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

Challenge Notebook

Problem: Determine whether you can win the Nim game given the remaining stones.

See the LeetCode problem page.

You are playing the following Nim Game with your friend: There is a heap of stones on the table, each time one of you take turns to remove 1 to 3 stones. The one who removes the last stone will be the winner. You will take the first turn to remove the stones.

Both of you are very clever and have optimal strategies for the game. Write a function to determine whether you can win the game given the number of stones in the heap.

For example, if there are 4 stones in the heap, then you will never win the game: no matter 1, 2, or 3 stones you remove, the last stone will always be removed by your friend.

Constraints

  • Is the input an int?
    • Yes
  • Is the output a boolean?
    • Yes
  • Can we assume the inputs are valid?
    • No
  • Can we assume this fits memory?
    • Yes

Test Cases

  • None -> TypeError
  • 1, 2, or 3 -> True
  • 4 -> False
  • 7 -> True
  • 40 -> False

Algorithm

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.

Code

In [ ]:
class Solution(object):

    def can_win_nim(self, num_stones_left):
        # TODO: Implement me
        pass

Unit Test

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

In [ ]:
# %load test_can_win_nim.py
import unittest


class TestSolution(unittest.TestCase):

    def test_can_win_nim(self):
        solution = Solution()
        self.assertRaises(TypeError, solution.can_win_nim, None)
        self.assertEqual(solution.can_win_nim(1), True)
        self.assertEqual(solution.can_win_nim(2), True)
        self.assertEqual(solution.can_win_nim(3), True)
        self.assertEqual(solution.can_win_nim(4), False)
        self.assertEqual(solution.can_win_nim(7), True)
        self.assertEqual(solution.can_win_nim(40), False)
        print('Success: test_can_win_nim')


def main():
    test = TestSolution()
    test.test_can_win_nim()


if __name__ == '__main__':
    main()

Solution Notebook

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