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 20.1, Problem 3E
Program Plan Intro
Explain how to find the successor of node x in a binary tree even x is not store in the tree.
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Your second function is called “isTree". Its input is a graph G, which is a dictionary
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- 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_forwarda. Given the definition of a binary tree, Insert, into an empty binary search tree, entries with keys {55, 34, 19, 78, 65, 8, 22, 97, 53, 26,76, 39, 93, 69, 11 ,83,2,35,70,77} (in this order). Draw the tree after each insertionarrow_forwardShow the result of inserting 3, 1, 4, 6, 9, 2, 5, 7 into an initially empty binary search tree.arrow_forward
- Consider the following statements: a. Kruskal’s algorithm might produce a non-minimal spanning tree.b. Kruskal’s algorithm can efficiently implemented using the disjoint-set data structure. a is true but b is falseBoth a and b are falseBoth a and b are trueb is true but a is falsearrow_forwardConsider 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_forwardGiven a binary tree, write a function to check if it is a valid binary search tree (BST). Discuss the approach you would take to validate the BST properties and handle edge cases.arrow_forward
- Another 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_forwardLet T be a binary search tree whose keys are all distinct. Suppose T is created by inserting each key into the growing tree. Let x be a leaf node and y be its parent node. Show that if x is the right child of y, then y.key is the largest key in T smaller than x.key. (Hint: Show that the assumption that there is another node z whose key satisfies y.key < z.key < x.key will lead to a contradiction.)arrow_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
- Develop a function that can quickly determine whether or not nodes u and v in a tree T starting with s are parents and children.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_forwardConsider a binary search tree (BST) whose elements are the name of animals. Starting with an empty BST, show the effect of successively adding the following elements: cow, fox, bat, ant, lion, cat, goat, dog,and pig. Show the effect of successively deleting fox, cow,and bat from the resulting BST and Traverse the original BST in pre-order, in-orderand post-order.arrow_forward
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