//Newton法求根程序
#include <math.h>
#include <iostream.h>
//Function
double f(double x)
{
	double y1,y2,y3;
	y1=x*exp(x)-1;
	y2=x*x*x-x-1;
	y3=(x-1)*(x-1)*(2*x-1);
	return(y3);
}
double fd(double x)
{
	double y1,y2,y3;
	y1=exp(x)+x*exp(x);
	y2=3*x*x-1;
	y3=2*(x-1)*(2*x-1)+2*(x-1)*(x-1);
	return(y3);
}

void main()
{
	double x0,x1;
	double root;
	double e1,e2;
	int N,k;


	cout<<"歡迎使Newton求根法程序"<<endl;
l1:	cout<<"請輸入初始值--->x0"<<endl;
	cin>>x0;
	cout<<"請輸入限制奇異標志--->e1"<<endl;
	cin>>e1;
	cout<<"請輸入計算精度--->e2"<<endl;
	cin>>e2;
	cout<<"請輸入限制跌代次數--->N"<<endl;
	cin>>N;

    for(k=1;k<=N;k++)
	{
		cout<<x0<<endl;
	    if(fd(x0)<e1)
		cout<<"ERROR,奇異方程，無法求解，難道是傳說中的XX在世，本程序無法處理"<<endl;
    

        x1=x0-f(x0)/fd(x0);
		if(fabs(x1-x0)<e2)
			goto l2;
		x0=x1;
		
	}
    if(k>N)
	{cout<<"FAILED:選擇初始值錯誤請重新選擇初始值"<<endl;
	 goto l1;
	}
l2: root=x1;
	cout<<"ROOT="<<root<<endl;

}