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

Database System Concepts
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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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.

For example, if A = [4,1,3,2,16,9,10,14,8,7], then BUILD-MAX-HEAP(A) makes a total of 7 swaps, and returns the array [16, 14, 10, 8, 7, 9, 3, 2, 4, 1].

The swaps are made in this order: (14, 2), (10, 3), (16, 1), (7, 1), (16, 4), (14, 4), (8, 4). Suppose A = [2,4,6,8,10,12,14,1,3,5,7,9,11,13,15].
Determine the total number of swaps made by BUILD-MAX-HEAP(A).

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