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python/TangDou/KaoShi/多重背包_二进制优化.cpp

44 lines
956 B

2 years ago
#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;
}