1 files changed, 121 insertions, 0 deletions
diff --git a/data_structures_and_algorithms/bst-checker.py b/data_structures_and_algorithms/bst-checker.py
new file mode 100644
index 000000000000..689be97a8503
--- /dev/null
+++ b/data_structures_and_algorithms/bst-checker.py
@@ -0,0 +1,121 @@
+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)