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

Challenge Notebook

Problem: Given a list of 2x2 matrices, minimize the cost of matrix multiplication.

Constraints

  • Do we just want to calculate the cost and not list the actual order of operations?
    • Yes
  • Can we assume the inputs are valid?
    • No
  • Can we assume this fits memory?
    • Yes

Test Cases

  • None -> Exception
  • [] -> 0
  • [Matrix(2, 3), Matrix(3, 6), Matrix(6, 4), Matrix(4, 5)] -> 124

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 Matrix(object):

    def __init__(self, first, second):
        self.first = first
        self.second = second
In [ ]:
class MatrixMultiplicationCost(object):

    def find_min_cost(self, matrices):
    # TODO: Implement me
    pass

Unit Test

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

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


class TestMatrixMultiplicationCost(unittest.TestCase):

    def test_find_min_cost(self):
        matrix_mult_cost = MatrixMultiplicationCost()
        self.assertRaises(TypeError, matrix_mult_cost.find_min_cost, None)
        self.assertEqual(matrix_mult_cost.find_min_cost([]), 0)
        matrices = [Matrix(2, 3),
                    Matrix(3, 6),
                    Matrix(6, 4),
                    Matrix(4, 5)]
        expected_cost = 124
        self.assertEqual(matrix_mult_cost.find_min_cost(matrices), expected_cost)
        print('Success: test_find_min_cost')


def main():
    test = TestMatrixMultiplicationCost()
    test.test_find_min_cost()


if __name__ == '__main__':
    main()

Solution Notebook

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