Merge pull request keon#87 from karpinski/knapsack

Adding an implementation for the knapsack problem.

Author: ankit167

README.md

@@ -60,6 +60,7 @@ Minimal and clean example implementations of data structures and algorithms in P
     - [climbing_stairs](dp/climbing_stairs.py)
     - [combination_sum](dp/combination_sum.py)
     - [house_robber](dp/house_robber.py)
+    - [knapsack](dp/knapsack.py)
     - [longest_increasing](dp/longest_increasing.py)
     - [max_product_subarray](dp/max_product_subarray.py)
     - [max_subarray](dp/max_subarray.py)

dp/knapsack.py

@@ -0,0 +1,38 @@
+"""
+Given the capacity of the knapsack and items specified by weights and values,
+return the maximum summarized value of the items that can be fit in the
+knapsack.
+
+Example:
+capacity = 5, items(value, weight) = [(60, 5), (50, 3), (70, 4), (30, 2)]
+result = 80 (items valued 50 and 30 can both be fit in the knapsack)
+
+The time complexity is O(n * m) and the space complexity is O(m), where n is
+the total number of items and m is the knapsack's capacity.
+"""
+
+
+class Item(object):
+
+    def __init__(self, value, weight):
+        self.value = value
+        self.weight = weight
+
+
+def get_maximum_value(items, capacity):
+    dp = [0] * (capacity + 1)
+    for item in items:
+        dp_tmp = [total_value for total_value in dp]
+        for current_weight in range(capacity + 1):
+            total_weight = current_weight + item.weight
+            if total_weight <= capacity:
+                dp_tmp[total_weight] = max(dp_tmp[total_weight],
+                                           dp[current_weight] + item.value)
+        dp = dp_tmp
+    return max(dp)
+
+
+print(get_maximum_value([Item(60, 10), Item(100, 20), Item(120, 30)],
+                        50))
+print(get_maximum_value([Item(60, 5), Item(50, 3), Item(70, 4), Item(30, 2)],
+                        5))