How do you validate a binary search tree?

I read on here of an exercise in interviews known as validating a binary search tree.

How exactly does this work? What would one be looking for in validating a binary search tree? I have written a basic search tree, but never heard of this concept.

Solution 1:

Actually that is the mistake everybody does in an interview.

Leftchild must be checked against (minLimitof node,node.value)

Rightchild must be checked against (node.value,MaxLimit of node)

IsValidBST(root,-infinity,infinity);

bool IsValidBST(BinaryNode node, int MIN, int MAX) 
{
     if(node == null)
         return true;
     if(node.element > MIN 
         && node.element < MAX
         && IsValidBST(node.left,MIN,node.element)
         && IsValidBST(node.right,node.element,MAX))
         return true;
     else 
         return false;
}

Another solution (if space is not a constraint): Do an inorder traversal of the tree and store the node values in an array. If the array is in sorted order, its a valid BST otherwise not.

Solution 2:

"Validating" a binary search tree means that you check that it does indeed have all smaller items on the left and large items on the right. Essentially, it's a check to see if a binary tree is a binary search tree.