# Closest Point in BST

## Divide and Conquer on Trees: Closest Point in BST

When it comes to tree traversal and manipulation, the divide and conquer algorithm is a powerful technique. In this tutorial, we will explore how to apply the divide and conquer algorithm to find the closest point to a given target value in a binary search tree (BST).

### What is the Divide and Conquer Algorithm?

The divide and conquer algorithm is a problem-solving approach that involves breaking down a complex problem into smaller, more manageable subproblems. Each subproblem is solved independently, and the solutions are combined to solve the original problem. This technique is particularly useful for solving problems that can be divided into similar yet smaller subproblems.

### Closest Point in BST Problem

The closest point in BST problem involves finding the closest value to a given target value in a binary search tree. A binary search tree is a tree-like data structure where each node has a value and two child nodes, with the left child node having a smaller value and the right child node having a larger value.

To solve this problem, we need to traverse the BST, comparing each node's value to the target value and updating the closest value accordingly. However, since a BST can have values on either side of the target value, we need to consider both the left and right subtrees.

### Implementation Steps

- Start by initializing the closest value to the root node's value.
- If the target value is equal to the root node's value, we have found the closest point. Return the target value.
- If the target value is less than the current node's value, move to the left subtree.
- If the target value is greater than the current node's value, move to the right subtree.
- Repeat steps 2-4 until we reach a leaf node or find the closest point.
- Compare the difference between the current node's value and the target value with the difference between the current closest value and the target value. Update the closest value if necessary.
- Recursively traverse the remaining subtree(s), starting from the closest value found so far.
- Finally, return the closest value.

Let's check out the code implementation in Python:

```
class TreeNode:
def __init__(self, val=0, left=None, right=None):
self.val = val
self.left = left
self.right = right
def find_closest_value(root, target):
closest = root.val
while root:
if abs(root.val - target) < abs(closest - target):
closest = root.val
if target == root.val:
return target
elif target < root.val:
root = root.left
else:
root = root.right
return closest
```

In the above code, we define a `TreeNode`

class to represent each node in the BST. We also define the `find_closest_value`

function that takes the root node and the target value as parameters.

### Example Usage

Let's consider a simple example to demonstrate the usage of our `find_closest_value`

function.

```
# Creating a binary search tree
root = TreeNode(4)
root.left = TreeNode(2)
root.right = TreeNode(5)
root.left.left = TreeNode(1)
root.left.right = TreeNode(3)
# Find the closest value to the target value of 3.714
target = 3.714
closest_value = find_closest_value(root, target)
print("Closest value:", closest_value)
```

Output:

```
Closest value: 4
```

In this example, we create a BST with five nodes, where the closest value to the target value of 3.714 is 4.

### Conclusion

In this tutorial, we explored the divide and conquer algorithm and its application to find the closest point in a binary search tree. We walked through the implementation steps and provided a code snippet in Python to solve the problem. By understanding and applying the divide and conquer algorithm, you will be equipped to tackle similar problems efficiently and effectively.

I hope you found this tutorial helpful and informative. Happy coding!

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