二分法求多项式曲线区间极值

　　二分法求解，设置left为左边界，right为右边界，则解一定位于left和right之间，当左右边界之间的差值小于某一精确度时，就认为找到了解。具体操作如下，若是先减后增，首先判断左右边界差值作为循环条件，接着每次循环找到左右边界的中间值，一旦该点导数值小于0，说明该点的右侧存在正确解，则将左边界设置为该点，反之将右边界缩进，左右边界通过循环不断的向正确解缩进（先增后减与之相反）。满足某一精确度后即可输出结果（注意这里的函数在区间中是比较常规简单的单调函数）。
　　代码如下：

#include <vector>
#include <iostream>

using namespace std;

//计算多项式曲线的在x处的值
double fx(vector<double> coefficient, double x)
{
	double fx = coefficient[coefficient.size() - 1];
	for (int i = coefficient.size() - 2; i >= 0; i--)
	{
		fx = fx*x + coefficient[i];
	}
	return fx;
}

//计算多项式曲线的导函数在x处的值
double fdx(vector<double> coefficient, double x)
{
	vector<double> coefficient_df;//导函数系数数组
	for (int i = 1; i < coefficient.size(); i++)
	{
		coefficient_df.push_back(coefficient[i] * i);
	}

	double fdx = coefficient_df[coefficient_df.size() - 1];
	for (int i = coefficient_df.size() - 2; i >= 0; i--)
	{
		fdx = fdx*x + coefficient_df[i];
	}

	return fdx;
}


int main()
{
	vector<double> m_coefficient;//多项式曲线系数数组
	m_coefficient.push_back(3813.237503);
	m_coefficient.push_back(2409.040543);
	m_coefficient.push_back(412.086525);
	m_coefficient.push_back(20.007034);
	m_coefficient.push_back(-0.887868);
	m_coefficient.push_back(-0.078038);
	m_coefficient.push_back(0.002762);
	m_coefficient.push_back(0.000329);
	m_coefficient.push_back(0.000007);

	double left = -10.0, right = 0.0;//设置区间范围
	int count = 0;
	double preci = 1e-6;//设置精确度
	while (right - left>preci) //若超时，在保证精度的情况下，可以改成count++<100
	{
		double mid = (left + right) / 2.0;
		if (fdx(m_coefficient,mid)<0)//左减右增
		//if (fdx(m_coefficient, mid)>0)//左增右减
		{
			left = mid;
		}
		else
		{
			right = mid;
		}
	}
	cout << "left:" << left << endl;
	cout << "fx(left):" << fx(m_coefficient, left) << endl;
	cout << "right:" << right << endl;
	cout << "fx(right):" << fx(m_coefficient, right) << endl;
}

　　运行结果如下：