knapsack problem linear programming code example
Example 1: greedy knapsack
def greedy_knapsack(values,weights,capacity):
n = len(values)
def score(i) : return values[i]/weights[i]
items = sorted(range(n) , key=score , reverse = True)
sel, value,weight = [],0,0
for i in items:
if weight +weights[i] <= capacity:
sel += [i]
weight += weights[i]
value += values [i]
return sel, value, weight
weights = [4,9,10,20,2,1]
values = [400,1800,3500,4000,1000,200]
capacity = 20
print(greedy_knapsack(values,weights,capacity))
Example 2: knapsack problem
// memory efficient and iterative approach to the knapsack problem
using namespace std;
// n is the number of items
// w is the knapsack's capacity
int n, w;
int main() {
/*
input format:
n w
value_1 cost_1
value_2 cost_2
.
.
value_n cost_n
*/
cin >> n >> w;
vector<long long> dp(w + 1, 0);
for (int i = 0; i < n; ++i) {
int value, cost;
cin >> value >> cost;
for (int j = w; j >= cost; --j)
dp[j] = max(dp[j], value + dp[j - cost]);
}
// the answer is dp[w]
cout << dp[w];
}