naive cake thief

Author: pwgraham91

cake_thief.py

@@ -0,0 +1,108 @@
+"""
+Write a function max_duffel_bag_value() that takes a list of cake type tuples and a weight capacity, and returns the maximum monetary value the duffel bag can hold.
+cake_tuples = [(7, 160), (3, 90), (2, 15)]
+capacity    = 20
+
+# Returns 555 (6 of the middle type of cake and 1 of the last type of cake)
+max_duffel_bag_value(cake_tuples, capacity)
+"""
+import unittest
+
+
+def find_best_value_cake(cake_tuples, max_capacity):
+    best_value_cake = None
+    best_ratio = None
+
+    for cake in cake_tuples:
+        if cake[0] > max_capacity:
+            continue
+
+        if cake[1] == 0:
+            # don't consider cakes without value
+            continue
+        cake_ratio_value = float(cake[1] / cake[0])
+
+        if best_value_cake is None:
+            best_value_cake = cake
+            best_ratio = cake_ratio_value
+        elif cake_ratio_value > best_ratio:
+            best_value_cake = cake
+            best_ratio = cake_ratio_value
+        elif cake_ratio_value == best_ratio and max_capacity % cake[0] == 0:
+            # only replace the cake if it's lighter (so we can fit more cakes!)
+            best_value_cake = cake
+            best_ratio = cake_ratio_value
+
+    return best_value_cake
+
+
+def max_duffel_bag_value(cake_tuples, capacity):
+    """ time complexity: n + cn where n is the number of cakes and c is capacity
+        space complexity: 1
+    """
+    status = {
+        'total_value': 0,
+        'capacity': capacity
+    }
+
+    if capacity == 0:
+        return 0
+
+    while True:
+        cake = find_best_value_cake(cake_tuples, status['capacity'])
+        if not cake:
+            return status['total_value']
+
+        if cake[0] <= status['capacity']:
+            status['total_value'] += cake[1]
+            status['capacity'] -= cake[0]
+
+
+class Test(unittest.TestCase):
+    def test_base_case(self):
+        actual = max_duffel_bag_value([(7, 160), (3, 90), (2, 15)], 20)
+        expected = 555
+        self.assertEqual(actual, expected)
+
+    def test_one_cake(self):
+        actual = max_duffel_bag_value([(2, 1)], 9)
+        expected = 4
+        self.assertEqual(actual, expected)
+
+    def test_two_cakes(self):
+        actual = max_duffel_bag_value([(4, 4), (5, 5)], 9)
+        expected = 9
+        self.assertEqual(actual, expected)
+
+    def test_two_cakes_ten(self):
+        actual = max_duffel_bag_value([(4, 4), (5, 5)], 10)
+        expected = 10
+        self.assertEqual(actual, expected)
+
+    def test_only_take_less_valuable_cake(self):
+        actual = max_duffel_bag_value([(4, 4), (5, 5)], 12)
+        expected = 12
+        self.assertEqual(actual, expected)
+
+    def test_lots_of_cakes(self):
+        actual = max_duffel_bag_value([(2, 3), (3, 6), (5, 1), (6, 1), (7, 1), (8, 1)], 7)
+        expected = 12
+        self.assertEqual(actual, expected)
+
+    def test_value_to_weight_ratio_is_not_optimal(self):
+        actual = max_duffel_bag_value([(51, 52), (50, 50)], 100)
+        expected = 100
+        self.assertEqual(actual, expected)
+
+    def test_zero_capacity(self):
+        actual = max_duffel_bag_value([(1, 2)], 0)
+        expected = 0
+        self.assertEqual(actual, expected)
+
+    def test_cake_with_zero_value_and_weight(self):
+        actual = max_duffel_bag_value([(0, 0), (2, 1)], 7)
+        expected = 3
+        self.assertEqual(actual, expected)
+
+
+unittest.main(verbosity=2)