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

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.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you

Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education

Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON

Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON

Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education

Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON

Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON

C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON

Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning

Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education