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6. Consider the following binary tree. 3 5 LO 5 8 1 2 10 1 7 6 a) List the nodes visited with a preorder traversal. List the nodes visited with an inorder traversal. b) c) List the nodes visited with a postorder traversal. How many internal no to thoro?

6. Consider the following binary tree. 3 5 LO 5 8 1 2 10 1 7 6 a) List the nodes visited with a preorder traversal. List the nodes visited with an inorder traversal. b) c) List the nodes visited with a postorder traversal. How many internal no to thoro?

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
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# Binary Tree Analysis Consider the following binary tree diagram: ``` 10 / \ 8 7 / \ / \ 5 2 1 6 / \ 3 1 ``` ### Questions: a) **Preorder Traversal:** Visit the root node first, followed by the left subtree, and then the right subtree. b) **Inorder Traversal:** Visit the left subtree first, then the root node, and finally the right subtree. c) **Postorder Traversal:** Visit the left subtree first, then the right subtree, and finally the root node. d) **Internal Nodes:** Count the nodes that have at least one child. e) **Leaves:** Count the nodes that have no children. f) **Maximum Width:** Determine the level with the maximum number of nodes. g) **Height of the Tree:** Measure the longest path from the root to any leaf. h) **Diameter of the Tree:** Measure the longest path between any two nodes in the tree. ### Diagram Explanation: - **Nodes:** Represented by circles. - **Edges:** Lines connecting nodes, representing the parent-child relationship. - **Root Node (10):** The topmost node with no parent. - **Subtrees:** Smaller sections of the tree originating from a node. ### Analytical Tasks: For each traversal type (preorder, inorder, postorder), list the sequence of nodes visited. Analyze the structure to identify internal nodes and leaves, and calculate width, height, and diameter.
Transcribed Image Text:# Binary Tree Analysis Consider the following binary tree diagram: ``` 10 / \ 8 7 / \ / \ 5 2 1 6 / \ 3 1 ``` ### Questions: a) **Preorder Traversal:** Visit the root node first, followed by the left subtree, and then the right subtree. b) **Inorder Traversal:** Visit the left subtree first, then the root node, and finally the right subtree. c) **Postorder Traversal:** Visit the left subtree first, then the right subtree, and finally the root node. d) **Internal Nodes:** Count the nodes that have at least one child. e) **Leaves:** Count the nodes that have no children. f) **Maximum Width:** Determine the level with the maximum number of nodes. g) **Height of the Tree:** Measure the longest path from the root to any leaf. h) **Diameter of the Tree:** Measure the longest path between any two nodes in the tree. ### Diagram Explanation: - **Nodes:** Represented by circles. - **Edges:** Lines connecting nodes, representing the parent-child relationship. - **Root Node (10):** The topmost node with no parent. - **Subtrees:** Smaller sections of the tree originating from a node. ### Analytical Tasks: For each traversal type (preorder, inorder, postorder), list the sequence of nodes visited. Analyze the structure to identify internal nodes and leaves, and calculate width, height, and diameter.
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