算法一：动态二维数组

#include <iostream>

using namespace std;

const int N = 20010;

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

int main()
{
    cin >> m >> n;

    for(int i = 1; i <= n; i++)
        cin >> v[i];

    for(int i = 1; i <= n; i++)

        for(int j = 1; j <= m; j ++)
        {
            f[i][j] = f[i - 1][j]; // 不选i
            if(j >= v[i])
                f[i][j] = max(f[i][j], f[i - 1][j - v[i]] + v[i]); 选i
        }

    int res = 0;
    for(int i = 0; i <= m; i ++) res = max(f[n][i],res);
    cout << m - res;
    return 0;
}

优化：

#include <iostream>

using namespace std;

const int N = 20010;

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

int main()
{
    cin >> m >> n;

    for(int i = 1; i <= n; i++)
        cin >> v[i];

    for(int i = 1; i <= n; i++)
        for(int j = m; j >= v[i]; j --)
            f[j] = max(f[j], f[j - v[i]] + v[i]);

    int res = 0;
    for(int i = 0; i <= m; i ++) res = max(f[i],res);
    cout << m - res;
    return 0;
}