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 3E
Program Plan Intro
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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, countHNodes(), that returns the number of H-nodes in a binary tree (pointed by p) using recursion.
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.
Create a binary linked tree, and traverse the tree by using the recursive function.
The structure of the tree is as follows:
//check pic//
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.
Hints:
Header file
typedef char ElemType;
typedef struct node//define the type of binary tree node
{
}BTnode;
Source file
#include <stdio.h>
#include <stdlib.h>
#include "tree.h"
BTnode * createTree()//create the binary tree,return the root
{
BTnode *tnode;// tnode is the root
char elem;
;//input the character
//if the input is a space,set the pointer as NULL
Else// if the input is not a space,generate the binary node and create its left…
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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- 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_forwardb. Given the array representation of a binary tree (null value means the node is empty]: [null, P, T, X, null, S, Q, U, null, null, Y, W, R, null, null, VM i. Draw the binary tree. [2]arrow_forwardB. 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)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. Also Count the height of the tree. PLEASE USE C LANGUAGEarrow_forwardGiven a binary tree, design an algorithm which creates a linked list of all the nodesat each depth (e.g., if you have a tree with depth D, you'll have D linked lists).arrow_forward#Print elements of all the Nodes of a tree using In-order Traversal. Note: Use PYTHON to solve this and do not use any built-in function.arrow_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_forwardb. Given the array representation of a binary tree [null value means the node is empty]: [null, P, T, X, null, S, Q, U, null, null, Y, W, R, null, null, V] i. Draw the binary tree. i. Write the post-order and in-order traversal sequence of the tree. i. Convert the tree to a complete binary tree.arrow_forwardpls write this code in c++ 1. An Preorder traversal {1, 9, 4, 8, 7, 6} and an Inorder traversal {3, 1, 9, 4, 7 , 6} of a binary tree is given print it's Postorder traversal. 2. Count all possible paths from A to E. B E A C Darrow_forward
- ) Consider the following binary tree. Write out the list of nodes for the preorder and postorder traversals. 12 24 29 36 39 41 42 56 62 90 75arrow_forwardA B D с G F E 5. For the following graph, (a) perform depth-first search by showing the changes of the stack and give a DFS tree;arrow_forwardDevelop a pseudo-code algorithm for a level-order traversal of a binary tree. Create an array-based implementation (write a program) of a binary tree using the computational strategy. Include the following methods: a. Remove a node from the binary tree. b. Insert a node into the binary tree. c. Remove the minimum (smallest) element from the treearrow_forward
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