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

Challenge Notebook

Problem: Given a knapsack with a total weight capacity and a list of items with weight w(i) and value v(i), determine which items to select to maximize total value.

Constraints

  • Can we replace the items once they are placed in the knapsack?
    • No, this is the 0/1 knapsack problem
  • Can we split an item?
    • No
  • Can we get an input item with weight of 0 or value of 0?
    • No
  • Can we assume the inputs are valid?
    • No
  • Are the inputs in sorted order by val/weight?
    • Yes, if not we'd need to sort them first
  • Can we assume this fits memory?
    • Yes

Test Cases

  • items or total weight is None -> Exception
  • items or total weight is 0 -> 0
  • General case
total_weight = 8
items
  v | w
  0 | 0
a 2 | 2
b 4 | 2
c 6 | 4
d 9 | 5

max value = 13
items
  v | w
b 4 | 2
d 9 | 5 

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 Item(object):

    def __init__(self, label, value, weight):
        self.label = label
        self.value = value
        self.weight = weight

    def __repr__(self):
        return self.label + ' v:' + str(self.value) + ' w:' + str(self.weight)
In [ ]:
class Knapsack(object):

    def fill_knapsack(self, input_items, total_weight):
        # TODO: Implement me
        pass

Unit Test

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

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


class TestKnapsack(unittest.TestCase):

    def test_knapsack_bottom_up(self):
        knapsack = Knapsack()
        self.assertRaises(TypeError, knapsack.fill_knapsack, None, None)
        self.assertEqual(knapsack.fill_knapsack(0, 0), 0)
        items = []
        items.append(Item(label='a', value=2, weight=2))
        items.append(Item(label='b', value=4, weight=2))
        items.append(Item(label='c', value=6, weight=4))
        items.append(Item(label='d', value=9, weight=5))
        total_weight = 8
        expected_value = 13
        results = knapsack.fill_knapsack(items, total_weight)
        self.assertEqual(results[0].label, 'd')
        self.assertEqual(results[1].label, 'b')
        total_value = 0
        for item in results:
            total_value += item.value
        self.assertEqual(total_value, expected_value)
        print('Success: test_knapsack_bottom_up')

    def test_knapsack_top_down(self):
        knapsack = KnapsackTopDown()
        self.assertRaises(TypeError, knapsack.fill_knapsack, None, None)
        self.assertEqual(knapsack.fill_knapsack(0, 0), 0)
        items = []
        items.append(Item(label='a', value=2, weight=2))
        items.append(Item(label='b', value=4, weight=2))
        items.append(Item(label='c', value=6, weight=4))
        items.append(Item(label='d', value=9, weight=5))
        total_weight = 8
        expected_value = 13
        self.assertEqual(knapsack.fill_knapsack(items, total_weight), expected_value)
        print('Success: test_knapsack_top_down')

def main():
    test = TestKnapsack()
    test.test_knapsack_bottom_up()
    test.test_knapsack_top_down()


if __name__ == '__main__':
    main()

Solution Notebook

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