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 13.3, Problem 5E
Program Plan Intro
To argue that if
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Consider an empty B-Tree with minimum degree of two(maximum 3 keys for each node). We insert 10 items to this B-Tree consecutively.
How many node splitting operations are required in the worst-case? Explain your answer for each insertion.
Consider the following B+ tree. Draw the final B+ tree after deleting 50, 24, 65, 93, 75 (in the given order).
Consider the values 19, 10, 4, 30, 55, 24, 9, 13, 11 and 22:
Draw the 2-3-4 tree that results from inserting these values in that order into an initially empty 2-3-4 tree. Show your workings.
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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- Consider an initially empty B-Tree with minimum degree t 3. Draw the B-Tree afterthe insertion of the keys 27,33,39,1,3,10,7,200,23,21,20, and then after the additional insertionof the keys 15,18,19, 13, 34, 200,100, 50, 51.arrow_forwarda) Draw updated AVL tree after insertion of 90? Draw each rotation Delete Node 80 after step (a), then delete 120.arrow_forwardConsider 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_forward
- Consider the binomial tree B6. How many nodes does it have? How many nodes are at depth 4? (Note: the root is at depth 0.)arrow_forwardFor a full 5-ary tree, where n = the number of nodes, i = the number of internal nodes, and l = the number of leaves: find i and l, if n = 996; find n and l, if i = 333; find n and i, if l = 569;arrow_forward(A) Show the 2-3 tree that results if we insert into an empty set, represented as a 2-3 tree, the elements 5, 2, 7, 0, 3, 4, 6, 1, 8, 9. (B) Show the result of deleting 3 from the 2-3 tree that results from (A).arrow_forward
- Write solution step by step Insert the following elements in an empty AVL tree one by one: 14,17,11,7,53,4,13. Balance the tree after each insertion. Then delete the elements: 53, 11 and balance it.arrow_forwardYou have a B-tree containing 99999 (approximately 100000) keys and with a minimum degree t=10. What is the maximum B-tree height. Hint: if minimum degree is t, then there are at least t-1 and at most 2t-1 keys in a node.arrow_forwardGiven the following AVL tree, if node 83 is deleted, how many rotations are needed to obtain an AVL tree again? Draw the tree after each rotation.arrow_forward
- Build a k-d tree, k = 2, for the keys {P: (5, 6), Q: (2, 7), U: (6, 1), S: (3, 9),T: (9, 4), R: (1, 8)}arrow_forwardConsider an AVL-Tree of positive integers in which duplicate values are not permitted. A double rotation is triggered when the number 10 is inserted into a minimum AVL-tree of height 3. Prior and then after the insert, draw a schematic of the tree.arrow_forwardConsider the AVL tree given in the following figure and delete 39 from it.arrow_forward
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