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

# Solution Notebook¶

## Constraints¶

• If there is no successor, do we return None?
• Yes
• If the input is None, should we throw an exception?
• Yes
• Can we assume we already have a Node class that keeps track of parents?
• Yes
• Can we assume this fits memory?
• Yes

## Test Cases¶

          _5_
/     \
3       8
/ \    /   \
2   4  6    12
/        \   / \
1          7 10  15
/
9

In: None  Out: Exception
In: 4     Out: 5
In: 5     Out: 6
In: 8     Out: 9
In: 15    Out: None


## Algorithm¶

• If the node has a right subtree, return the left-most node in the right subtree
• Else, go up until you find a node that is its parent's left node
• If you get to the root (ie node.parent is None), return None
• The original input node must be the largest in the tree
• Else, return the parent

Complexity:

• Time: O(h), where h is the height of the tree
• Space: O(h), where h is the recursion depth (tree height), or O(1) if using an iterative approach

## Code¶

In [1]:
%run ../bst/bst.py

In [2]:
class BstSuccessor(object):

def get_next(self, node):
if node is None:
raise TypeError('node cannot be None')
if node.right is not None:
return self._left_most(node.right)
else:
return self._next_ancestor(node)

def _left_most(self, node):
if node.left is not None:
return self._left_most(node.left)
else:
return node.data

def _next_ancestor(self, node):
if node.parent is not None:
if node.parent.data > node.data:
return node.parent.data
else:
return self._next_ancestor(node.parent)
# We reached the root, the original input node
# must be the largest element in the tree.
return None


## Unit Test¶

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

class TestBstSuccessor(unittest.TestCase):

def test_bst_successor_empty(self):
bst_successor = BstSuccessor()
bst_successor.get_next(None)

def test_bst_successor(self):
nodes = {}
node = Node(5)
nodes[5] = node
bst = Bst(nodes[5])
nodes[3] = bst.insert(3)
nodes[8] = bst.insert(8)
nodes[2] = bst.insert(2)
nodes[4] = bst.insert(4)
nodes[6] = bst.insert(6)
nodes[12] = bst.insert(12)
nodes[1] = bst.insert(1)
nodes[7] = bst.insert(7)
nodes[10] = bst.insert(10)
nodes[15] = bst.insert(15)
nodes[9] = bst.insert(9)

bst_successor = BstSuccessor()
self.assertEqual(bst_successor.get_next(nodes[4]), 5)
self.assertEqual(bst_successor.get_next(nodes[5]), 6)
self.assertEqual(bst_successor.get_next(nodes[8]), 9)
self.assertEqual(bst_successor.get_next(nodes[15]), None)

print('Success: test_bst_successor')

def main():
test = TestBstSuccessor()
test.test_bst_successor()
test.assertRaises(TypeError, test.test_bst_successor_empty)

if __name__ == '__main__':
main()

Overwriting test_bst_successor.py

In [4]:
%run -i test_bst_successor.py

Success: test_bst_successor