LeetCode69 Sqrt(x) 开方 C++

问题描述：
Implement int sqrt(int x).

Compute and return the square root of x, where x is guaranteed to be a non-negative integer.

Since the return type is an integer, the decimal digits are truncated and only the integer part of the result is returned.

Example 1:

Input: 4
Output: 2

Example 2:

Input: 8
Output: 2

Explanation: The square root of 8 is 2.82842…, and since the decimal part is truncated, 2 is returned.
题源：here；完整实现：here
思路：
三种方案：1 直接调用库函数；2 牛顿方法；3 二分法。从时间上，三种方式很接近。
1 调用库函数

    int mySqrt(int x) {
        return int(sqrt(x));
    }

运行结果：

2 牛顿方法

    int mySqrt2(int x){
        if (x <= 0) return 0;
        double last = 0, rest = 1;
        while (last != rest){
            last = rest; rest = (rest + x / rest) / 2;
        }

        return int(last);
    }

运行结果：

3 二分法

    int mySqrt3(int x){
        if (x <= 0) return 0;
        int left = 0, right = x/2 + 1;
        while (left < right){
            long long mid = (left + right + 1) / 2;
            long long sq = mid*mid;
            if (sq == x) return int(mid);
            else if (sq < x) left = mid;
            else right = mid - 1;
        }

        return left;
    }

运行结果：