dynamic programming 0/1 knapsack problem code example
Example 1: 0-1 knapsack problem dynamic programming using single array
int dp[MAXW];
int solve()
{
memset(dp, 0, sizeof(dp));
for(int i =1; i <= N; i++) {
for(int j = W; j >= 0; j--) {
dp[j] = (w[i] > j) ? dp[j]: max(dp[j], dp[j-w[i]] + v[i]);
}
}
return dp[W];
}
Example 2: knapsack problem using dynamic approach inc++
#include <iostream>
using namespace std;
int max(int x, int y) {
return (x > y) ? x : y;
}
int knapSack(int W, int w[], int v[], int n) {
int i, wt;
int K[n + 1][W + 1];
for (i = 0; i <= n; i++) {
for (wt = 0; wt <= W; wt++) {
if (i == 0 || wt == 0)
K[i][wt] = 0;
else if (w[i - 1] <= wt)
K[i][wt] = max(v[i - 1] + K[i - 1][wt - w[i - 1]], K[i - 1][wt]);
else
K[i][wt] = K[i - 1][wt];
}
}
return K[n][W];
}
int main() {
cout << "Enter the number of items in a Knapsack:";
int n, W;
cin >> n;
int v[n], w[n];
for (int i = 0; i < n; i++) {
cout << "Enter value and weight for item " << i << ":";
cin >> v[i];
cin >> w[i];
}
cout << "Enter the capacity of knapsack";
cin >> W;
cout << knapSack(W, w, v, n);
return 0;
}