Suppose we want to use the Heapsort algorithm to sort a large list of numbers. Our first step is to convert the input list to a heap, and then run BUILD-MAX-HEAP, which applies MAX-HEAPIFY on all the nodes in the heap, starting at the bottom and moving towards the top. (Think about why we do it bottom-up instead of top-down.) An example is provided on pg. 157 of the textbook. In this example, A = [4,1,3,2,16,9,10,14,8,7]. The end result of BUILD- MAX-HEAP is [16,14,10,8,7,9,3,2,4,1]. I strongly encourage you to go through this example, step by step. A total of 7 swaps are made by BUILD-MAX-HEAP. You can check that the seven swaps occur in this order: (14,2), (10,3), (16,1), (7,1), (16,4), (14,4), (8,4). Here is another way to see this: 2 goes down one level, 3 goes down one level, 1 goes down two levels, and 4 goes down three levels. Adding the underlined numbers, we see that the total number of swaps is 1+1+2+3 = 7. %3D Suppose A = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Determine BUILD-MAX-HEAP(A), and also determine the total number of swaps.

Suppose we want to use the Heapsort algorithm to sort a large list of numbers. Our first step is to convert the input list to a heap, and then run BUILD-MAX-HEAP, which applies MAX-HEAPIFY on all the nodes in the heap, starting at the bottom and moving towards the top. (Think about why we do it bottom-up instead of top-down.) An example is provided on pg. 157 of the textbook. In this example, A = [4,1,3,2,16,9,10,14,8,7]. The end result of BUILD- MAX-HEAP is [16,14,10,8,7,9,3,2,4,1]. I strongly encourage you to go through this example, step by step. A total of 7 swaps are made by BUILD-MAX-HEAP. You can check that the seven swaps occur in this order: (14,2), (10,3), (16,1), (7,1), (16,4), (14,4), (8,4). Here is another way to see this: 2 goes down one level, 3 goes down one level, 1 goes down two levels, and 4 goes down three levels. Adding the underlined numbers, we see that the total number of swaps is 1+1+2+3 = 7. %3D Suppose A = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Determine BUILD-MAX-HEAP(A), and also determine the total number of swaps.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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