public class MySqrtDemo {
    public static void main(String[] args) {
        System.out.println(sqrt(10));// 3.1622772216796875
        System.out.println(Math.sqrt(10));// 3.1622776601683795
    }

    public static double sqrt(int i) {
        if (i <= 0) return i;
        double result;
        //从1开始疯狂试探
        for (int j = 1; true; j++) {
            if (j * j == i) {
                result = j;
                //记得跳出循环
                break;
            } else if ((j * j < i) && ((j + 1) * (j + 1) > i)) {
                result = half(i, j, j + 1);
                //记得跳出循环
                break;
            }
        }
        return result;
    }

    public static double half(int i, double small, double big) {
        double average = (small + big) / 2;
        double result = average * average;
        if (result == i) {
            //如果平均值*平均值等于入参，直接返回
            return average;
        } else if (result > i) {
            //大于，则在前一个数和平均值之间递归二分
            if (String.valueOf(average).length() >= 18) return average;
            return half(i, small, average);
        } else {
            //小于，则在平均值后一个数之间递归二分
            if (String.valueOf(average).length() >= 18) return average;
            return half(i, average, big);
        }
    }
}