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7. Given the BST below, show the BST that would result after inserting the key of value 10 if splaying is performed starting at the node that was inserted. 100 50 150) 40 60 200 30

7. Given the BST below, show the BST that would result after inserting the key of value 10 if splaying is performed starting at the node that was inserted. 100 50 150) 40 60 200 30

Computer Networking: A Top-Down Approach (7th Edition)
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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### Problem Statement 7. Given the Binary Search Tree (BST) below, show the BST that would result after inserting the key of value 10 if splaying is performed starting at the node that was inserted. ### Diagram Explanation The BST provided before insertion is structured as follows: - **Root Node**: 100 - **Left Subtree of Root**: - Node: 50 - Left Child: 40 - Left Child: 30 - Right Child: 60 - **Right Subtree of Root**: - Node: 150 - Right Child: 200 ### Insertion and Splaying Process 1. **Insert 10 into the BST**: Begin by adding the key 10. As 10 is less than 50, 40, and 30, it will be inserted as the left child of node 30. 2. **Splay Operation**: Perform splaying starting at the newly inserted node (10). Splaying is a process that moves the accessed node to the root of the tree through a series of tree rotations. - **Zig-Zig Rotation**: Since 10 is a left child of 30, and 30 is a left child of 40, perform a right rotation on 40, then on 50. - **Zig Rotation**: Perform a right rotation on 100 to bring 10 to the root. After these operations, the final tree structure will have 10 as the root, balancing the tree and potentially improving access times for recently accessed nodes.
Transcribed Image Text:### Problem Statement 7. Given the Binary Search Tree (BST) below, show the BST that would result after inserting the key of value 10 if splaying is performed starting at the node that was inserted. ### Diagram Explanation The BST provided before insertion is structured as follows: - **Root Node**: 100 - **Left Subtree of Root**: - Node: 50 - Left Child: 40 - Left Child: 30 - Right Child: 60 - **Right Subtree of Root**: - Node: 150 - Right Child: 200 ### Insertion and Splaying Process 1. **Insert 10 into the BST**: Begin by adding the key 10. As 10 is less than 50, 40, and 30, it will be inserted as the left child of node 30. 2. **Splay Operation**: Perform splaying starting at the newly inserted node (10). Splaying is a process that moves the accessed node to the root of the tree through a series of tree rotations. - **Zig-Zig Rotation**: Since 10 is a left child of 30, and 30 is a left child of 40, perform a right rotation on 40, then on 50. - **Zig Rotation**: Perform a right rotation on 100 to bring 10 to the root. After these operations, the final tree structure will have 10 as the root, balancing the tree and potentially improving access times for recently accessed nodes.
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