Merge pull request #79 from bamsarts/knapsack-problem/python

implement knapsack problem in python

dynamic_programing/knapsack_problem/python/knapsack.py

@@ -0,0 +1,58 @@
+from sys import stdin
+from sys import stdout
+'''
+Knapsack Problem implementation
+
+Created on Dec 6, 2010
+@author: rohanbk
+'''
+capacity=10;
+num_of_items=6;
+total_weight=0;
+total_value=0;
+
+#Initialize backpack
+B=[[0]*(capacity+1) for i in range(num_of_items)];
+#Keep list will help determine which items to keep once we've solved the Knapsack problem
+keep=[[0]*(capacity+1) for i in range(num_of_items)];
+
+#Dictionary to store item numbers and corresponding weights
+#<Item number, weight>
+item_weight={0:4,1:2,2:3,3:1,4:7,5:10};
+#Dictionary to store item numbers and corresponding values
+#<Item number, value>
+item_value={0:6,1:4,2:5,3:3,4:9,5:7};
+
+total_weight=sum([value for value in item_weight.values()])
+total_value=sum([value for value in item_value.values()])
+
+#Solve Knapsack problem
+for k in range(num_of_items):
+    for w in range(capacity+1):
+        if(w>=item_weight[k]):
+            p1=B[k-1][w];
+            p2=B[k-1][w-item_weight[k]]+item_value[k];
+            if(p1>p2):
+                keep[k][w]=0;
+                B[k][w]=p1;
+            else:
+                keep[k][w]=1;
+                B[k][w]=p2;
+        else:
+            B[k][w]= B[k-1][w];
+            keep[k][w]=0;
+
+rem_capacity=capacity;
+items_to_take=[];
+valueofgoods=0;
+
+#Determine which items to keep and what their total value is       
+for k in range(num_of_items-1,-1,-1):
+    if(keep[k][rem_capacity]==1):
+        items_to_take.append(k);
+        rem_capacity=rem_capacity-item_weight[k];
+        valueofgoods+=item_value[k];
+print 'Total value of all goods: %s'%(total_value)
+print 'Goods to choose: %s'%(items_to_take)
+print 'Maximized Value of goods: %s'%(valueofgoods)
+print 'Opportunity cost: %s'%(total_value-valueofgoods)