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 13.2, Problem 3E
Program Plan Intro
To explain the method for changing the values of depth a, b and c when a left rotation is performed on node x in the figure.
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Show the results of inserting the keys: F, L, O, R, I, D, A, U, N, V, M, Y, C, S in order into an empty B-tree with minimal degree 2. Draw only the configurations of the tree just before some node being split, and also draw the final configuration.
Please make sure your tree configurations are drawn neatly and are easy to read and understand.
Draw 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)?
Consider a B-Tree with order as 3. Which of the following will be the correct B-tree for the given key value sequence? 12, 13, 7, 16, 19, 20, 25, 3, 6
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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- Problem 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_forwardDraw the diagrams of an AVL tree as the following items are inserted into an empty tree in the specified order: 8, 71, 90, 80, 84, 75. In your diagrams, indicate the balance factors after insertion (but before rotation), which rotations are done, and the balance factors after each step.arrow_forwardForm a B-tree with t = 4 by inserting in order nodes with the following keys: I,W,A,N,T,T,O,P,A,S,S,T,H,I,S,T,E,S,T, Draw the B-tree obtained after each improvement.arrow_forward
- Consider a B Tree used as an index that has THREE levels including the root node. If a newkey is inserted in this index, then what shall be the maximum number of nodes? Explain youranswer with an example.arrow_forwardConsider the sequence of keys (5,16,22,45,2,10,18,30,50,12,1, 77, 66, 55). Draw the result of inserting entries with these keys (in the given order) into an initially empty red-black tree.arrow_forwarda)Draw a red-black tree for the following values inserted in this order. Illustrate each operation that occurs: 11 20 30 28 16 13 55 52 26 50 87 b) Draw a 2-3-4 B-tree that corresponds to your red-black tree in problem a).arrow_forward
- 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_forwardShow the results of inserting the keys: F, L, O, R, I, D, A, U, N, V, M, Y, C, S in order into an empty B-tree with minimal degree 2. Draw only the configurations of the tree just before some node being split, and also draw the final configuration. Please make sure your tree configurations are drawn neatly and are easy to read and understand. See attached image for how the tree configurations should be presentedarrow_forwardDraw the BST constructed by inserting the values [53, 25, 11, 63, 4, 88,59, 3, 15, 82, 92, 27, 55, 14] in the order shown, into an initially empty tree. 2. Using the tree traversal algorithms and the BST from above, show theoutput sequence for a (a) Preorder traversal(b) Postorder traversal 3. Delete the node with value 25 and draw the resultant tree.(a) Use two methods to delete the node with value 25 and draw the resul-tant tree. also describe both methods that you have usedarrow_forward
- Draw the tree that results in building a MaxHeap, top-down, by inserting keys in the order given below in an initially empty maxHeap: 4, 20, 26, 14, 10, 35, 30, 8, 12, 2, 45arrow_forwardQuestion 7: Given a step-by-step to build a Red Black tree with sequence of 2, 1, 4, 5, 9, 3, 6, 7arrow_forwardThe following items are inserted into an AVL tree: 1, 2, 3, 8, and 9. How many rotations are performed in total to maintain an AVL tree?arrow_forward
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