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 1E
Program Plan Intro
To draw the binary tree rooted at index 6 for the given attributes.
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Create an array-based implementation (write a program) of a binary tree using the computational strategy. Include methods to remove and insert a node from the binary tree
For a binary tree, the pre-order traversal is H D A C B G F E the in-order traversal is: A D C B H F E G (A) Draw this binary tree (B) Give the post-order traversal
Recall that the set of full binary trees is defined as follows:
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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- From the below array representation of a binary tree, find the father of node K? Node Y P A K Index 0. 1 3 5. 8. 10 11 12 13 14 Oa. E Ob. Q Oc. X O d. P ump to. - Compler link 日 21arrow_forwardi. ii. Using an array-based representation of a binary tree, the following array represents a binary tree. 0 1 2 3 59 39 75 4 48 5 6 70 80 111. Draw the binary tree that is represented by the above array. 7 8 9 10 11 12 13 14 44 68 90 What is the postorder traversal of the binary tree that is created in (i). What is the parent of 72?arrow_forward. Give the binary-tree representation of the following trees in the forest. (Join these three trees in the forest to form a binary tree.) A 71 BC D | E K / 1 L M P Q X I Yarrow_forward
- Given that a tree with a single node has a height of 1, how many nodes could possibly be included in a balanced binary tree with a height of 5?arrow_forwardGiven the following Binary Tree, what is the result of a post-order traversal? What is the height of node N?arrow_forward5. The maximum number of nodes at level n for a binary tree is: A. n C. 2h D. n+1 B. 2n Ihm whicharrow_forward
- 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.arrow_forwardConsider the following binary tree: A В E F D J G H K L A)Give the inorder traverse of the tree wwhn B)Give the postorder traverse of the tree wwwarrow_forwardSuppose an array is given A = [A, C, E, F, K, L, M, N, Y, Z] a. Draw a complete BINARY tree from array A. b. Write preorder, inorder, and postorder traversal for the created complete binary tree. c. Draw a complete TERNARY tree from array A. d. Write preorder and postorder traversal for the created complete ternary. Draw the adjacency matrix and adjacency list for the complete ternary tree/graph. [You must consider the tree direction from top to bottom when drawing adjacency matrix and list]arrow_forward
- Create a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follow: //PICTURE// You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space. Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes. Count the height of the tree.arrow_forwardTl and T2 are two very large binary trees, with Tl much bigger than T2. Create analgorithm to determine ifT2 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_forwardWhat is the maximum number of nodes in a balanced binary tree of height 5 given that a tree with only one node has height 1?arrow_forward
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