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By using the binary tree in Figure 1; (a) List the nodes that are visited by the function insert to insert 87 into the tree in Figure 1. (b) What is the height of the tree after inserting 87? (c) Redraw the tree after inserting 87. (d) List the nodes that are visited by the function insert to insert 79 into the tree in Figure 1. (e) What is the height of the tree after inserting 79? (f) Redraw the tree after inserting 79.

By using the binary tree in Figure 1; (a) List the nodes that are visited by the function insert to insert 87 into the tree in Figure 1. (b) What is the height of the tree after inserting 87? (c) Redraw the tree after inserting 87. (d) List the nodes that are visited by the function insert to insert 79 into the tree in Figure 1. (e) What is the height of the tree after inserting 79? (f) Redraw the tree after inserting 79.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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By using the binary tree in Figure 1;

(a) List the nodes that are visited by the function insert to insert 87 into the tree in Figure 1.

(b) What is the height of the tree after inserting 87?

(c) Redraw the tree after inserting 87.

(d) List the nodes that are visited by the function insert to insert 79 into the tree in Figure 1.

(e) What is the height of the tree after inserting 79?

(f) Redraw the tree after inserting 79.

## Binary Tree Structure The image depicts a binary tree data structure. ### Description of the Binary Tree: - **Root Node**: The topmost node is 70. #### Left Subtree: - **Level 1**: The root node has two children. The left child is 60 and the right child is 92. - **Level 2 - Left Subtree (of 60)**: - Node 60 has two children: 50 (left) and 63 (right). - **Level 3 - Left Subtree (of 50)**: - Node 50 has two children: 40 (left) and 45 (right). - **Level 4 - Left Subtree (of 40)**: - Node 40 has two children: 20 (left) and 35 (right). - **Level 4 - Right Subtree (of 63)**: - Node 63 has two children: 68 (left) and 65 (right). #### Right Subtree: - **Level 2 - Right Subtree (of 92)**: - Node 92 has two children: 82 (left) and 94 (right). - **Level 3 - Left Subtree (of 82)**: - Node 82 has two children: 72 (left) and 88 (right). - **Level 3 - Right Subtree (of 94)**: - Node 94 has two children: 98 (left) and 96 (right). - **Level 4 - Left Subtree (of 72)**: - Node 72 has two children: 75 (left) and 80 (right). - **Level 4 - Right Subtree (of 88)**: - Node 88 has two children: 85 (left) and 78 (right). ### Key Points: 1. **Binary Tree**: Each node has at most two children. 2. **Hierarchy**: The tree depicts a hierarchical structure with parent-child relationships. 3. **Leaf Nodes**: The nodes without any children (e.g., 20, 35, 45, 65, 68, 75, 85, 78, 80, 96, 98) are called leaf nodes. 4. **Internal Nodes**: Nodes with at least one child (e.g.,
Transcribed Image Text:## Binary Tree Structure The image depicts a binary tree data structure. ### Description of the Binary Tree: - **Root Node**: The topmost node is 70. #### Left Subtree: - **Level 1**: The root node has two children. The left child is 60 and the right child is 92. - **Level 2 - Left Subtree (of 60)**: - Node 60 has two children: 50 (left) and 63 (right). - **Level 3 - Left Subtree (of 50)**: - Node 50 has two children: 40 (left) and 45 (right). - **Level 4 - Left Subtree (of 40)**: - Node 40 has two children: 20 (left) and 35 (right). - **Level 4 - Right Subtree (of 63)**: - Node 63 has two children: 68 (left) and 65 (right). #### Right Subtree: - **Level 2 - Right Subtree (of 92)**: - Node 92 has two children: 82 (left) and 94 (right). - **Level 3 - Left Subtree (of 82)**: - Node 82 has two children: 72 (left) and 88 (right). - **Level 3 - Right Subtree (of 94)**: - Node 94 has two children: 98 (left) and 96 (right). - **Level 4 - Left Subtree (of 72)**: - Node 72 has two children: 75 (left) and 80 (right). - **Level 4 - Right Subtree (of 88)**: - Node 88 has two children: 85 (left) and 78 (right). ### Key Points: 1. **Binary Tree**: Each node has at most two children. 2. **Hierarchy**: The tree depicts a hierarchical structure with parent-child relationships. 3. **Leaf Nodes**: The nodes without any children (e.g., 20, 35, 45, 65, 68, 75, 85, 78, 80, 96, 98) are called leaf nodes. 4. **Internal Nodes**: Nodes with at least one child (e.g.,
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