利用bigInteger实现了一下大数阶乘的算法，实测比直接迭代相乘快一个数量级，但是不知道怎么求时间和空间复杂，想大家帮忙看下。

private static String factorial(int n) {
        java.math.BigInteger ans = java.math.BigInteger.valueOf(1);
        int bits = 0;
        for (int i = 2; i <= n; i++) {
            if (Integer.bitCount(i) == 1) {
                bits += Integer.numberOfTrailingZeros(i);
                continue;
            }
//            ans = ans.multiply(java.math.BigInteger.valueOf(i));
        }
        ans = subFactorial(1, n);

        return ans.shiftLeft(bits).toString();
    }

    private static java.math.BigInteger subFactorial(long a, long b) {
        if ((b - a) < 10) {
            java.math.BigInteger res = java.math.BigInteger.ONE;
            for (long i = a; i <= b; i++) {
                if (Long.bitCount(i) == 1) {
                    continue;
                }
                res = res.multiply(java.math.BigInteger.valueOf(i));
            }
            return res;
        } else {
            long mid = a + b >>> 1;
            return subFactorial(a, mid).multiply(subFactorial(mid + 1, b));
        }
    }