https://file.aiquickdraw.com/mathbot/file/17251604683124ceurthw.jpg

**Remove** the following integers in the order presented from the given BST and show each step of removal by drawing the BSTs after each step of removal in the box below (i.e. 5 trees in total). When removing a node with 2 children, you must replace it with its **in-order successor** to get credits. Then add the resulting tree in a string format to BSTManual.java.

To remove the nodes from the given Binary Search Tree (BST) and show each step, we must follow the specified order and rules:

### **Nodes to be removed:**
1. 65
2. 80
3. 40
4. 60
5. 70

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

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

#### **1. Remove 65:**
- 65 has one child (62). It can be replaced directly by its child.

**Resulting Tree:**
```
        60
       /  \
     40    70
    /  \     \
  25   43    80
 /        \   / \
31        62 76 94
```

#### **2. Remove 80:**
- 80 has two children. The in-order successor is 94, so replace 80 with 94.

**Resulting Tree:**
```
        60
       /  \
     40    70
    /  \     \
  25   43    94
 /        \   /
31        62 76
```

#### **3. Remove 40:**
- 40 has two children. The in-order successor is 43, so replace 40 with 43.

**Resulting Tree:**
```
        60
       /  \
     43    70
    /       \
  25        94
 /         /  \
31        62  76
```

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

**Resulting Tree:**
```
        62
       /  \
     43    70
    /       \
  25        94
 /         /  \
31        76
```

#### **5. Remove 70:**
- 70 has one child (94). It can be replaced directly by its child.

**Final Tree:**
```
        62
       /  \
     43    94
    /     /
  25    76
 /      
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(43(25(31)(null))(null))(94(76)(null))"
```

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. How do you find the in-order successor in a BST?
2. What happens when a node with no children is removed from a BST?
3. Can you explain the difference between the in-order predecessor and in-order successor?
4. How would you remove a node from a BST using its in-order predecessor instead of the successor?
5. What is the time complexity of removing a node in a BST?

### Tip:
When dealing with large BSTs, it's helpful to practice visualizing the process of node removal to ensure accuracy, especially when dealing with nodes that have two children.

Learn how to remove specific nodes from a Binary Search Tree (BST) step-by-step, including handling nodes with one or two children by replacing them with their in-order successor. This detailed guide includes visual representations of BST changes and a final tree representation suitable for Java implementation.

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