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 13.4, Problem 1E
Program Plan Intro
To argue that after executing RB-DELETE-FIXUP procedure, the root of the tree must be black.
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Node 84 is to be removed from the above BST Tree. The first step is to find the rightmost node of 84.
Problem 2 :
Consider the following binary search tree:
42
24
57
12
30
44
63
29
36
49
31
Show the resulting tree if you delete the entry with key = 42 from the above tree. You need to
describe, step by step, how the resulting tree is generated.
In a B+-tree, it always requires reorganizing the entire index file to maintain performance. True or False?
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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- A. Show the result of inserting 7, 10, 2, 4, 5, 11, 1, 8, 9, 6, 12, 3 into an initially empty binary search tree (in that order). 1. Which node is the root? II. Which nodes are the leaves? III. Which nodes are siblings? IV. What is the depth of each node? V. What is the height of each node? B. Show the result of deleting the root.arrow_forward(a) You have an empty binary search tree. After that, you do the following sequence of insertions:20, 30, 10, 50, 40, 60. Draw the status of the binary search tree after the first 3 insertions, and at the endof all 6 insertions (you only need to show 2 trees). (b) Start now with a binary search tree with a single node containing an unknown key X. You mustchoose the value X so that if you later add the 6 keys in question 1(a) in the same order, you get aperfect tree with 7 nodes. Give a value for X and show the final tree obtained.arrow_forwardInsert the following keys into an initially empty binary search tree: 22, 34, 7, 18, 28, 34, 65, 50, 6, 10, 19. Show the resulting BST after deleting its root and Print the keys using preorder and in-order traversals.arrow_forward
- Write a program that inserts the numbers into an initially empty BST such that the treeproduced is equivalent to binary search tree.Insert 15 as a root node then add 1 into 15 to generate 2nd number for insertion, add 2 to the2nd number to generate 3rd number continue adding according to the level of the tree till 5thlevel. Then subtract 1 from root node to generate 7th node Continue subtracting till level of 5thlevelA. The Insert function will only take the root node and construct the entire treeB. Implement a remove function which can remove the 3rd layer numbers from right andleft both sub trees.C. Implement a function to find the number which is nearby to your given age.arrow_forward13 46 65 58 84 94 98 Node 84 is to be removed from the above BST Tree. The first step is to find the rightmost node of 84. How will you find it? and What is the rightmost node of 84?arrow_forwardCreate a binary search tree using the following insertions.44, 88, 55, 77, 33, 99, 66, 22, 25, 75Based on the final tree, what is the postorder traversal of the tree?arrow_forward
- Dear Sir, Please Help me to solve the given question. Question: Implement (C++ code) of the red-black tree, which has the following operations. Insertion operation: Insert at least 8 values in a red-black tree. Deletion operation: Delete 3 different nodes from a red-black tree you have created. Make sure, after the deletion, the remaining tree must be a red-black tree. Searching operation: Search elements in the red-black tree you have created.arrow_forwardWrite code to merge two binary trees. given root node of two binary trees,return root node of sum tree.arrow_forwardPart (a): Show the result of inserting 2, 0, 5, 7, 9, 1, 6, 8, 3, 4 into an initially empty binary search tree. Part (b): Show the result of deleting the root. Note: in this question use the successor node (not the predecessor) for the replacement Note this is a BST, not a Balanced BST.arrow_forward
- In which order would you need to insert the values 68, 99, 24, 47, 30, 74, 97 into an initially empty binary search tree in order to get a full binary search tree? A 'full binary search tree' is a tree in which every node other than the leaves has two children. Draw the resulting tree. IMPORTANT: The penalty scheme for this question is 0, 50, 100%. Answer: (penalty regime: 0, 50, 100 %) Help Clear Checkarrow_forwardAnother important property of a binary search tree is being able to easily find the maximum and minimum key in the tree. Discuss a simple rule to identify these keys. What is the output of a BFS traversal in a normal binary search tree if the key insert order is "1,2,3,4,5,6,7"?arrow_forwardImplement an iterator for a binary search tree (BST) that returns the set of all values stored in the tree in sorted order (from least to greatest). Important: Both your hasNext () and next () implementations – as well as the constructor – should operate in O(h) time (worst-case), where h is the height of the tree. You do not need to implement the remove () method. You may assume that each value stored in the BST is unique. class BinarySearchTree> implements Iterable { private static class Node { private T _data; private Node _parent; private Node _leftChild; private Node _rightChild; } private Node _root; // ... public Iterator iterator () { return new BSTIterator () ; } private class BSTIterator implements Iterator { // Implement me ..arrow_forward
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