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

Solution Notebook¶

Problem: Implement the Towers of Hanoi with 3 towers and N disks.¶

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 [1]:

%run ../../stacks_queues/stack/stack.py

In [2]:

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 [3]:

%%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 [4]:

%run -i test_hanoi.py

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