import java.util.*;

public class Main {
    static final int N = 110, M = 10010;
    static int[][] f = new int[N][M];
    static int[] a = new int[N];
    static int n, m;

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        String[] str = sc.nextLine().split(" ");
        n = Integer.parseInt(str[0]);
        m = Integer.parseInt(str[1]);

        str = sc.nextLine().split(" ");
        for (int i = 1; i <= n; i++) a[i] = Integer.parseInt(str[i - 1]);

        //从前i个物品中选，且价值为0的方案数均为1
        //什么都不选就是一种选法
        for (int i = 0; i < N; i++) f[i][0] = 1;
        for (int i = 1; i <= n; i++)
            for (int j = 1; j <= m; j++) {
                //不选当前物品
                f[i][j] = f[i - 1][j];
                //选当前物品
                //选法为从前i - 1个数中选且价值为j - v的所有选法
                //即f[i - 1][j - v]
                if (a[i] <= j)
                    f[i][j] += f[i - 1][j - a[i]];
            }

        System.out.println(f[n][m]);
    }
}

一维优化

f[j]表示前i个数的和恰好为j的方案数的个数

import java.util.*;

public class Main {
    static final int N = 110, M = 10010;
    static int[] f = new int[M];
    static int[] a = new int[N];
    static int n, m;

    public static void main(String[] args) {

        Scanner sc = new Scanner(System.in);
        String[] str = sc.nextLine().split(" ");
        n = Integer.parseInt(str[0]);
        m = Integer.parseInt(str[1]);

        str = sc.nextLine().split(" ");
        for (int i = 1; i <= n; i++) a[i] = Integer.parseInt(str[i - 1]);

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

        System.out.println(f[m]);
    }
}