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)