Add 'universe/' from commit '8ad51b24dd'

git-subtree-dir: universe
git-subtree-mainline: 15110e6de9
git-subtree-split: 8ad51b24dd

universe/data_structures_and_algorithms/knapsack-0-1.py

@@ -0,0 +1,38 @@
+import unittest
+from math import floor
+
+
+def knapify(xs, capacity=None):
+    assert capacity is not None
+    n = len(xs)
+    # For 0/1 Knapsack, we must use a table, since this will encode which values
+    # work for which items. This is cleaner than including a separate data
+    # structure to capture it.
+    maxes = [[0 for x in range(capacity + 1)] for x in range(n + 1)]
+
+    # Build table maxes[][] in bottom up manner
+    for row in range(n + 1):
+        for col in range(capacity + 1):
+            if row == 0 or col == 0:
+                maxes[row][col] = 0
+            elif xs[row - 1][0] <= col:
+                maxes[row][col] = max(
+                    xs[row - 1][1] + maxes[row - 1][col - xs[row - 1][0]],
+                    maxes[row - 1][col])
+            else:
+                maxes[row][col] = maxes[row - 1][col]
+
+    return maxes[-1][capacity]
+
+
+################################################################################
+# Tests
+################################################################################
+class Test(unittest.TestCase):
+    def test_one_cake(self):
+        actual = knapify([(3, 10), (2, 15), (7, 2), (12, 20)], capacity=12)
+        expected = None
+        self.assertEqual(actual, expected)
+
+
+unittest.main(verbosity=2)