//分段拋物插值算法源程序:
#include<iostream.h>
#define SIZE 10
void main()
{
	int n,i=1,j=1;
	double xx,yy=1,result=0;
	double x[SIZE];
	double y[SIZE];
	cout<<"**********分段拋物插值**********"<<endl<<endl;
	cout<<"輸入已知插值結點總數目(未剔除時應當大于3):   ";
	cin>>n;
	while(n<3)
	{
		cout<<"輸入錯誤,點的數目必須大于3!請重新輸入:  ";
		cin>>n;
	}
	cout<<"依次輸入第結點的坐標:   x y"<<endl;
	while(i<=n)
	{
		cout<<"第 "<<i<<" 個點的坐標為  ";
		cin>>x[i]>>y[i];
		i++;
	}
	cout<<"輸入所求插值結點x坐標:   ";
	cin>>xx;
	if(xx>=x[n-1])
	{
		x[1]=x[n-2];
		x[2]=x[n-1];
		x[3]=x[n];

		y[1]=y[n-2];
		y[2]=y[n-1];
		y[3]=y[n];
	}
{
		for(j=1;j<n;j++)
		{
			if(xx>=x[j]&&xx<=x[j+1])
			{
				if((xx-x[j-1])<=(x[j+2]-xx))
				{
					x[1]=x[j-1];
					x[2]=x[j];
					x[3]=x[j+1];

					y[1]=y[j-1];
					y[2]=y[j];
					y[3]=y[j+1];
				
				}
				else
				{
					x[1]=x[j];
					x[2]=x[j+1];
					x[3]=x[j+2];

					y[1]=y[j];
					y[2]=y[j+1];
					y[3]=y[j+2];
				}
			}
		}
	}
	cout<<"自動篩選后坐標為: "<<x[1]<<","<<y[1]<<"    "<<x[2]<<","<<y[2]<<"    "<<x[3]<<","<<y[3]<<endl;	
	for(i=1;i<=3;i++)
	{
		for(j=1,yy=1;j<=3;j++)
			if(j!=i)yy=yy*(xx-x[j])/(x[i]-x[j]);
		result=result+yy*y[i];
	}
	cout<<"所求y坐標為:  "<<result;
}