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 12.3, Problem 2E
Program Plan Intro
To show that the number of nodes in searching a value in the tree is one plus the number of nodes when the first value inserted into the tree.
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Consider a complete binary tree with 7 nodes. Let A denote the set of first 3 elements obtained by performing Breadth-First Search (BFS) starting from the root. Let B denote the set of first 3 elements obtained by performing Depth-First Search (DFS) starting from the root.
The value of |A - B| is
Create a binary search tree using the following insertions.
55, 44, 66, 99, 88, 22, 77, 33, 25, 75
Based on the final tree, what is the preorder traversal of the tree?
(Ensure that there is A SPACE between each number)
If you have a binary search tree with n nodes, what are the minimum and maximum levels in that tree? Justify your answer mathematically.
Chapter 12 Solutions
Introduction to Algorithms
Ch. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5E
Ch. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.3 - Prob. 1ECh. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - Prob. 4ECh. 12.3 - Prob. 5ECh. 12.3 - Prob. 6ECh. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Prob. 3ECh. 12.4 - Prob. 4ECh. 12.4 - Prob. 5ECh. 12 - Prob. 1PCh. 12 - Prob. 2PCh. 12 - Prob. 3PCh. 12 - Prob. 4P
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- Consider a complete binary tree whose bottom level is completely filled. 1.If the height of this tree is h, what is the number n of nodes in this tree? 2.In terms of n, how many leaves are in this tree? 3.In terms of n or h, how many ancestors does each of the leaves in this tree have? 4.Let d be the depth of a node in this tree. In terms of d and either n or h, how many descendants does each node in this tree have?arrow_forwardDraw a binary search tree by inserting the following numbers and determine the predecessor and successor of 10, 1, and 6. numbers to insert {8,1,5,4,9,10,6,3,15}arrow_forwardConsider a binary search tree (BST) whose elements are the integer values: Starting with an empty BST, show the effect of successively adding the following elements: 15, 78, 10, 5, 12, 82, 60, 68, 11 and 65. Show the effect of successively deleting 10, 78, and 15 from the resulting BST. Traverse the original BST in pre-order and post-order.arrow_forward
- Create a binary search tree using the following insertions.44, 88, 55, 77, 33, 99, 66, 22, 25, 75Based on the final tree, what is the postorder traversal of the tree?arrow_forwardDraw the binary search tree that would result if the given elements were added to an empty binary search tree in the given order. Use paint to draw. a. Lisa, Bart, marge, maggie, flanders, smithers, miljouse b. 12,34,1,5,-5,6,19,45,2,-7,47arrow_forwardDefine the external path length of a tree to be the sum of the number of nodes onthe paths from the root to all null links. Prove that the difference between the externaland internal path lengths in any binary tree with N nodes is 2Narrow_forward
- Create a binary search tree using the following insertions. 55, 44, 66, 99, 88, 22, 77, 33, 25, 75 Based on the final tree, what is the inorder traversal of the tree?arrow_forwardThis exercise is about drawing BSTs. You are asked to: Show the result of inserting 3, 1, 4, 6, 9, 2, 5, and 7 in an initially empty binary search tree. Then show the result of deleting the root. Draw all binary search trees that can result from inserting permutations of 1, 2 and 3. How many types of trees are there? What are the probabilities of each type of tree’s occurring if all permutations are equally likely Given the input {4371, 1323, 6173, 4199, 4344, 9679, 1989}, a fixed table size of 10, and a hash function H(X) = X mod 10, show the resulting Linear probing hash table Separate chaining hash tablearrow_forwardPlease draw the binary tree for the answer to this problem through divide and conquer, thanksarrow_forward
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