Set up LinkedBinaryTree class and then create a simple test driver to perform some basic operations on a binary tree of strings. Once it is working correctly, modify LinkedBinaryTree to support in-order traversal. It is best to add/modify positions() to perform in-order traversal. Add code to construct a tree in lab question 1 below and then perform an in- order traversal on that tree. Question 1: Provide pre-order traversal, in-order traversal and post-order traversal traversal for the following binary tree. A ВС DEF G Question 2: Which traversal in question 1 is not used for a general tree? Explain why that is the case.

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
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### Binary Tree Traversal

In this exercise, we will set up a `LinkedBinaryTree` class and create a test driver to perform basic operations on a binary tree of strings. After successfully setting up the `LinkedBinaryTree`, we'll modify it to support in-order traversal by adding or modifying the `positions()` method. 

#### Task:
1. **Construct the Tree**: Write code to construct a tree as shown in the first question.
2. **Perform Traversals**: Implement functions to perform in-order, pre-order, and post-order traversals on the tree.

#### Tree Structure:
The binary tree structure for this exercise is represented as:

```
    A
   / \
  B   C
 / \   \
D   E   F
/
G
```

#### Exercise Description:
**Question 1**: Provide pre-order traversal, in-order traversal, and post-order traversal for the binary tree.

**Question 2**: Which traversal in question 1 is not used for a general tree? Explain why that is the case.

#### Graph Descriptions:
The tree displayed above exhibits the following node hierarchy:
- `A` is the root node.
- `B` and `C` are the children of `A`.
- `D` and `E` are the children of `B`.
- `G` is the left child of `D`.
- `F` is the right child of `C`.

### Binary Tree Traversal Methods:
1. **Pre-order Traversal**:
   - Visit the root node.
   - Traverse the left subtree in pre-order.
   - Traverse the right subtree in pre-order.

2. **In-order Traversal**:
   - Traverse the left subtree in in-order.
   - Visit the root node.
   - Traverse the right subtree in in-order.

3. **Post-order Traversal**:
   - Traverse the left subtree in post-order.
   - Traverse the right subtree in post-order.
   - Visit the root node.

### Solution to Question 2:
- In a general tree, **in-order traversal** is not typically defined or used. This is because general trees are not binary and can have more than two children per node. In-order traversal specifically relies on the binary tree property of having at most two children, where the "in-order" sequence is well-defined.
Transcribed Image Text:### Binary Tree Traversal In this exercise, we will set up a `LinkedBinaryTree` class and create a test driver to perform basic operations on a binary tree of strings. After successfully setting up the `LinkedBinaryTree`, we'll modify it to support in-order traversal by adding or modifying the `positions()` method. #### Task: 1. **Construct the Tree**: Write code to construct a tree as shown in the first question. 2. **Perform Traversals**: Implement functions to perform in-order, pre-order, and post-order traversals on the tree. #### Tree Structure: The binary tree structure for this exercise is represented as: ``` A / \ B C / \ \ D E F / G ``` #### Exercise Description: **Question 1**: Provide pre-order traversal, in-order traversal, and post-order traversal for the binary tree. **Question 2**: Which traversal in question 1 is not used for a general tree? Explain why that is the case. #### Graph Descriptions: The tree displayed above exhibits the following node hierarchy: - `A` is the root node. - `B` and `C` are the children of `A`. - `D` and `E` are the children of `B`. - `G` is the left child of `D`. - `F` is the right child of `C`. ### Binary Tree Traversal Methods: 1. **Pre-order Traversal**: - Visit the root node. - Traverse the left subtree in pre-order. - Traverse the right subtree in pre-order. 2. **In-order Traversal**: - Traverse the left subtree in in-order. - Visit the root node. - Traverse the right subtree in in-order. 3. **Post-order Traversal**: - Traverse the left subtree in post-order. - Traverse the right subtree in post-order. - Visit the root node. ### Solution to Question 2: - In a general tree, **in-order traversal** is not typically defined or used. This is because general trees are not binary and can have more than two children per node. In-order traversal specifically relies on the binary tree property of having at most two children, where the "in-order" sequence is well-defined.
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