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import unittest
################################################################################
# Implementation
################################################################################
# is_leaf :: Node(a) -> Boolean
def is_leaf(node):
return not node.left and not node.right
# is_binary_search_tree :: Node(Integer) -> Set(Int) -> Set(Int) -> Boolean
def is_binary_search_tree_a(node, la=set(), ra=set()):
"""My first solution for this problem."""
for x in la:
if not node.value < x:
return False
for x in ra:
if not node.value > x:
return False
if is_leaf(node):
return True
elif not node.left:
return is_binary_search_tree(
node.right,
la=la,
ra=ra ^ {node.value},
)
elif not node.right:
return is_binary_search_tree(node.left, la=la ^ {node.value}, ra=ra)
else:
return all([
is_binary_search_tree(node.left, la=la ^ {node.value}, ra=ra),
is_binary_search_tree(node.right, la=la, ra=ra ^ {node.value})
])
# is_binary_search_tree :: Node(Int) -> Maybe(Int) -> Maybe(Int) -> Boolean
def is_binary_search_tree(node, lb=None, ub=None):
if lb:
if node.value < lb:
return False
if ub:
if node.value > ub:
return False
if is_leaf(node):
return True
elif not node.right:
return is_binary_search_tree(node.left, lb=lb, ub=node.value)
elif not node.left:
return is_binary_search_tree(node.right, lb=node.value, ub=ub)
else:
return is_binary_search_tree(
node.left, lb=lb, ub=node.value) and is_binary_search_tree(
node.right, lb=node.value, ub=ub)
################################################################################
# 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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