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

Solution Notebook

Problem: Determine the height of a tree.

Constraints

  • Is this a binary tree?
    • Yes
  • Can we assume we already have a Node class with an insert method?
    • Yes
  • Can we assume this fits memory?
    • Yes

Test Cases

  • 5 -> 1
  • 5, 2, 8, 1, 3 -> 3

Algorithm

We'll use a recursive algorithm.

  • If the current node is None, return 0
  • Else, return 1 + the maximum height of the left or right children

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 BstHeight(Bst):

    def height(self, node):
        if node is None:
            return 0
        return 1 + max(self.height(node.left),
                       self.height(node.right))

Unit Test

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


class TestHeight(unittest.TestCase):

    def test_height(self):
        bst = BstHeight(Node(5))
        self.assertEqual(bst.height(bst.root), 1)
        bst.insert(2)
        bst.insert(8)
        bst.insert(1)
        bst.insert(3)
        self.assertEqual(bst.height(bst.root), 3)

        print('Success: test_height')


def main():
    test = TestHeight()
    test.test_height()


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