Important Note:

1) Pay attention to the number that is less than 1.0, because x^0.5 will larger than x. So we need to always set the right side to be 1.0

2) For double, just let end - start less than 1e-12, which means end and start are almost the same. This will use to control the accuracy. 

public class Solution {    /**     * @param x a double     * @return the square root of x     */    public double sqrt(double x) {        // Write your code here        double start = 0;        double end = x;        double eps = 1e-12;        if (end < 1.0) {            end = 1.0;        }        while (end - start > eps) {            double mid = start + (end - start) / 2.0;            //double mid = (end + start) / 2.0;            if (mid * mid < x) {                start = mid;            } else {                end = mid;            }        }                return start;    }}