Check whether Binary Tree is a Binary Search Tree

bst_check.py

# from HackerRank.com
""" Node is defined as
class node:
  def __init__(self, data):
      self.data = data
      self.left = None
      self.right = None
"""
def check_binary_search_tree_(root, lower_bound=None, upper_bound=None):
    if not root:
        return True
    if lower_bound is not None and root.data <= lower_bound:
        return False
    if upper_bound is not None and root.data >= upper_bound:
        return False
    if not check_binary_search_tree_(root.left, lower_bound, root.data):
        return False
    if not check_binary_search_tree_(root.right, root.data, upper_bound):
        return False
    if root.left and root.left.data >= root.data:
        return False
    if root.right and root.right.data <= root.data:
        return False
    return True