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 B.5, Problem 1E
Program Plan Intro
To draw:
- All the free possible trees with three vertices x, y and z.
- All the rootedtrees with three vertices x, y and z with x as a root node.
- The ordered tree with vertices x, y and z with x as a root node.
- All the binary treeswith vertices x, y and z with x as a root node.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Construct a Huffman tree for the given eight leaf nodes {a, b, c, d, e, f, g, h} with
weights of 5, 7, 18, 3, 24, 9, 13, 10} respectively. Please draw the Huffman tree and
show the Huffman code for each node.
5
18
a
7
b
3
P
24
D
9
f
13
g
10
h
Please draw the following:Form a binary tree with the root node holding 20, the left and right child of the node holding 20 respectively holding 75 and 43. The next level nodes hold the data 84, 90, 57 and 71 from left to right. The node holding 84 has left and right children that respectively hold 96 and 91 and the node holding 90 has a left child that holds 93.
Let n be 22 . Let T be a binary rooted tree with n vertices.
(a) What is the least number of levels that T can have? Explain your answer.
(b) What is the greatest number of levels that T can have? Explain your answer.
Please answer both a and b. I will provide you positive response.
Thanks
Chapter B Solutions
Introduction to Algorithms
Ch. B.1 - Prob. 1ECh. B.1 - Prob. 2ECh. B.1 - Prob. 3ECh. B.1 - Prob. 4ECh. B.1 - Prob. 5ECh. B.1 - Prob. 6ECh. B.2 - Prob. 1ECh. B.2 - Prob. 2ECh. B.2 - Prob. 3ECh. B.2 - Prob. 4E
Ch. B.2 - Prob. 5ECh. B.3 - Prob. 1ECh. B.3 - Prob. 2ECh. B.3 - Prob. 3ECh. B.3 - Prob. 4ECh. B.4 - Prob. 1ECh. B.4 - Prob. 2ECh. B.4 - Prob. 3ECh. B.4 - Prob. 4ECh. B.4 - Prob. 5ECh. B.4 - Prob. 6ECh. B.5 - Prob. 1ECh. B.5 - Prob. 2ECh. B.5 - Prob. 3ECh. B.5 - Prob. 4ECh. B.5 - Prob. 5ECh. B.5 - Prob. 6ECh. B.5 - Prob. 7ECh. B - Prob. 1PCh. B - Prob. 2PCh. B - Prob. 3P
Knowledge Booster
Similar questions
- Answer the following questions about the rooted tree shown. For questions in which you need to list more than one vertex, list the vertices in alphabetical order and separate them with a comma. 1) Which vertix is the root? 2) What is the height of the graph? 3) What is the level of H? 4) List the children of B. If B has no chidren, write NONE. 5) What is the parent of K? 6) What are the sibling(s) of E? 7) What are the ancestor(s) of Q? 8) What are the descendant(s) of C? 9) List the leaves of the graph. 10) How many internal vertices does the graph have?arrow_forward1. For the given Red Black Tree, draw the tree, when the following entries are inserted: Jade, Bob, and Dave. You must show the intermediate states (after each rotation). Eddie Веyonce George Alicia Chris Frank Janearrow_forwardi. ii. Using an array-based representation of a binary tree, the following array represents a binary tree. 0 1 2 3 59 39 75 4 48 5 6 70 80 111. Draw the binary tree that is represented by the above array. 7 8 9 10 11 12 13 14 44 68 90 What is the postorder traversal of the binary tree that is created in (i). What is the parent of 72?arrow_forward
- The postorder traversal of a binary tree is 10, 24, 32, 30, 26, 16, 40, 90, 80, 60, 50, 36. The inorder traversal of the same tree is 10, 16, 24, 26, 30, 32, 36, 40, 50, 60, 80, 90. The height of the tree is the length of the longest path from the root to any leaf. The height of the binary tree will bearrow_forwardConsider a binary tree. The POSTORDER traversal of the tree is 19, 12, 26, 31, 23, 49, 57, 63, 58, 54, 35 and the INORDER traversal 12, 19, 23, 26, 31, 35, 49, 54, 57, 58, 63. If the height of the root node is 0 then what is the height of the binary tree?arrow_forward2. Draw a tree with a depth of 3 and indicate all the nodes as either a parent, child, root, or leaf node(s).arrow_forward
- 1. A binary tree is a connected graph, where there is a path between two of its vertices, and acyclic, that is, it does not allow cycles, connected, directed and that each node has no degree (or order) greater than 2.Based on this definition and what was presented in the lesson content, which tree corresponds to a binary tree with a depth of 05, being two levels with 03 nodes, and containing 05 leaves. Select the correct option (A) (B) (C) (D)arrow_forwardA binary tree is a kind of rooted tree that does not have more than two offspring per node at any point in its structure. Show that the number of nodes in a binary tree that are responsible for creating two offspring is precisely one fewer than the number of leaves in that tree. Demonstrate this by subtracting one from the total number of leaves.arrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Computer science. You are given n chains of lengths l1,l2,… ,ln. You intend to fabricate a tree utilizing some of them. Every vertex of the tree is either white or dark. The tree at first just has a white root vertex. All chains at first comprise just of white vertices. You can take one of the chains and interface any of its vertices to any white vertex of the tree with an edge. The chain turns out to be important for the tree. The two endpoints of this edge become dark. Each chain can be utilized close to once. A few chains can be left unused. The distance between two vertices of the tree is the number of edges on the most brief way between them. Assuming there is essentially k white vertices in the subsequent tree, the worth of the tree is the distance between the root and the k-th nearest white vertex. What's the base worth of the tree you can get? In case it is absolutely impossible to construct…arrow_forward
- Exercise 6. A binary tree T has height 8. (Recall that the height of a tree is the number of edges along the longest path from root to leaves). (a) What is the minimum number of nodes in T. (b) What is the maximum number of nodes in T.arrow_forwardIn a tree classification task, the set X associated with node t, contains N, = 14 vectors. Four of these belong to class w, two to class w2, and eight to class @3, in a three-class classification task. The node splitting results into two new subsets Xry, with three vectors from @, and two from @2, and XIN with one vectors from @1, none from w2 and eight from w3. Compute the decrease in node impurity after splitting. %3Darrow_forwardA rooted tree that has no more than two children per node is referred to as a binary tree. Demonstrate that the number of nodes in a binary tree that are responsible for producing two children is exactly one less than the number of leaves in that tree.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