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

# Solution Notebook¶

## Constraints¶

• If this is called on a None input or a single node, should we raise an exception?
• Yes
• None -> TypeError
• Single node -> ValueError
• Can we assume we already have a Node class with an insert method?
• Yes
• Can we assume this fits memory?
• Yes

## Test Cases¶

• None or single node -> Exception
Input:
_10_
_/    \_
5        15
/ \       / \
3   8     12  20
/     \         \
2       4        30

Output: 20

Input:
10
/
5
/ \
3   7
Output: 7


## Algorithm¶

If there is no right node, the second largest is the right most left subtree:

10
/
5
/ \
3   7

If there is a right node and the right node has children, recurse to that right child:

_10_
_/    \_
5        15
/ \       / \
3   8     12  20
/     \         \
2       4        30

Eventually we'll get to the following scenario:

20
\
30

If the right node has no children, the second largest is the current node.



Complexity:

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

## Code¶

In [1]:
%run ../bst/bst.py

In [2]:
class Solution(Bst):

def _find_second_largest(self, node):
if node.right is not None:
if node.right.left is not None or node.right.right is not None:
return self._find_second_largest(node.right)
else:
return node
else:
return self._find_right_most_node(node.left)

def _find_right_most_node(self, node):
if node.right is not None:
return self._find_right_most_node(node.right)
else:
return node

def find_second_largest(self):
if self.root is None:
raise TypeError('root cannot be None')
if self.root.right is None and self.root.left is None:
raise ValueError('root must have at least one child')
return self._find_second_largest(self.root)


## Unit Test¶

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

class TestBstSecondLargest(unittest.TestCase):

def test_bst_second_largest(self):
bst = Solution(None)
self.assertRaises(TypeError, bst.find_second_largest)
root = Node(10)
bst = Solution(root)
node5 = bst.insert(5)
node15 = bst.insert(15)
node3 = bst.insert(3)
node8 = bst.insert(8)
node12 = bst.insert(12)
node20 = bst.insert(20)
node2 = bst.insert(2)
node4 = bst.insert(4)
node30 = bst.insert(30)
self.assertEqual(bst.find_second_largest(), node20)
root = Node(10)
bst = Solution(root)
node5 = bst.insert(5)
node3 = bst.insert(3)
node7 = bst.insert(7)
self.assertEqual(bst.find_second_largest(), node7)
print('Success: test_bst_second_largest')

def main():
test = TestBstSecondLargest()
test.test_bst_second_largest()

if __name__ == '__main__':
main()

Overwriting test_bst_second_largest.py

In [4]:
%run -i test_bst_second_largest.py

Success: test_bst_second_largest