#include <iostream>
#include<bits/stdc++.h>
using namespace std;
int main()
{
double y[50][50],x[50];
int n,i,j,st,v=0;
double p,e,s,d,sum=0,r,sum1=0,r1,g1,g2,g3,g4;
cout<<"Enter n="<<endl;
cin>>n;
cout<<"Starting Point="<<endl;
cin>>s;
cout<<"End Point="<<endl;
cin>>e;
cout<<"Difference="<<endl;
cin>>d;
p=(e-s)/d;
st=n/2;
cout<<"X"<<"\t"<<"Y"<<endl;
for(i=0;i<n;i++)
{
cin>>x[i]>>y[0][i];
}
cout<<"X"<<"\t"<<"Y"<<endl;
for(i=1;i<n;i++)
{
for(j=0;j<n-i;j++)
{
y[i][j]=y[i-1][j+1]-y[i-1][j];
}
}
cout<<"Forward Difference Table"<<endl;
for(j=0;j<n;j++)
{
printf("%lf",x[j]);
for(i=0;i<n-j;i++)
{
if(y[i][j]>0.0001)
{
printf("\t%lf",y[i][j]);
}
}
printf("\n");
}
g1=p;
g2=(p*(p-1))/2;
g3=((p+1)*p*(p-1))/6;
g4=((p+1)*p*(p-1)*(p-2))/24;
r=y[v][st]+g1*y[v+1][st]+g2*y[v+2][st]+g3*y[v+3][st]+g4*y[v+4][st];
cout<<"Root is="<<r<<endl;
return 0;
}
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