69.x 的平方根

给你一个非负整数 x ，计算并返回 x 的 算术平方根 。

方法一：袖珍计算器法：

class Solution {
    public int mySqrt(int x) {
        if (x == 0) {
            return 0;
        }
        int ans = (int) Math.exp(0.5 * Math.log(x));
        return (long) (ans + 1) * (ans + 1) <= x ? ans + 1 : ans;
    }
}

方法二：二分查找

class Solution {
    public int mySqrt(int x) {
        int l = 0, r = x, ans = -1;
        while (l <= r) {
            int mid = l + (r - l) / 2;
            if ((long) mid * mid <= x) {
                ans = mid;
                l = mid + 1;
            } else {
                r = mid - 1;
            }
        }
        return ans;
    }
}

方法三：牛顿迭代

class Solution {
    public int mySqrt(int x) {
        if (x == 0) {
            return 0;
        }

        double C = x, x0 = x;
        while (true) {
            double xi = 0.5 * (x0 + C / x0);
            if (Math.abs(x0 - xi) < 1e-7) {
                break;
            }
            x0 = xi;
        }
        return (int) x0;
    }
}