is_binary_tree.py

import unittest


def is_bst(root):
    """
    Given the root of a binary tree, return true if it is a binary search tree.
    """

    def is_bst_recursive(root, smallest, largest):

        if root is None:
            return True

        if largest is not None and root.data > largest:
            return False

        if smallest is not None and root.data < smallest:
            return False

        if not is_bst_recursive(root.left, smallest, root.data):
            return False

        if not is_bst_recursive(root.right, root.data, largest):
            return False

        return True

    return is_bst_recursive(root, smallest=None, largest=None)


class Node(object):
    def __init__(self, data, left=None, right=None):
        self.data = data
        self.left = left
        self.right = right


class Tests(unittest.TestCase):

    def create_bst_1(self):
        return Node(5, Node(3, Node(1), Node(9)), Node(6))

    def create_bst_2(self):
        return Node(5, Node(3, Node(1), Node(4)), Node(7, Node(6), Node(8)))

    def test_is_bst(self):
        self.assertFalse(is_bst(self.create_bst_1()))
        self.assertTrue(is_bst(self.create_bst_2()))


if __name__ == '__main__':
    unittest.main()