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What is the height of the tree?

What is the height of the tree?

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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**Question:** What is the height of the tree? **Diagram Explanation:** The diagram is a representation of a binary tree consisting of the following nodes: - The root node is 16. - The left child of 16 is 4. - The right child of 16 is 21. - The left child of 4 is 12. - The right child of 21 is 30. - The left child of 30 is 28. **Tree Height Calculation:** The height of a tree is defined as the number of edges on the longest path from the root to a leaf. In this tree, the height is determined as follows: - Starting from the root (16), the longest path is 16 -> 21 -> 30 -> 28. - This path has three edges. **Options:** - ○ 2 - ○ 3 - ○ 4 - ○ 1 Correct answer: ○ 3
Transcribed Image Text:**Question:** What is the height of the tree? **Diagram Explanation:** The diagram is a representation of a binary tree consisting of the following nodes: - The root node is 16. - The left child of 16 is 4. - The right child of 16 is 21. - The left child of 4 is 12. - The right child of 21 is 30. - The left child of 30 is 28. **Tree Height Calculation:** The height of a tree is defined as the number of edges on the longest path from the root to a leaf. In this tree, the height is determined as follows: - Starting from the root (16), the longest path is 16 -> 21 -> 30 -> 28. - This path has three edges. **Options:** - ○ 2 - ○ 3 - ○ 4 - ○ 1 Correct answer: ○ 3
### Understanding Frontier Nodes in a Tree Structure #### Question What nodes are in the frontier? #### Diagram Explanation The diagram represents a tree structure with the following nodes: - Node 16 as the root, with edges pointing to nodes 4 and 21. - Node 4 has a child node, 12. - Node 21 has a child node, 30. - Node 30 has a child node, 28. #### Answer Options - ○ node 28 - ○ none of the above - ○ node 12 - ○ both node 12 and node 18 ### Explanation The frontier of a tree consists of the leaf nodes—nodes that do not have any children. In this diagram: - Node 12 and node 28 are leaf nodes. Selecting the correct nodes in the frontier involves identifying which nodes are leaf nodes based on the given structure.
Transcribed Image Text:### Understanding Frontier Nodes in a Tree Structure #### Question What nodes are in the frontier? #### Diagram Explanation The diagram represents a tree structure with the following nodes: - Node 16 as the root, with edges pointing to nodes 4 and 21. - Node 4 has a child node, 12. - Node 21 has a child node, 30. - Node 30 has a child node, 28. #### Answer Options - ○ node 28 - ○ none of the above - ○ node 12 - ○ both node 12 and node 18 ### Explanation The frontier of a tree consists of the leaf nodes—nodes that do not have any children. In this diagram: - Node 12 and node 28 are leaf nodes. Selecting the correct nodes in the frontier involves identifying which nodes are leaf nodes based on the given structure.
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The height of a tree is calculated as the longest path from the root to a leaf node in this we calculate the number of edged in that path.

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