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
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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### 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
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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