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:

javaCopy code
"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.