算法1

对于天平来说,可以称出J 那么-J 也可以（反过来） 所以 f[i][j] = f[i][-j] = f[i][Math.abs(j)]

JAVA 代码

import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = in.nextInt();
        int m = 0;
        for (int i = 0; i < a.length; i++) {
            m += a[i];
        }
        work(a, n, m);
    }

    public static void work(int[] a, int n, int m) {
        boolean[][] f = new boolean[n][m + 1];
        f[0][0] = true;
        f[0][a[0]] = true;
        for (int i = 1; i < n; i++) {
            for (int j = 0; j <= m; j++) {
                f[i][j] |= f[i - 1][j];
                f[i][j] |= f[i - 1][Math.abs(j - a[i])];
                if (j + a[i] <= m) f[i][j] |= f[i - 1][j + a[i]];
            }
        }
        int ans = 0;
        for (int i = 1; i <= m; i++) {
            if (f[n - 1][i]) ans++;
        }
        System.out.println(ans);
    }

}