Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 6.1, Problem 1E
Program Plan Intro
To find the minimum and maximum numbers of elements in a heap of height
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The list that follows is a maximum-heap.
What will the array look like after removing the node with the highest key?
Prior to extraction:
30 50 16 60 59 95 77 61 72 63 30 50 16 60 59
Following extraction:
What is the time complexity of converting a random array of size m to a heap?
Given a heap with 2022 nodes, how many leaves are there with the longest pathfrom the root?
Chapter 6 Solutions
Introduction to Algorithms
Ch. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Prob. 5ECh. 6.1 - Prob. 6ECh. 6.1 - Prob. 7ECh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Prob. 3E
Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.5 - Prob. 1ECh. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6 - Prob. 1PCh. 6 - Prob. 2PCh. 6 - Prob. 3P
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- The following is a max-heap. After inserting a new node with key equal to 88, what will the array look like? Before inserting: 87 78 30 65 35 28 19 16 28 After inserting:arrow_forwardWhat is the maximum number of nodes that can be stored in a binary search tree of height 5?arrow_forwardWhat is the time complexity of converting a randomly generated array of sizem to a heap?arrow_forward
- The optimal number of elements for a linked list is unknown.Which of the following is the longest?arrow_forwardIs the array with values {29, 19, 20, 15, 13, 10, 2, 13, 11, 12} a max heap?arrow_forwardConstruct a minheap with the following numbers and answer the question according to the minheap.30, 80, 12, 28, 42, 78, 17, 71, 32, 48, 16, 59, 63, 14, 79 How many levels are there in the heap?arrow_forward
- In a linked list, create an algorithm to eliminate any nodes that have the same key.arrow_forwardHow would you reverse the order of nodes in a singly linked list? Provide an algorithm and discuss its time complexity.arrow_forwardWhat is the minimum number of items that must be exchanged during a remove the maximum operation in a heap of size N with no duplicate keys? Give a heapof size 15 for which the minimum is achieved. Answer the same questions for two andthree successive remove the maximum operationsarrow_forward
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