import unittest
from collections import deque


# is_balanced :: Node(a) -> Bool
def is_balanced(node):
    q = deque()
    q.append((0, node))
    mn, mx = None, None

    while q:
        depth, node = q.popleft()
        # Current node is a leaf node
        if not node.left and not node.right:
            mx = depth if mx is None else max(mx, depth)
            mn = depth if mn is None else min(mn, depth)
            if mx - mn > 1:
                return False
        if node.left:
            q.append((depth + 1, node.left))
        if node.right:
            q.append((depth + 1, node.right))

    return mx - mn <= 1


# 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)