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

- Is this a binary search tree?
- No

- Can we assume the two nodes are in the tree?
- No

- Can we assume this fits memory?
- Yes

_10_ / \ 5 9 / \ / \ 12 3 18 20 / \ / 1 8 40

- 0, 5 -> None
- 5, 0 -> None
- 1, 8 -> 3
- 12, 8 -> 5
- 12, 40 -> 10
- 9, 20 -> 9
- 3, 5 -> 5

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.

In [ ]:

```
class Node(object):
def __init__(self, key, left=None, right=None):
self.key = key
self.left = left
self.right = right
def __repr__(self):
return str(self.key)
```

In [ ]:

```
class BinaryTree(object):
def lca(self, root, node1, node2):
# TODO: Implement me
pass
```

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

In [ ]:

```
# %load test_lca.py
import unittest
class TestLowestCommonAncestor(unittest.TestCase):
def test_lca(self):
node10 = Node(10)
node5 = Node(5)
node12 = Node(12)
node3 = Node(3)
node1 = Node(1)
node8 = Node(8)
node9 = Node(9)
node18 = Node(18)
node20 = Node(20)
node40 = Node(40)
node3.left = node1
node3.right = node8
node5.left = node12
node5.right = node3
node20.left = node40
node9.left = node18
node9.right = node20
node10.left = node5
node10.right = node9
root = node10
node0 = Node(0)
binary_tree = BinaryTree()
self.assertEqual(binary_tree.lca(root, node0, node5), None)
self.assertEqual(binary_tree.lca(root, node5, node0), None)
self.assertEqual(binary_tree.lca(root, node1, node8), node3)
self.assertEqual(binary_tree.lca(root, node12, node8), node5)
self.assertEqual(binary_tree.lca(root, node12, node40), node10)
self.assertEqual(binary_tree.lca(root, node9, node20), node9)
self.assertEqual(binary_tree.lca(root, node3, node5), node5)
print('Success: test_lca')
def main():
test = TestLowestCommonAncestor()
test.test_lca()
if __name__ == '__main__':
main()
```

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