This notebook was prepared by Donne Martin. Source and license info is on GitHub.

Solution Notebook

Problem: Check if a binary tree is balanced.

Constraints

  • Is a balanced tree one where the heights of two sub trees of any node doesn't differ by more than 1?
    • Yes
  • If this is called on a None input, should we raise an exception?
    • Yes
  • Can we assume we already have a Node class with an insert method?
    • Yes
  • Can we assume this fits memory?
    • Yes

Test Cases

  • None -> No
  • 1 -> Yes
  • 5, 3, 8, 1, 4 -> Yes
  • 5, 3, 8, 9, 10 -> No

Algorithm

The algorithm will be similar to where we get the height of a tree as seen in here.

However, we could check whether the tree is balanced while also checking for the heights.

  • Base case: If the root is None, return 0
  • Recursively check whether the left sub tree is balanced, and get its height left_height
  • Recursively check whether the right sub tree is balanced, and get its height right_height
  • Compare left_height and right_height
  • Return 1 + max(left_height, right_height)

Complexity:

  • Time: O(n)
  • Space: O(h), where h is the height of the tree

Code

In [1]:
%run ../bst/bst.py
In [2]:
class BstBalance(Bst):

    def _check_balance(self, node):
        if node is None:
            return 0
        left_height = self._check_balance(node.left)
        if left_height == -1:
            return -1
        right_height = self._check_balance(node.right)
        if right_height == -1:
            return -1
        diff = abs(left_height - right_height)
        if diff > 1:
            return -1
        return 1 + max(left_height, right_height)

    def check_balance(self):
        if self.root is None:
            raise TypeError('root cannot be None')
        height = self._check_balance(self.root)
        return height != -1

Unit Test

In [3]:
%%writefile test_check_balance.py
import unittest


class TestCheckBalance(unittest.TestCase):

    def test_check_balance_empty(self):
        bst = BstBalance(None)
        bst.check_balance()

    def test_check_balance(self):
        bst = BstBalance(Node(5))
        self.assertEqual(bst.check_balance(), True)

        bst.insert(3)
        bst.insert(8)
        bst.insert(1)
        bst.insert(4)
        self.assertEqual(bst.check_balance(), True)

        bst = BstBalance(Node(5))
        bst.insert(3)
        bst.insert(8)
        bst.insert(9)
        bst.insert(10)
        self.assertEqual(bst.check_balance(), False)

        bst = BstBalance(Node(3))
        bst.insert(2)
        bst.insert(1)
        bst.insert(5)
        bst.insert(4)
        bst.insert(6)
        bst.insert(7)
        self.assertEqual(bst.check_balance(), True)

        print('Success: test_check_balance')


def main():
    test = TestCheckBalance()
    test.assertRaises(TypeError, test.test_check_balance_empty)
    test.test_check_balance()


if __name__ == '__main__':
    main()
Overwriting test_check_balance.py
In [4]:
%run -i test_check_balance.py
Success: test_check_balance