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A Heap Implementation

Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X. Chapter Contents. Reprise: The ADT HeapUsing an Array to Represent a HeapAdding an EntryRemoving the RootCreating a HeapHeapsort. Carrano, Data Structures an

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A Heap Implementation

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    1. A Heap Implementation Chapter 28

    2. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Chapter Contents Reprise: The ADT Heap Using an Array to Represent a Heap Adding an Entry Removing the Root Creating a Heap Heapsort

    3. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Reprise: The ADT Heap A complete binary tree Nodes contain Comparable objects In a maxheap Object in each node = objects in descendants Note contrast of uses of the word "heap" The ADT heap The heap of the operating system from which memory is allocated when new executes

    4. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Reprise: The ADT Heap Interface used for implementation of maxheap

    5. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Using an Array to Represent a Heap

    6. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Using an Array to Represent a Heap When a binary tree is complete Can use level-order traversal to store data in consecutive locations of an array Enables easy location of the data in a node's parent or children Parent of a node at i is found at i/2 (unless i is 1) Children of node at i found at indices 2i and 2i + 1

    7. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Class MaxHeap

    8. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Class MaxHeap Begin at next available position for a leaf Follow path from this leaf toward root until find correct position for new entry As this is done Move entries from parent to child Makes room for new entry

    9. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Adding an Entry

    10. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Adding an Entry

    11. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Adding an Entry

    12. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Adding an Entry

    13. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Removing the Root

    14. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Removing the Root

    15. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Removing the Root To remove a heap's root Replace the root with heap's last child This forms a semiheap Then use the method reheap Transforms the semiheap to a heap View method removeMax

    16. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Creating a Heap

    17. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Creating a Heap

    18. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Heapsort Possible to use a heap to sort an array Place array items into a maxheap Then remove them Items will be in descending order Place them back into the original array and they will be in order

    19. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Heapsort

    20. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Heapsort

    21. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Heapsort

    22. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Heapsort

    23. Carrano, Data Structures and Abstractions with Java, Second Edition, (c) 2007 Pearson Education, Inc. All rights reserved. 0-13-237045-X Heapsort View implementation of a heapSort Efficiency is O(n log n). However, quicksort is usually a better choice Note it also uses reheap View source code of reheap

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