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:

javaCopy code
"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.