Elements to remove: [70, 43, 60, 80, 65]


Let's proceed with removing the elements from the given Binary Search Tree (BST) in the order you provided: [70, 43, 60, 80, 65]. We will follow the rule of replacing a node with its in-order successor when it has two children.

### **Initial BST:**
```
        60
       /  \
     40    70
    /  \   /  \
  25   43 65  80
 /        \    / \
31        62  76 94
```

### **Step-by-Step Removal Process:**

#### **1. Remove 70:**
- **70** has two children. The in-order successor is **76**, so replace 70 with 76.

**Resulting Tree:**
```
        60
       /  \
     40    76
    /  \   /  \
  25   43 65  80
 /        \     \
31        62    94
```

#### **2. Remove 43:**
- **43** has no children. We simply remove it.

**Resulting Tree:**
```
        60
       /  \
     40    76
    /      /  \
  25     65   80
 /         \    \
31         62   94
```

#### **3. Remove 60:**
- **60** has two children. The in-order successor is **62**, so replace 60 with 62.

**Resulting Tree:**
```
        62
       /  \
     40    76
    /      /  \
  25     65   80
 /            \
31            94
```

#### **4. Remove 80:**
- **80** has one child (94). It can be replaced directly by its child.

**Resulting Tree:**
```
        62
       /  \
     40    76
    /      /  \
  25     65   94
 /      
31     
```

#### **5. Remove 65:**
- **65** has no children. We simply remove it.

**Final Tree:**
```
        62
       /  \
     40    76
    /        \
  25         94
 /      
31     
```

### **BST in String Format:**
The final tree can be represented in a string format suitable for `BSTManual.java`. Here's an example:

```java
"62(40(25(31)(null))(null))(76(null)(94))"
```

This format represents the tree where each node follows the format `Node(LeftSubtree)(RightSubtree)`.

### Would you like further details or have any questions?

### 5 Related Questions:
1. What is the significance of the in-order successor in a BST?
2. How does the removal of a node affect the height of a BST?
3. Can you describe the process of balancing a BST after multiple deletions?
4. What are the implications of removing the root node from a BST?
5. How does the removal of nodes in different orders affect the structure of the BST?

### Tip:
When removing nodes from a BST, always ensure that the tree remains valid by carefully replacing nodes with their correct in-order successors, especially when dealing with nodes that have two children.

Explore how to remove specific nodes from a Binary Search Tree (BST) in a step-by-step manner. This detailed guide covers the process of removing nodes, including the replacement of nodes with their in-order successors. Suitable for advanced learners studying data structures and algorithms.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation