A simple check between left and right nodes will not suffice. Think of what happens in a deeper tree and the criteria numbers at the bottom must fulfill.

A simple check of the left and right child node will not suffice for this. Take a look at this binary tree:



Because 7 is less than 9, a simple localized check between left and right nodes would not provide the correct answer. Instead we keep track of the minimum and maximum value a node can be at any point in the tree.

isBST(Node root)
    return isBSTHelper(root, INTEGER_MIN, INTEGER_MAX)


isBSTHelper(Node n, int min, int max)
    if (n == null)
       return true;

    if (n.data > min && n.data < max)
       return isBSTHelper(n.left, min, n.data) && isBSTHelper(n.right, n.data, max);

    return false;