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Analyzing Heapify(): Formal Fixing up relationships between i, 1, and r takes (1) time • If the heap at i has n elements, how many elements can the subtrees at l or r have? ■Draw it • Answer: 2n/3 (worst case: bottom row 1/2 full) • So time taken by Heapify () is given by T(n)T(2n/3) + (1) provide proof

Analyzing Heapify(): Formal Fixing up relationships between i, 1, and r takes (1) time • If the heap at i has n elements, how many elements can the subtrees at l or r have? ■Draw it • Answer: 2n/3 (worst case: bottom row 1/2 full) • So time taken by Heapify () is given by T(n)T(2n/3) + (1) provide proof

C++ Programming: From Problem Analysis to Program Design
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter17: Linked Lists
Section: Chapter Questions
Problem 3SA
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How can I provide a proof for this question regarding the Heapify function for Heapsort?

Analyzing Heapify(): Formal Fixing up relationships between i, 1, and r takes (1) time • If the heap at i has n elements, how many elements can the subtrees at l or r have? ■Draw it • Answer: 2n/3 (worst case: bottom row 1/2 full) • So time taken by Heapify () is given by T(n)T(2n/3) + (1) provide proof
Transcribed Image Text:Analyzing Heapify(): Formal Fixing up relationships between i, 1, and r takes (1) time • If the heap at i has n elements, how many elements can the subtrees at l or r have? ■Draw it • Answer: 2n/3 (worst case: bottom row 1/2 full) • So time taken by Heapify () is given by T(n)T(2n/3) + (1) provide proof
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