Introduction to Java Programming and Data Structures  Comprehensive Version (11th Edition)
Introduction to Java Programming and Data Structures Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134700144
Author: Liang
Publisher: PEARSON
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Chapter 23.6, Problem 23.6.4CP
Program Plan Intro

Complete binary tree:

  • A binary tree is said to be a complete if every level of the tree are full except the last level.
  • The last level need not be full and all the leaves on the last level are placed left most.

Heap:

  • A heap is considered to be binary tree if it has following properties
    • When it is complete binary tree.
    • Every node is greater than or equal to its children.

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Show the resulting heap after 33, 22, and 8 are added to the following heap 50 30 40 20 10 25 35 10 5
1. Heap and Heapsort. (a) Run Build-Heap on the array [10, 9,4,7,6,2,3,1, 8,5] to construct a min heap. Write down the resulting array. Then, run the loop in Heapsort for three iterations. For each iteration write down the array after Heapify-Down is finished. You do not need to show intermediate steps. (b) Show that the leaves of a heap occupy the positions [],...,n-1 of the array. (c) In the procedure Build-Heap, why do we decrease i from [2]-1 to 0 instead of increasing from 0 to [2]-1? Give an example array where increasing i fails to create a valid min heap.
4. Draw a new heap that is created by inserting 52 into the following heap: 100 71 67 68 50 44 51 60 49 25 30
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