locate either children or parent of any node by performing simple computation on node’s number Copyright ©2012 by Pearson Education, Inc. All rights reserved

7. Figure 26-1 (a) A complete binary tree with its nodes numbered in level order; (b) its representation as an array Copyright ©2012 by Pearson Education, Inc. All rights reserved

8. Array to Represent a Heap View code of class MaxHeap, Listing 26-1 Listing 26-1 Data fields:  Array of Comparable heap entries  Index of last entry in the array  A constant for default initial capacity of heap Copyright ©2012 by Pearson Education, Inc. All rights reserved Note: Code listing files must be in same folder as PowerPoint files for links to work Note: Code listing files must be in same folder as PowerPoint files for links to work

9. Figure 26-2 The steps in adding 85 to the maxheap in Figure 26-1a Copyright ©2012 by Pearson Education, Inc. All rights reserved

10. Figure 26-2 The steps in adding 85 to the maxheap in Figure 26-1a Copyright ©2012 by Pearson Education, Inc. All rights reserved

11. Figure 26-2 The steps in adding 85 to the maxheap in Figure 26-1a Copyright ©2012 by Pearson Education, Inc. All rights reserved

12. Figure 26-3 A revision of the steps shown in Figure 26-2, to avoid swaps Copyright ©2012 by Pearson Education, Inc. All rights reserved

13. Figure 26-3 A revision of the steps shown in Figure 26-2, to avoid swaps Copyright ©2012 by Pearson Education, Inc. All rights reserved

14. Figure 26-4 An array representation of the steps in Figure 26-3 Copyright ©2012 by Pearson Education, Inc. All rights reserved

15. Figure 26-4 An array representation of the steps in Figure 26-3 Copyright ©2012 by Pearson Education, Inc. All rights reserved

16. Figure 26-5 The steps to remove the entry in the root of the maxheap in Figure 26-3d Copyright ©2012 by Pearson Education, Inc. All rights reserved

17. Figure 26-5 The steps to remove the entry in the root of the maxheap in Figure 26-3d Copyright ©2012 by Pearson Education, Inc. All rights reserved

18. Figure 26-6 The steps that transform a semiheap into a heap without swaps Copyright ©2012 by Pearson Education, Inc. All rights reserved

19. Figure 26-6 The steps that transform a semiheap into a heap without swaps Copyright ©2012 by Pearson Education, Inc. All rights reserved

20. Figure 26-7 The steps in adding 20, 40, 30, 10, 90, and 70 to an initially empty heap Copyright ©2012 by Pearson Education, Inc. All rights reserved

21. Figure 26-7 The steps in adding 20, 40, 30, 10, 90, and 70 to an initially empty heap Copyright ©2012 by Pearson Education, Inc. All rights reserved

22. Figure 26-7 The steps in adding 20, 40, 30, 10, 90, and 70 to an initially empty heap Copyright ©2012 by Pearson Education, Inc. All rights reserved

23. Figure 26-8 the steps in creating a heap of the entries 20, 40, 30, 10, 90, and 70 by using reheap Copyright ©2012 by Pearson Education, Inc. All rights reserved

24. Figure 26-8 the steps in creating a heap of the entries 20, 40, 30, 10, 90, and 70 by using reheap Copyright ©2012 by Pearson Education, Inc. All rights reserved

25. Figure 26-8 the steps in creating a heap of the entries 20, 40, 30, 10, 90, and 70 by using reheap Complexity Copyright ©2012 by Pearson Education, Inc. All rights reserved

26. Figure 26-9 A trace of heap sort Copyright ©2012 by Pearson Education, Inc. All rights reserved

27. Figure 26-9 A trace of heap sort Copyright ©2012 by Pearson Education, Inc. All rights reserved

28. Figure 26-9 A trace of heap sort Copyright ©2012 by Pearson Education, Inc. All rights reserved

29. Efficiency Copyright ©2012 by Pearson Education, Inc. All rights reserved

30. End Chapter 26 Copyright ©2012 by Pearson Education, Inc. All rights reserved