python/TangDou/KaoShi/多重背包_二进制优化.cpp

#include <bits/stdc++.h>

using namespace std;
const int N = 12010, M = 2010;

int n, m;
int v[N], w[N];
int f[M];

//多重背包的二进制优化
int main() {
    //优化输入
    ios::sync_with_stdio(false);
    cin >> n >> m;

    int cnt = 0;
    for (int i = 1; i <= n; i++) {
        int a, b, s;
        cin >> a >> b >> s;
        //二进制优化,能打包则打包之，1,2,4,8,16,...
        int k = 1;
        while (k <= s) {
            cnt++;
            v[cnt] = a * k;
            w[cnt] = b * k;
            s -= k;
            k *= 2;
        }
        //剩下的
        if (s > 0) {
            cnt++;
            v[cnt] = a * s;
            w[cnt] = b * s;
        }
    }
    n = cnt; //数量减少啦
    // 01背包
    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;
}