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 10.4, Problem 4E
Program Plan Intro
To write a procedure that prints all the keys of an arbitrary rooted tree with n nodes where the tree is represented by left-child and right-sibling representation in
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Some implementations of binary search trees allow for duplicates by introducing the following
rule: for each node n. the left subtree of n contains only nodes smaller than n, and the right
subtree of n contains only nodes greater or equal to n. Implement a successor and
predecessor operation on such a tree. Discuss their time complexity as a function of the height
of the tree.
Q16. *
In the following array representation of a Binary tree, the Left child of the node (D) is:
1 2 3
6 7
8
9 10 11 12 13 14 15
A
F G
H
I J
K
L M N O
0
E
F
O G
H
OI
4
B C D
5
E
Draw separate trees with 8 nodes that are either: balanced; binary tree; neither of these. As per the tree, write a pseudo code in python to carry out a breadth first search the binary tree.
Explain the answer briefly
Chapter 10 Solutions
Introduction to Algorithms
Ch. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3E
Ch. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10 - Prob. 1PCh. 10 - Prob. 2PCh. 10 - Prob. 3P
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- Draw a binary search tree and AVL tree from the following traversals: {15, 5, 20, 70, 3, 10, 60, 90, 16} Convert Binary Search Tree into Binary Tree such that sum of all greater keys is added to every key. Write a code to Convert Binary Search Tree drawn into Balanced Binary Search TreeNOTE: Code is required in Javaarrow_forwardGiven the preorder and inorder traversals of a binary tree, you build that binary tree. 5. Preorder: X В G Y E Inorder: Y G В D E Narrow_forwardIn the main method, create the following binary tree and print all the nodes in this tree using the postorder traversal 1 500 1 100 700 400 1 20 30 10arrow_forward
- Given the preorder and inorder traversals of a binary tree, you build that binary tree. Preorder: X In-order: A Y A E Y EX C C K D D L KLarrow_forwardA D F H J K L M N P Q R a. What is the post-order traversal of the tree? b. Write down all leaves. c. What is the height of node B? d. Write down all siblings of node J. e. Write down all descendants of node D.arrow_forwardTl and T2 are two very large binary trees, with Tl much bigger than T2. Create an algorithm to determine if T2 is a subtree of Tl.A tree T2 is a subtree of Tl if there exists a node n in Tl such that the subtree of n is identical to T2. That is, if you cut off the tree at node n, the two trees would be identical.arrow_forward
- Some implementations of a binary tree do not use null to indicate the absence of a child. Instead, they use references to a single dummy node. A reference to an empty tree is to this same dummy node. Modify the implementation of BinaryTree in this way. Java programarrow_forwardWhen inorder traversing a complete binary tree resulted E A C K F H D; the postorder traversal would return Select one: a.E C A F H D K b.E C A F D H K c.E A C F D H K d.E C F A D H Karrow_forwardGiven a binary tree, let an H-node be defined as a non-leaf node in the tree whose value is greater than or equal to its children nodes (1 or 2 children). Write a function, countHNodes(), that returns the number of H-nodes in a binary tree (pointed by p) using recursion.arrow_forward
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