Binary Search Tree Validation

So, I’ve been thinking about how to check if a binary tree is a valid BST. Here’s how I’d go about it!

Key Rules of a BST

• Left subtree values should be less than the current node.
• Right subtree values should be greater than the current node.

Approach

I think using a recursive function would be a good way to tackle this. The main idea is to traverse the tree and check if the nodes follow the BST rules. We can create a helper function that takes parameters like the current node and the allowable range (minimum and maximum).

Recursive Function

The function might look something like this:

    function isBST(node, min, max) {
        if (node == null) return true; // An empty tree is a valid BST
        if (node.value <= min || node.value >= max) return false; // Violation of BST rules
        
        // Recursively check the left and right subtree with updated boundaries
        return isBST(node.left, min, node.value) && isBST(node.right, node.value, max);
    }
    

How It Works

Basically, I start with the whole range of values (like negative infinity to positive infinity). As I go deeper into the tree, I adjust the boundaries based on the current node’s value. This way, I ensure all the left descendants are less and all the right descendants are greater.

Edge Cases

Now, talking about edge cases:

• Empty Tree: It’s valid because there are no nodes to break the rules.
• Duplicate Values: I’d have to decide—if duplicates are allowed in the BST because typically they are not. So, my check might need to ensure each value is unique.
• Invalid Trees: If a node doesn’t follow BST properties with its children, the function should catch it and return false.

Example Trees

Here are a couple of examples:

• Valid BST:

                 10
                /  \
               5    15
              / \     \
             3   7     20
              

• Invalid BST:

                 10
                /  \
               5    15
              / \     \
             3   12    20
              

  – Here, 12 is wrong because it’s in the right subtree of 10 but it’s less than 10.

That’s how I’d approach this problem! It feels like a fun challenge to work with trees! What do you think?