Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 13.3, Problem 1E
Program Plan Intro
To observe that if the color of newly inserted node z to red then properties 4 of red black tree is violated or not and also describe the reason of not choosing the color as black.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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?
Given 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.
Consider 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.
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
Knowledge Booster
Similar questions
- 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_forwardWrite 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_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 an avl tree also check balancing factor on each and every node: 45, 70, 35,3,7425,81,60arrow_forwardConsider 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.arrow_forwardWe'd like build a Red-Black(RB) Tree by inserting the numbers (15,5,20,25,23) one by one and maintaining the RB-properties. Which one is the preorder traversal sequence of the RB tree after 15,5,20, 25 ,23 is inserted? Here B- and R- denote the color of the node PLEASE EXPLAIN THE OPERATION IN DETAILarrow_forward
- 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.arrow_forwardUse the given AVL tree to answer each of the following questions: (a) Which is the deepest unbalanced node after inserting key 5, but before re-balancing, and what is its balance factor? (b) After the insertion, perform all the necessary rotations required to re-balance the tree, and after each rotation,state the type of rotation done and list the keys of the resulting tree in the form: After Left/Right rotation: e1, e2, e3, ...., en.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_forward
- Let T1, T2 be 2-3-4 trees and let x be a key [in neither T1, T2], such that for each pair of keys x1 ∈ T1 and x2 ∈ T2, we have x1 < x < x2. Thus, every key in T1 is smaller than every key in T2. Devise an algorithm that constructs the union of x with these two trees. Of course, the trees T1, T2 may be of different height, and the result must be a valid 2-3-4 tree. Your algorithm should run in O(1 + |h(T1) − h(T2)|).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_forwardUse the given AVL tree to answer each of the following questions: (a) Which is the deepest unbalanced node after inserting key 5, but before re-balancing, and what is its balance factor? (b) After the insertion, perform all the necessary rotations required to re-balance the tree, and after each rotation, state the type of rotation done and list the keys of the resulting tree in the form: After Left/Right rotation: e1, e2, e3, ...., en. (breadth-first order)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill Education
Starting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSON
Digital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSON
Database Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage Learning
Programmable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education