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 5E
Program Plan Intro
To write a non-recursive procedure that print out the key of each node in
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Given the following Binary Tree, what is the result of a post-order traversal? What is the height of node N?
Write a recursive method isBinaryTree() that takes a Nodeas argument and returns true if the subtree count field N is consistent in the data structure rooted at that node, false otherwise. Note : This check also ensures that the datastructure has no cycles and is therefore a binary tree (!).
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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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- Given 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 called countHNodes(TreeNode* p), that returns the number of H-nodes in a binary tree (pointed by p). Use recursion in the function.arrow_forwardCreate 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 treearrow_forwardDraw 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 brieflyarrow_forward
- Tl 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_forwardWrite a recursive method isBinaryTree() that takes a Nodeas argument and returns true if the subtree count field N is consistent in the data structure rooted at that node, false otherwise. Note : This check also ensures that the data structure has no cycles and is therefore a binary tree (!).arrow_forwardWrite a binary search tree method that takes two keys, low and high, and prints all elements X that are in the range specified by low and high. Your program should run in O(K + log N) average time, where K is the number of keys printed. Thus, if K is small, you should be examining only a small part of the tree. Use a hidden recursive method and do not use an in-order iterator. Bound the running time of your algorithmarrow_forward
- The following binary tree has as many nodes as possible for a tree of height 5. Definition: A climb is a path that starts at the root and ends at a leaf. For example, the path indicated by the black lines is a climb. First, determine how many different climbs are in this tree. Then, suppose you have a list of 115 names, and you need to assign a name from this list to each climb. You may not repeat names. How many different ways are there to do this? There are --Select-- ways to assign the names to the climbs in this tree.arrow_forwardWrite the algorithm that finds the number of leaf nodes in a binary tree, that is, nodes that have no children, given a pointer to the root node, as pseudocode. Solve by writing the "recurrence" equation of your algorithm and write down the time complexity please.arrow_forward: You are implementing a binary search tree class from scratch, which, in additionto insert, find, and delete, has a method getRandomNode() which returns a random nodefrom the tree. All nodes should be equally likely to be chosen. Design and implement an algorithmfor getRandomNode, and explain how you would implement the rest of the methods.arrow_forward
- Consider a traversal of a binary tree. Suppose that visiting a node means to simply display the data in the node. What are the results of each of the following traversals of the tree in the following figures according to: a. Pre-order technique b. Post-order technique c. In-order technique A B D E F G Harrow_forwardCreate 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_forwardExplain how to implement a complete binary tree by using an array. Note that you have to point out how to derive the indices of a node i's parent, left child, and right child individually. Also, explain pros and cons of this representation.arrow_forward
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