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

# Solution Notebook¶

## Constraints¶

• Can we assume we already have a stack class that can be used for this problem?
• Yes
• Can we assume the inputs are valid?
• No
• Can we assume this fits memory?
• Yes

## Test Cases¶

• None tower(s) -> Exception
• 0 disks -> None
• 1 disk
• 2 or more disks

## Algorithm¶

• Create three stacks to represent each tower
• def hanoi(n, src, dest, buffer):
• If 0 disks return
• hanoi(n-1, src, buffer, dest)
• Move remaining element from src to dest
• hanoi(n-1, buffer, dest, src)

Complexity:

• Time: O(2^n)
• Space: O(m) where m is the number of recursion levels

## Code¶

In :
%run ../../stacks_queues/stack/stack.py

In :
class Hanoi(object):

def move_disks(self, num_disks, src, dest, buff):
if src is None or dest is None or buff is None:
raise TypeError('Cannot have a None input')
self._move_disks(num_disks, src, dest, buff)

def _move_disks(self, num_disks, src, dest, buff):
if num_disks == 0:
return
self.move_disks(num_disks - 1, src, buff, dest)
dest.push(src.pop())
self.move_disks(num_disks - 1, buff, dest, src)


## Unit Test¶

In :
%%writefile test_hanoi.py
import unittest

class TestHanoi(unittest.TestCase):

def test_hanoi(self):
hanoi = Hanoi()
num_disks = 3
src = Stack()
buff = Stack()
dest = Stack()

print('Test: None towers')
self.assertRaises(TypeError, hanoi.move_disks, num_disks, None, None, None)

print('Test: 0 disks')
hanoi.move_disks(num_disks, src, dest, buff)
self.assertEqual(dest.pop(), None)

print('Test: 1 disk')
src.push(5)
hanoi.move_disks(num_disks, src, dest, buff)
self.assertEqual(dest.pop(), 5)

print('Test: 2 or more disks')
for disk_index in range(num_disks, -1, -1):
src.push(disk_index)
hanoi.move_disks(num_disks, src, dest, buff)
for disk_index in range(0, num_disks):
self.assertEqual(dest.pop(), disk_index)

print('Success: test_hanoi')

def main():
test = TestHanoi()
test.test_hanoi()

if __name__ == '__main__':
main()

Overwriting test_hanoi.py

In :
%run -i test_hanoi.py

Test: None towers
Test: 0 disks
Test: 1 disk
Test: 2 or more disks
Success: test_hanoi