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Which of the following is a valid binary search tree? O

Which of the following is a valid binary search tree? O

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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**Title: Identifying Valid Binary Search Trees** **Question:** Which of the following is a valid binary search tree? **Options:** 1. **Option 1:** - Root Node: 9 - Left Subtree: - Node: 6 - Left Child: 5 - Right Child: 7 - Right Subtree: - Node: 7 - Left Child: 3 - Right Child: 2 2. **Option 2:** - Root Node: 6 - Left Subtree: - Node: 4 - Left Child: 2 - Right Child: 5 - Right Subtree: - Node: 7 - Right Child: 9 3. **Option 3:** - Root Node: 7 - Left Subtree: - Node: 7 - Left Child: 3 - Right Child: 4 - Right Subtree: - Node: 8 4. **Option 4:** - Root Node: 5 - Left Subtree: - Node: 3 - Left Child: 2 - Right Child: 4 - Right Subtree: - Node: 8 - Left Child: 6 - Right Child: 9 **Explanation:** A binary search tree (BST) is a binary tree in which each node has at most two children. For each node, the left subtree contains only nodes with values less than the node’s key, and the right subtree only nodes with values greater than the node’s key. - **Option 1** violates the BST property as the right subtree of the root contains a node with the value 7, which is not greater than 9. - **Option 2** satisfies BST properties, making it a valid binary search tree. - **Option 3** has a duplicate value (7) in the left subtree, violating the strict ordering rule of a BST. - **Option 4** has a node with the value 6 on the right subtree of root 5, which does not satisfy the BST property that requires all right subtree nodes to be greater than the root. Therefore, **Option 2** is the correct answer.
Transcribed Image Text:**Title: Identifying Valid Binary Search Trees** **Question:** Which of the following is a valid binary search tree? **Options:** 1. **Option 1:** - Root Node: 9 - Left Subtree: - Node: 6 - Left Child: 5 - Right Child: 7 - Right Subtree: - Node: 7 - Left Child: 3 - Right Child: 2 2. **Option 2:** - Root Node: 6 - Left Subtree: - Node: 4 - Left Child: 2 - Right Child: 5 - Right Subtree: - Node: 7 - Right Child: 9 3. **Option 3:** - Root Node: 7 - Left Subtree: - Node: 7 - Left Child: 3 - Right Child: 4 - Right Subtree: - Node: 8 4. **Option 4:** - Root Node: 5 - Left Subtree: - Node: 3 - Left Child: 2 - Right Child: 4 - Right Subtree: - Node: 8 - Left Child: 6 - Right Child: 9 **Explanation:** A binary search tree (BST) is a binary tree in which each node has at most two children. For each node, the left subtree contains only nodes with values less than the node’s key, and the right subtree only nodes with values greater than the node’s key. - **Option 1** violates the BST property as the right subtree of the root contains a node with the value 7, which is not greater than 9. - **Option 2** satisfies BST properties, making it a valid binary search tree. - **Option 3** has a duplicate value (7) in the left subtree, violating the strict ordering rule of a BST. - **Option 4** has a node with the value 6 on the right subtree of root 5, which does not satisfy the BST property that requires all right subtree nodes to be greater than the root. Therefore, **Option 2** is the correct answer.
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