多重背包

一、思路

二、代码

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#include <bits/stdc++.h>
using namespace std;
const int N = 110;
int n, m;
int v[N], w[N], s[N];
int f[N][N];

int main() {
	cin >> n >> m;
	for (int i = 1; i <= n; i++) cin >> v[i] >> w[i] >> s[i];
	
	for (int i = 1; i <= n; i++) 
		for (int j = 0; j <= m; j++) 
			for (int k = 0; k <= s[i] && k * v[i] <= j; k++) 
				f[i][j] = max(f[i][j], f[i - 1][j - k * v[i]] + k * w[i]);
	
	cout << f[n][m] << endl;
	return 0;	
}

三、优化思路

四、优化代码

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#include <bits/stdc++.h>
using namespace std;
const int N = 12010, M = 2010;
int n, m;
int v[N], w[N];
int f[M];

int main() {
    cin >> n >> m;
    int cnt = 0;
    for (int i = 1; i <= n; i++) {
        int a, b, s;
        cin >> a >> b >> s;
        int k = 1;
        while (k <= s) {
            cnt++;
            v[cnt] = a * k;
            w[cnt] = b * k;
            s -= k;
            k *= 2;
        }
        if (s > 0) {
            cnt++;
            v[cnt] = a * s;
            w[cnt] = b * s;
        }
    }
    n = cnt;
    for (int i = 1; i <= n; i++)
        for (int j = m; j >= v[i]; j--) 
            f[j] = max(f[j], f[j - v[i]] + w[i]);
    cout << f[m] << endl;
    return 0;
}