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

# Solution Notebook¶

## 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