Finding the largest subtree in a BST

Question

Given a binary tree, I want to find out the largest subtree which is a BST in it.

Naive approach:

I have a naive approach in mind where I visit every node of

Answer 1

I would think you could avoid checking if every node is the root of a BST by working top down instead of bottom up. If a subtree is a BST it's going to be larger than any subtree in itself so you don't need to check inside a subtree if it has passed the isBST test. Then you just have isBST return the size of a valid tree and store that along with a pointer to the root of the subtree if you need to be able to find it again instead of just knowing how large the largest one is.

UPDATE:

Some of the code posted here to check if something is a BST are going to fail some cases since they're only checking the parent of a node.

Take for example:

       10
     /    \
   4      99
          /
         2

This is not a valid BST, (the 2 is out of position with regards to the 10) but if you don't send a min and max value down through the tree you will incorrectly verify it as valid. This pseudocode takes that into account.

main
{
    Verify(root, MIN_VALUE, MAX_VALUE)
}

boolean Verify(node , min, max)
{

 if(node == null)
   return true;

  if(node.value > min &&
     node.value < max &&
     Verify(node.leftchild, min, node.value) &&
     Verify(node.rightchild,node.value,max)
  {
      return true;
  }
  else
  {
      return false;
  }
}