Created
December 6, 2010 21:06
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Python implementation of classic Knapsack problem
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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) | |
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