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import unittest
from collections import deque
# While this function solves the problem, it uses O(n) space since we're storing
# all of the less-thans and greater-thans.
def is_binary_search_tree_first_attempt(root):
q = deque()
q.append((set(), set(), root))
while q:
lts, gts, node = q.popleft()
if not all([node.value < lt for lt in lts]):
return False
if not all([node.value > gt for gt in gts]):
return False
if node.left:
q.append((lts | {node.value}, gts, node.left))
if node.right:
q.append((lts, gts | {node.value}, node.right))
return True
# While I did not originally solve this problem this way, when I learned that I
# could condense the space of my solution's runtime, I wrote this.
def is_binary_search_tree(root):
q = deque()
q.append((None, None, root))
while q:
lt, gt, node = q.popleft()
if not lt is None and node.value >= lt:
return False
if not gt is None and node.value <= gt:
return False
if node.left:
q.append((node.value, gt, node.left))
if node.right:
q.append((lt, node.value, node.right))
return True
# Tests
class Test(unittest.TestCase):
class BinaryTreeNode(object):
def __init__(self, value):
self.value = value
self.left = None
self.right = None
def insert_left(self, value):
self.left = Test.BinaryTreeNode(value)
return self.left
def insert_right(self, value):
self.right = Test.BinaryTreeNode(value)
return self.right
def test_valid_full_tree(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(30)
right = tree.insert_right(70)
left.insert_left(10)
left.insert_right(40)
right.insert_left(60)
right.insert_right(80)
result = is_binary_search_tree(tree)
self.assertTrue(result)
def test_both_subtrees_valid(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(30)
right = tree.insert_right(80)
left.insert_left(20)
left.insert_right(60)
right.insert_left(70)
right.insert_right(90)
result = is_binary_search_tree(tree)
self.assertFalse(result)
def test_descending_linked_list(self):
tree = Test.BinaryTreeNode(50)
left = tree.insert_left(40)
left_left = left.insert_left(30)
left_left_left = left_left.insert_left(20)
left_left_left.insert_left(10)
result = is_binary_search_tree(tree)
self.assertTrue(result)
def test_out_of_order_linked_list(self):
tree = Test.BinaryTreeNode(50)
right = tree.insert_right(70)
right_right = right.insert_right(60)
right_right.insert_right(80)
result = is_binary_search_tree(tree)
self.assertFalse(result)
def test_one_node_tree(self):
tree = Test.BinaryTreeNode(50)
result = is_binary_search_tree(tree)
self.assertTrue(result)
unittest.main(verbosity=2)
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