1 files changed, 145 insertions, 0 deletions
diff --git a/scratch/data_structures_and_algorithms/balanced-binary-tree.py b/scratch/data_structures_and_algorithms/balanced-binary-tree.py
new file mode 100644
index 000000000000..01fd965fd540
--- /dev/null
+++ b/scratch/data_structures_and_algorithms/balanced-binary-tree.py
@@ -0,0 +1,145 @@
+import unittest
+from itertools import combinations
+
+
+def balanced(xs):
+    """Return True if `xs` contains no two values that differ by more than
+    one."""
+    if len(xs) == 0 or len(xs) == 1:
+        return True
+    if len(xs) == 2:
+        return math.abs(xs[0] - xs[1]) <= 1
+    else:
+        pass
+
+
+def is_leaf(node):
+    return node.left is None and node.right is None
+
+
+def is_balanced(tree_root):
+    """Returns True if the difference between the depths of any two leaf nodes
+    does not exceed 1."""
+    depths = set()
+    populate_depths(tree_root, 0, depths)
+
+    # cartesian product - only the top half
+    for diff in set(abs(a - b) for a, b in combinations(depths, 2)):
+        if diff > 1:
+            return False
+
+    return True
+
+
+def populate_depths(node, depth, depths):
+    if is_leaf(node):
+        depths.add(depth)
+    else:
+        if node.left is not None:
+            populate_depths(node.left, depth + 1, depths)
+        if node.right is not None:
+            populate_depths(node.right, depth + 1, depths)
+
+
+################################################################################
+# 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_full_tree(self):
+        tree = Test.BinaryTreeNode(5)
+        left = tree.insert_left(8)
+        right = tree.insert_right(6)
+        left.insert_left(1)
+        left.insert_right(2)
+        right.insert_left(3)
+        right.insert_right(4)
+        result = is_balanced(tree)
+        self.assertTrue(result)
+
+    def test_both_leaves_at_the_same_depth(self):
+        tree = Test.BinaryTreeNode(3)
+        left = tree.insert_left(4)
+        right = tree.insert_right(2)
+        left.insert_left(1)
+        right.insert_right(9)
+        result = is_balanced(tree)
+        self.assertTrue(result)
+
+    def test_leaf_heights_differ_by_one(self):
+        tree = Test.BinaryTreeNode(6)
+        left = tree.insert_left(1)
+        right = tree.insert_right(0)
+        right.insert_right(7)
+        result = is_balanced(tree)
+        self.assertTrue(result)
+
+    def test_leaf_heights_differ_by_two(self):
+        tree = Test.BinaryTreeNode(6)
+        left = tree.insert_left(1)
+        right = tree.insert_right(0)
+        right_right = right.insert_right(7)
+        right_right.insert_right(8)
+        result = is_balanced(tree)
+        self.assertFalse(result)
+
+    def test_three_leaves_total(self):
+        tree = Test.BinaryTreeNode(1)
+        left = tree.insert_left(5)
+        right = tree.insert_right(9)
+        right.insert_left(8)
+        right.insert_right(5)
+        result = is_balanced(tree)
+        self.assertTrue(result)
+
+    def test_both_subtrees_superbalanced(self):
+        tree = Test.BinaryTreeNode(1)
+        left = tree.insert_left(5)
+        right = tree.insert_right(9)
+        right_left = right.insert_left(8)
+        right.insert_right(5)
+        right_left.insert_left(7)
+        result = is_balanced(tree)
+        self.assertFalse(result)
+
+    def test_both_subtrees_superbalanced_two(self):
+        tree = Test.BinaryTreeNode(1)
+        left = tree.insert_left(2)
+        right = tree.insert_right(4)
+        left.insert_left(3)
+        left_right = left.insert_right(7)
+        left_right.insert_right(8)
+        right_right = right.insert_right(5)
+        right_right_right = right_right.insert_right(6)
+        right_right_right.insert_right(9)
+        result = is_balanced(tree)
+        self.assertFalse(result)
+
+    def test_only_one_node(self):
+        tree = Test.BinaryTreeNode(1)
+        result = is_balanced(tree)
+        self.assertTrue(result)
+
+    def test_linked_list_tree(self):
+        tree = Test.BinaryTreeNode(1)
+        right = tree.insert_right(2)
+        right_right = right.insert_right(3)
+        right_right.insert_right(4)
+        result = is_balanced(tree)
+        self.assertTrue(result)
+
+
+unittest.main(verbosity=2)