#include<stdio.h>
#include<math.h>
double sw(double x)
{
	double t,z;
	
    z=(int)((fabs(x)*pow(10,1))+0.5);
    t=z/pow(10.0,1);
    if(x>=0)
    	return t; 
    else
  	    return -t;
}

main()
{
	int i,n;
	double y[30],y1[30],s1[30],s2[30],s3[30],z,l,min=9999.0,mse=0.0;
	printf("ge shu:\n");
	scanf("%d",&n);
	printf("gshu ju:\n");
	for(i=1;i<=n;i++)
	{
		scanf("%lf",&y[i]);
	}
	s1[0]=s2[0]=s3[0]=sw((y[1]+y[2]+y[3])/3);
	for(z=0.01;z<1.000;z=z+0.01)
	{
		for(i=1;i<=n;i++)
		{	
			s1[i]=sw(z*y[i]+(1-z)*s1[i-1]);
			s2[i]=sw(z*s1[i]+(1-z)*s2[i-1]);
			s3[i]=sw(z*s2[i]+(1-z)*s3[i-1]);
			y1[i]=sw(((3-3*z+z*z)*s1[i-1]-(3-z)*s2[i-1]+s3[i-1])/pow(1-z,2));
			mse=mse+pow(y[i]-y1[i],2);
		}
		mse=sqrt(mse/n);
		if(mse<min)
		{
			min=mse;
			l=z;
		}
	}
	printf("%lf,%lf",l,z);
	system("pause");
}





#include<stdio.h>
#include<math.h>
double sw(double x)
{
	double t,z;
	
    z=(int)((fabs(x)*pow(10,1))+0.5);
    t=z/pow(10.0,1);
    if(x>=0)
    	return t; 
    else
  	    return -t;
}

main()
{
	int i,n;
	double y[30],y1[30],s1[30],s2[30],s3[30],z,mse,a,b,c;
	printf("ge shu:\n");
	scanf("%d",&n);
	printf("z:\n");
	scanf("%lf",&z);
	printf("gshu ju:\n");
	for(i=1;i<=n;i++)
	{
		scanf("%lf",&y[i]);
	}
	s1[0]=s2[0]=s3[0]=sw((y[1]+y[2]+y[3])/3);

		for(i=1;i<=n;i++)
		{	
			s1[i]=sw(z*y[i]+(1-z)*s1[i-1]);
			s2[i]=sw(z*s1[i]+(1-z)*s2[i-1]);
			s3[i]=sw(z*s2[i]+(1-z)*s3[i-1]);
			y1[i]=sw(((3-3*z+z*z)*s1[i-1]-(3-z)*s2[i-1]+s3[i-1])/pow(1-z,2));
			mse=mse+pow(y[i]-y1[i],2);
		}
		mse=sqrt(mse/n);
		a=3*s1[n]-3*s2[n]+s3[n];
		b=z*((6-5*z)*s1[n]-(10-8*z)*s2[n]+(4-3*z)*s3[n])/(2*pow(1-z,2));
		c=z*(s1[n]-2*s2[n]+s3[n])/(2*pow(1-z,2));
	
	printf("a=%lf,b=%lf,c=%lf,mse=%lf\n",a,b,c,mse);
	printf("s1[i]\n");
	for(i=1;i<=n;i++)
	{
		
	    printf("%lf  ",s1[i]);
    }
    printf("\ns2[i]\n");
	for(i=1;i<=n;i++)
	{
		
	    printf("%lf  ",s2[i]);
    }
    printf("\ns3[i]\n");
	for(i=1;i<=n;i++)
	{
		
	    printf("%lf  ",s3[i]);
    }
    printf("\ny1[i]\n");
	for(i=1;i<=n;i++)
	{
		
	    printf("%lf  ",y1[i]);
    }
    printf("\n");
	system("pause");
}