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

Challenge Notebook

Problem: Create a binary search tree with minimal height from a sorted array.

Constraints

  • Is the array in increasing order?
    • Yes
  • Are the array elements unique?
    • Yes
  • Can we assume we already have a Node class with an insert method?
    • Yes
  • Can we assume this fits memory?
    • Yes

Test Cases

  • 0, 1, 2, 3, 4, 5, 6 -> height 3
  • 0, 1, 2, 3, 4, 5, 6, 7 -> height 4

Algorithm

Refer to the Solution Notebook. If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start.

Code

In [ ]:
%run ../bst/bst.py
%load ../bst/bst.py
In [ ]:
class MinBst(object):

    def create_min_bst(self, array):
    # TODO: Implement me

Unit Test

The following unit test is expected to fail until you solve the challenge.

In [ ]:
# %load test_bst_min.py
import unittest


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


class TestBstMin(unittest.TestCase):

    def test_bst_min(self):
        min_bst = MinBst()
        array = [0, 1, 2, 3, 4, 5, 6]
        root = min_bst.create_min_bst(array)
        self.assertEqual(height(root), 3)

        min_bst = MinBst()
        array = [0, 1, 2, 3, 4, 5, 6, 7]
        root = min_bst.create_min_bst(array)
        self.assertEqual(height(root), 4)

        print('Success: test_bst_min')


def main():
    test = TestBstMin()
    test.test_bst_min()


if __name__ == '__main__':
    main()

Solution Notebook

Review the Solution Notebook for a discussion on algorithms and code solutions.