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Demonstrate, step by step, how to sort a list of integers (2, 4, 1, 5, 6, 7) using a max-heap, following Example 4.15.

Demonstrate, step by step, how to sort a list of integers (2, 4, 1, 5, 6, 7) using a max-heap, following Example 4.15.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Demonstrate, step by step, how to sort a list of integers (2, 4, 1,

5, 6, 7) using a max-heap, following Example 4.15.

8 12 5 6 '1 10 5 A 14 10 8 12 56 1 A 14 8 12 6 1 10 5 15 15 10 "8 12 5 6 "6 1 10 14 A 1 14 10 8 12 56 15 A58 12 61 10 14 15 (a) (b)
Transcribed Image Text:8 12 5 6 '1 10 5 A 14 10 8 12 56 1 A 14 8 12 6 1 10 5 15 15 10 "8 12 5 6 "6 1 10 14 A 1 14 10 8 12 56 15 A58 12 61 10 14 15 (a) (b)
Example 4.15 Sort a list of integers A[1.8] = (10,8, 14, 15, 12, 5,6, 1) using a max-heap. The list of n = 8 unsorted integers is first converted to a max-heap, i.e. a partially sorted, left complete binary tree with the largest integer at the root as in Figure 4.12. The first position A[1] is the root element. During the sorting process, the list is divided into two sections: A[1.k), the heap and A[k + 1.n), the sorted part (in shade in Figures 4.17-4.19). We shall each time remove the root element at A[11, the largest integer from the current heap and insert it to location k +1, and k-k – 1. This is followed by a restoring of the order property of the heap. When the root r is removed, we move the larger one of its children to the root position, and similarly, the larger one of the child's children to its position. The process repeats until the order property is restored.
Transcribed Image Text:Example 4.15 Sort a list of integers A[1.8] = (10,8, 14, 15, 12, 5,6, 1) using a max-heap. The list of n = 8 unsorted integers is first converted to a max-heap, i.e. a partially sorted, left complete binary tree with the largest integer at the root as in Figure 4.12. The first position A[1] is the root element. During the sorting process, the list is divided into two sections: A[1.k), the heap and A[k + 1.n), the sorted part (in shade in Figures 4.17-4.19). We shall each time remove the root element at A[11, the largest integer from the current heap and insert it to location k +1, and k-k – 1. This is followed by a restoring of the order property of the heap. When the root r is removed, we move the larger one of its children to the root position, and similarly, the larger one of the child's children to its position. The process repeats until the order property is restored.
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