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 13.4, Problem 3E
Program Plan Intro
To show the red black tree with successive deletion of the keys in the order of 8, 12, 19, 31, 38, 41.
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What is the level of node 17, and node 11, respectively? Insert integers 11, 22, 15, 44, 6, 9, 3, 33, 17, 5 into a BST in that order. Draw the final tree. From the BST, delete node with 3, and then delete the node with 22, respectively; Then insert a node with 18 into the BST. Draw the final tree after above operations are finished.
Insert the following values into an initially empty Red-Black tree in the order given.Insert: 93, 85, 24, 13, 47, 59, 18, 36, 14, 35, 77, 63 Also, answer the questions below.What is the black-height of node 59?What is the height of node 24?
Generate an AVL tree by inserting the following keys (in the given order) into an initially empty AVL tree: 10, 85, 25, 80, 65, 95, 40, 50, 75, 70. Draw an AVL tree after an insertion of each key, one by one.
From the final AVL tree in the first part, delete the keys in the order of their insertion: 10, 85, 25, 80, 65, 95, 40, 50, 75, 70. Draw an AVL tree after the removal of each key, one by one.
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Chapter 13 Solutions
Introduction to Algorithms
Ch. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7ECh. 13.2 - Prob. 1ECh. 13.2 - Prob. 2ECh. 13.2 - Prob. 3E
Ch. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.4 - Prob. 1ECh. 13.4 - Prob. 2ECh. 13.4 - Prob. 3ECh. 13.4 - Prob. 4ECh. 13.4 - Prob. 5ECh. 13.4 - Prob. 6ECh. 13.4 - Prob. 7ECh. 13 - Prob. 1PCh. 13 - Prob. 2PCh. 13 - Prob. 3PCh. 13 - Prob. 4P
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- Exercise 4 Consider the B-tree which is a result of inserting 15,14,1,2,13,12,3,4,11,10,5,6,9, (in that order) for t = 2. (a) Draw the trees before and after adding 9. (b) Draw the final tree after adding all numbers. (c) Next draw the tree after removing 14.arrow_forwardConsider the bottom most BST drawn on page 401 of the text. Draw what the resulting tree looks like if “E” is deleted from this tree.arrow_forwardProblem 1. Insert the following set of keys {1, 7, 6, 8, 0, 5, 2, 12, 3, 18} in an empty red-black tree in the order they are listed.arrow_forward
- Create a binary search tree as discussed in class, using the given numbers in the order they’re presented. State if the resulting tree is has the attributes of being FULL, BALANCED, or COMPLETE. 37, 20, 18, 56, 40, 42, 12, 5, 6, 77, 21, 54arrow_forwardDraw a KD Tree in the space below with these points inserted in the following order: (7,2), (6,4), (9,6), (8,1), (4,9), and (2,3). Assume the first level of the KD Tree is split along the x-axis. What point (from the KD Tree ) is the nearest neighbor of the point (1,4)?arrow_forwardSuppose the keys 3, 4, 45, 21, 92, 12 are inserted into a BST in this order. What is the preorder traversal of the elements after deleting 45 from the tree? Group of answer choices 3 4 21 12 92 12 21 92 45 4 3 4 21 12 92 3 4 21 12 92 3 3 4 12 21 92arrow_forward
- Build an AVL tree with the following values: 15, 20, 24, 10, 13, 7, 30, 36, 25arrow_forwardConsider the bottom most BST drawn on page 401 of section 3.2 of the text. Draw what the resulting tree looks like if “H” is deleted from this tree.arrow_forwardWhat will be the Inorder traversal of the following tree?* 11, 20, 29, 32, 41, 50, 65, 72, 91, 99 11, 20, 29, 32, 50, 65, 72, 91, 99, 41 11, 32, 50, 72, 99, 29, 65, 91, 20, 41 41, 20, 11, 29, 32, 65, 50, 91, 72, 99 41, 20, 11, 65, 91, 99, 29, 32, 50, 72arrow_forward
- Show the result of inserting 30, 10, 40, 60, 90, 20, 50, 70 into an initially empty binary search tree. b) Is the above tree a full binary tree? Why? Why not? c)Draw the subtree with the root node as 60.arrow_forwardDraw the Red-Black BST that results when you insert the keys 43, 47, 35, 40, 55, 20, 30, 68. 57, 52, 18 in that order into an initially empty tree. Show the intermediate steps, including rotations, color flips, and the final tree during EACH insertion. You cannot simply draw the final trees based on the previous question. Show the Red and Black node in color or use solid line to indicate a black link and dashed line to indicate red link (red node). Show the value in the corresponding node next to key. Black link: Red link: Please draw the solution. No code requiredarrow_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_forward
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