1. A Heap Implementation
Chapter 26
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2. Contents Reprise: The ADT Heap Using an Array to Represent a Heap
Adding an Entry
Removing the Root
Creating a Heap
Heap Sort
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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
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4. Heaps (ch23) Complete binary tree: nodes contain Comparable objects
Organization
Each node contains object no smaller (or no larger) than objects in descendants
Maxheap, object in node greater than or equal to descendant objects
Minheap, object in node less than or equal to descendant objects
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5. Reprise: The ADT Heap Interface considered in Chapter 23 Listing 23-6
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6. Example
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7. Possible Implementation of a PQ as Sorted List (ch 11)
Figure Two possible implementations of a priority queue using (a) an array; (b) a chain of linked nodes
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8. Possible Implementation of a PQ as a Heap (ch 23)
public class PriorityQueue <T extends Comparable<? super T >> implements PriorityQueueInterface < T > { private MaxHeapInterface < T > pq; public PriorityQueue () { pq = new MaxHeap < T > (); } // end default constructor public void add (T newEntry) { pq.add (newEntry); } // end add //Implementations of remove, peek, isEmpty, getSize, and clear are here. } // end PriorityQueue
Adapted from Pearson Education, Inc.

9. 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
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10. Array to Represent a Heap
View code of class MaxHeap, 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
Adapted from Pearson Education, Inc.

11. The steps in adding 85 to a maxheap
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12. A revision of the steps to avoid swaps
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13. An array representation of the steps
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14. An array representation of the steps
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15. RemoveMax
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16. Adding 20, 40, 30, 10, 90, and 70
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17. The steps in creating a heap of the entries 20, 40, 30, 10, 90, and 70 by using reheap
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18. The steps in creating a heap of the entries 20, 40, 30, 10, 90, and 70 by using reheap
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19. Figure 26-9 A trace of heap sort
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20. Figure 26-9 A trace of heap sort
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21. Figure 26-9 A trace of heap sort
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22. Efficiency
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23. End
Chapter 26
Adapted from Pearson Education, Inc.