二分法求平方根

 1.问题

利用二分法求一个数的平方根,精度要求 e < 10^-6;

2.思路

1.要求x（x>0）的完全平方根，则二分法范围为[low,up] 其中 low = 0, up = x

2.令mid = （up+low）/2

3.以fabs(mid * mid - x) >=1e-6为循环条件

3.1若满足条件，令mid = （up+low）/2，判断mid*mid与x的关系

3.1.1若mid * mid > x 则 up = mid 继续循环

3.1.2若mid * mid < x 则 low = mid 继续循环

3.2若不满足条件，mid即为完全平方根

3.代码

c++

//二分法求平方根
double kaiFang(double low, double up)
{
	double x = up;
	double mid = low + (up - low)/ 2;
	while (fabs(mid * mid - x) >=1e-6)
	{
		mid = low + (up - low) / 2;
		if (mid * mid > x) up = mid;
		else if (mid * mid < x) low = mid;

	}
	return mid;
}

go 

func sqrt(num float64) (ret float64, err string) {
	if num < 0 {
		err = "num should >= 0"
		return
	}
	lo, hi := 0.0, num
	mid := lo + (hi-lo)/2
	for (num-mid*mid) > 10e-6 {
		mid = lo + (hi-lo)/2
		if mid*mid > num {
			hi = mid
		} else if mid*mid < num {
			lo = mid
		}
	}
	return mid, ""
}