Mastering Node Removal in Binary Search Trees

How can a node with two children be removed from a tree?

• A. Replace it with the left child node
• B. Move the successor's child up to the root node
• C. Delete the node and leave a null
• D. Move the predecessor's child up to the root node

Answer: (B)

When removing a node with two children from a binary search tree, the appropriate method is to replace it with either its in-order successor or its in-order predecessor. In the context of this question, moving the successor's child up to the root node is a valid strategy. The in-order successor is the smallest value node in the right subtree of the node to be deleted. By replacing the node with its successor, you effectively maintain the structure and properties of the binary search tree because the successor will have at most one child. This allows you to easily reconnect any remaining nodes after the replacement, ensuring that the tree remains valid. In contrast, simply replacing the node with its left child (as suggested in one of the incorrect options) would not suffice since it would disrupt the binary search tree properties. Leaving a null would lead to gaps in the tree structure. Moving the predecessor's child up to the root node is also a viable approach, but the question specifically asks for the action regarding the successor, making that the most fitting answer in this context.

Understanding how to remove a node with two children from a binary search tree (BST) can feel a bit like navigating through a maze, but fear not—once you've cracked the basics, you've got yourself a handy tool for maintaining order in your data structure. This process hinges on a key concept: the in-order successor.

So, picture this: you've got a node with two children. What happens next? The question prompts us to consider four possible actions.

A. Replace it with the left child node? Not quite! That would throw the whole tree structure out of whack, wouldn’t it?

Now, B. Move the successor's child up to the root node? Ding, ding! We have a winner! This approach is essential because it keeps the properties of a binary search tree intact.

But let’s backtrack a bit. Just what is the in-order successor? Great question! The in-order successor refers to the smallest value node that resides in the right subtree of the node you want to delete. So, why do we prefer this method over others? It’s all about maintaining the integrity of the BST. When we replace the node with its in-order successor, it will have, at most, one child—making it a clean swap. This way, we can reconnect the remaining nodes without any fuss.

Consider the alternative options. C. Delete the node and leave a null? That’s like trying to fit a piece of jigsaw puzzle where there’s a sizable gap—just doesn’t belong. It leads to unsightly gaps and disrupts the overall balance.

Then there's D. Move the predecessor's child up to the root node. While this is a viable strategy, the focus of the question is on the successor.

Let’s visualize this with a simple example. Imagine you have a tree with numbers. If you wanted to remove the number 5, and it has both left and right children (like 3 and 7, respectively), you’d seek the in-order successor. If 6 is the next smallest number (present in the right subtree), you’ll put 6 in 5’s place and keep the tree organized.

Removing a node from a tree may come with its challenges, but it’s an essential skill, especially when you’re pursuing a degree in computer science like at Western Governors University. As you prepare for the ICSC2100 C949 exam, mastering this concept will not only boost your confidence but ensure that you’re well-equipped for practical programming challenges as well.

In summation, always lean toward moving the in-order successor’s child up when you're faced with the task of removing a node with two children from a BST. It's a strategic move that upholds the structure and properties of the tree, keeping everything neatly in order. And remember, understanding these concepts doesn't just help with exams but also fortifies your foundation in data structures and algorithms, crucial tools in your software development toolkit.