LeetCode 1467: Probability of a Two Boxes Having The Same Number of Distinct Balls Solution

class Solution {
    public double getProbability(int[] balls) {
        int sum = 0;
        for (int b : balls) {
            sum += b;
        }
        int n = sum / 2; // Total number of balls in each box
        return dfs(balls, new int[balls.length], 0, 0, n, n) / perm(sum / 2);
    }
    
    private double dfs(int[] balls, int[] cnt, int idx, int sum1, int sum2, int n) {
        if (sum1 > n || sum2 > n) return 0;
        if (idx == balls.length) {
            return sum1 == n && sum2 == n ? 1 : 0;
        }
        
        double res = 0;
        for (int i = 0; i <= balls[idx]; i++) {
            cnt[idx] = i;
            res += dfs(balls, cnt, idx + 1, sum1 + i, sum2 + (balls[idx] - i), n);
        }
        
        return res;
    }
    
    private double perm(int n) {
        double res = 1;
        for (int i = 1; i <= n; i++) {
            res *= i;
        }
        return res;
    }
}