[AcWing 7] 混合背包问题

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点击查看代码

#include<iostream>

using namespace std;

const int N = 1e3 + 10;

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

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1. 三种背包模型
   0-1 背包可以看作是只有一件物品的多重背包
2. 多重背包二进制优化的另一种写法