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

Solution Notebook¶

Problem: Determine if a tree is a valid binary search tree.¶

Constraints¶

Can the tree have duplicates?
- Yes
If this is called on a None input, should we raise an exception?
- Yes
Can we assume we already have a Node class?
- Yes
Can we assume this fits in memory?
- Yes

Test Cases¶

None -> exception

Algorithm¶

We'll use a recursive solution that validates left <= current < right, passing down the min and max values as we do a depth-first traversal.

If the node is None, return True
If min is set and the node's value <= min, return False
if max is set and the node's value > max, return False
Recursively call the validate function on node.left, updating max
Recursively call the validate function on node.right, updating min

Complexity:

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

Code¶

In [1]:

%run ../bst/bst.py

In [2]:

import sys


class BstValidate(Bst):

    def validate(self):
        if self.root is None:
            raise TypeError('No root node')
        return self._validate(self.root)

    def _validate(self, node, minimum=-sys.maxsize, maximum=sys.maxsize):
        if node is None:
            return True
        if node.data <= minimum or node.data > maximum:
            return False
        if not self._validate(node.left, minimum, node.data):
            return False
        if not self._validate(node.right, node.data, maximum):
            return False
        return True

Unit Test¶

In [3]:

%%writefile test_bst_validate.py
import unittest


class TestBstValidate(unittest.TestCase):

    def test_bst_validate_empty(self):
        bst = BstValidate(None)
        bst.validate()

    def test_bst_validate(self):
        bst = BstValidate(Node(5))
        bst.insert(8)
        bst.insert(5)
        bst.insert(6)
        bst.insert(4)
        bst.insert(7)
        self.assertEqual(bst.validate(), True)

        bst = BstValidate(Node(5))
        left = Node(5)
        right = Node(8)
        invalid = Node(20)
        bst.root.left = left
        bst.root.right = right
        bst.root.left.right = invalid
        self.assertEqual(bst.validate(), False)

        print('Success: test_bst_validate')


def main():
    test = TestBstValidate()
    test.assertRaises(TypeError, test.test_bst_validate_empty)
    test.test_bst_validate()


if __name__ == '__main__':
    main()

Overwriting test_bst_validate.py

In [4]:

%run -i test_bst_validate.py

Success: test_bst_validate