Question Which of the following statements about balanced search trees are true? Unless otherwise specified, assume that the 2-3 tree and red-black BSTS are as described in lecture (e.g., 2-3 trees are perfectly balanced and red-black BST are left-leaning red-black BSTS with internal links colored either red or black). Answer Mark all that apply. OThe minimum height of any 2-3 tree containing n keys is - log_3 n. OThe subtree rooted at any node of a 2-3 tree is itself a 2-3 tree. OThe number of structurally different (with respect to tree shape and link colors) red-black BSTS containing 4 keys is 2. UThe height of any red-black BST equals the height of the corresponding 2-3 tree plus the maximum number of 3-nodes on any path from the root to a leaf node. OFor any sequence of n>1 keys inserted into an initially empty red-black BST, the resulting red-black BST has at least one red link.
Question Which of the following statements about balanced search trees are true? Unless otherwise specified, assume that the 2-3 tree and red-black BSTS are as described in lecture (e.g., 2-3 trees are perfectly balanced and red-black BST are left-leaning red-black BSTS with internal links colored either red or black). Answer Mark all that apply. OThe minimum height of any 2-3 tree containing n keys is - log_3 n. OThe subtree rooted at any node of a 2-3 tree is itself a 2-3 tree. OThe number of structurally different (with respect to tree shape and link colors) red-black BSTS containing 4 keys is 2. UThe height of any red-black BST equals the height of the corresponding 2-3 tree plus the maximum number of 3-nodes on any path from the root to a leaf node. OFor any sequence of n>1 keys inserted into an initially empty red-black BST, the resulting red-black BST has at least one red link.
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![**Question**
Which of the following statements about balanced search trees are true? Unless otherwise specified, assume that the 2-3 tree and red-black BSTs are as described in lecture (e.g., 2-3 trees are perfectly balanced and red-black BST are left-leaning red-black BSTs with internal links colored either red or black).
**Answer**
*Mark all that apply.*
- [ ] The minimum height of any 2-3 tree containing n keys is ~log₃ n.
- [ ] The subtree rooted at any node of a 2-3 tree is itself a 2-3 tree.
- [ ] The number of structurally different (with respect to tree shape and link colors) red-black BSTs containing 4 keys is 2.
- [ ] The height of any red-black BST equals the height of the corresponding 2-3 tree plus the maximum number of 3-nodes on any path from the root to a leaf node.
- [ ] For any sequence of n > 1 keys inserted into an initially empty red-black BST, the resulting red-black BST has at least one red link.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce768285-628a-4724-9f2b-b5d3bc5907ae%2Fe979c671-c0cb-4f41-9b90-e7ce441dfb31%2Fmn6363b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question**
Which of the following statements about balanced search trees are true? Unless otherwise specified, assume that the 2-3 tree and red-black BSTs are as described in lecture (e.g., 2-3 trees are perfectly balanced and red-black BST are left-leaning red-black BSTs with internal links colored either red or black).
**Answer**
*Mark all that apply.*
- [ ] The minimum height of any 2-3 tree containing n keys is ~log₃ n.
- [ ] The subtree rooted at any node of a 2-3 tree is itself a 2-3 tree.
- [ ] The number of structurally different (with respect to tree shape and link colors) red-black BSTs containing 4 keys is 2.
- [ ] The height of any red-black BST equals the height of the corresponding 2-3 tree plus the maximum number of 3-nodes on any path from the root to a leaf node.
- [ ] For any sequence of n > 1 keys inserted into an initially empty red-black BST, the resulting red-black BST has at least one red link.
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