Pre-order: 7 2 9 14 16 Post-order: 2 16 14 9 7 In-order: 2 7 9 14 16

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
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The solution is provided. Could you explain this question step by step.
Consider the following tree traversals:
Pre-order: 7 2 9 14 16
Post-order: 2 16 14 9 7
In-order: 2 7 9 14 16
Is it possible for a single binary search tree to give rise to all three of those traversals? If so, draw the
tree. If not, clearly explain why it's not possible.
Solution:
7
2
14
16
Transcribed Image Text:Consider the following tree traversals: Pre-order: 7 2 9 14 16 Post-order: 2 16 14 9 7 In-order: 2 7 9 14 16 Is it possible for a single binary search tree to give rise to all three of those traversals? If so, draw the tree. If not, clearly explain why it's not possible. Solution: 7 2 14 16
Expert Solution
Step 1

ANS: The given solution is correct;

If a pre-order and In-order is given  OR a post-order and In-order is given then we can draw a unique binary tree.

pre-order + IN-order = Unique binary tree;

post-order + IN-order =Unique binary tree;

here, pre-order , post -order , In-order is given, so obviously we can draw a unique binary tree.

 

First of all you need to understand the Traversal:

pre-order:    In pre-order traversal , first we write Node , then goto left child and then right child;

           The first node of pre-order traversal is always Root node.

Post-order:  In post-order traversal , first we goto the left then right  , then node;

              The last node of post -order is Root node.

In-order: In in-order traversal , first we goto left then node then right;

 

 

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