Let's say you used post-order traversal to print the nodes of this tree. What nodes would be printed first and last in post-order traversal?
Let's say you used post-order traversal to print the nodes of this tree. What nodes would be printed first and last in post-order traversal?
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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Transcribed Image Text:### Post-Order Traversal of a Binary Tree
In a post-order traversal of a binary tree, we visit the nodes in the following order: left subtree, right subtree, and then the root node. Let's use this approach to traverse the given binary tree and determine which nodes would be printed first and last.
#### The Tree Structure
The tree is structured as follows:
1. **Root Node (12)**
- Left Subtree:
- Node (6)
- Left Subtree:
- Node (2)
- Left Subtree:
- Node (1)
- Right Subtree:
- Node (4)
- Right Subtree:
- Node (8)
- Right Subtree:
- Node (18)
- Left Subtree:
- Node (13)
- Right Subtree:
- Node (23)
- Left Subtree:
- Node (19)
- Right Subtree:
- Node (29)
#### Post-Order Traversal Explanation
To perform a post-order traversal, we visit nodes in the following sequence:
1. Traverse the left subtree of the root.
2. Traverse the right subtree of the root.
3. Visit the root node.
Following this procedure for our tree:
1. **Left Subtree of 12:**
- **Left Subtree of 6:**
- **Left Subtree of 2:**
- Visit Node 1 (No children)
- **Right Subtree of 2:**
- Visit Node 4 (No children)
- Visit Node 2 (after visiting children 1 and 4)
- **Right Subtree of 6:**
- Visit Node 8 (No children)
- Visit Node 6 (after visiting children 2 and 8)
2. **Right Subtree of 12:**
- **Left Subtree of 18:**
- Visit Node 13 (No children)
- **Right Subtree of 18:**
- **Left Subtree of 23:**
- Visit Node 19 (No children)
- **Right Subtree of 23:**
- Visit Node 29 (No children)
- Visit Node 23 (after visiting children 19 and 29)
- Visit Node 18 (after visiting children 13 and 23)
3. Visit Root
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