[AcWing 278] 数字组合

---

点击查看代码

#include<iostream>

using namespace std;

const int N = 110, M = 10010;

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

int main()
{
	cin >> n >> m;
	for (int i = 1; i <= n; i ++)	cin >> v[i];
	f[0] = 1;
	for (int i = 1; i <= n; i ++)
		for (int j = m; j >= v[i]; j --)
			f[j] += f[j - v[i]];
	cout << f[m] << endl;
	return 0;
}

---

1. 状态表示
   \(f[i][j]\) 表示所有从前 \(i\) 个物品中选，且总体积是 \(j\) 的选法的个数
2. 状态计算
   \(f[i][j] = f[i - 1][j] + f[i - 1][j - v[i]]\)