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 13.1, Problem 1E
Program Plan Intro
To draw the red black tree with different heights 2, 3 and 4 from the complete binary tree of height 3 on the keys
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A binary tree can be used to sort n elements of an array data. First, create acomplete binary tree, a tree with all leaves at one level, whose height h = (lg n) + 1, and store all elements of the array in the first n leaves. In each empty leaf, store an element E greater than any element in the array.Figure (a) shows an example for data = 8, 20, 41, 7, 2, h = (lg(5)) + 1 = 4,and E = 42. Then, starting from the bottom of the tree, assign to each node the minimum of its two children values, as in Figure (b), so that the smallest element emin in the tree is assigned to the root.If a leaf node is to be removed, this node is replaced by a new node with the same value of its parent node. If a node is added into the tree, it will be a leaf node. Normally a node with value E is replaced with new value. It’s necessary to verify recursively all values of its parent and make any possible modification if necessary so that the tree rules are respected. Implement this tree structure in C/C++ with…
Recall your implementation of a binary search tree. Write a function int levelOf(int k) that computes and returns the level of the node with the key k. (Consider the root at level 1)
Exercise 8. In a red-black tree which is initially empty, we insert in order nodes with keys 1,2,3,4.
Draw the tree after these insertions (single-circled nodes are black, and double-circled nodes are red).
Chapter 13 Solutions
Introduction to Algorithms
Ch. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3E
Ch. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4P
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