1. We can build a heap by repeatedly calling MAX-HEAP-INSERT to insert the ele- ments into the heap. Consider the following variation on the BUILD-MAX-HEAP procedure: BUILD MAX HEAP' (A) 1 A. heap_size=1 2 for i=2 to A. length 3 MAX HEAP INSERT (A, A[i]) (a) (10 points) Do the procedures BUILD-MAX-HEAP and BUILD-MAX-HEAP' always create the same heap when run on the same input array? Prove that they do, or provide a counterexample. (b) (10 points) Show that in the worst case, BUILD-MAX-HEAP' requires (nlgn) time to build an n-element heap.

1. We can build a heap by repeatedly calling MAX-HEAP-INSERT to insert the ele- ments into the heap. Consider the following variation on the BUILD-MAX-HEAP procedure: BUILD MAX HEAP' (A) 1 A. heap_size=1 2 for i=2 to A. length 3 MAX HEAP INSERT (A, A[i]) (a) (10 points) Do the procedures BUILD-MAX-HEAP and BUILD-MAX-HEAP' always create the same heap when run on the same input array? Prove that they do, or provide a counterexample. (b) (10 points) Show that in the worst case, BUILD-MAX-HEAP' requires (nlgn) time to build an n-element heap.

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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Concept explainers

Heap Sort

A Heap is a type of data structure that is built on trees. It's a binary tree that's virtually complete. Except for the very bottom level, all levels of the tree must be filled in a heap. The last (bottom) level should be filled from left to right. The heap data structure is used for the efficient implementation of priority queues.Heap can be of two types:

Question

1. We can build a heap by repeatedly calling MAX-HEAP-INSERT to insert the ele- ments into the heap.
Consider the following variation on the BUILD-MAX-HEAP procedure:
BUILD MAX HEAP' (A)
1 A. heap_size=1
2 for i=2 to A. length
3
MAX HEAP INSERT (A, A[i])
(a) (10 points) Do the procedures BUILD-MAX-HEAP and BUILD-MAX-HEAP' always create the
same heap when run on the same input array? Prove that they do, or provide a counterexample.
(b) (10 points) Show that in the worst case, BUILD-MAX-HEAP' requires (nlgn) time to build an
n-element heap.

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