和为t的子集的个数

给一个正整数序列，再给一个t值，求其中和为t的子集的个数

#include<iostream>
#include<map>

using namespace std;

const int N = 10010, M = 20;

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

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

空间优化

#include<iostream>
#include<map>

using namespace std;

const int N = 10010, M = 20;

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

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