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

# Challenge Notebook¶

## 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.