#include<iostream>
#include<math.h>
#include<iomanip>
using namespace std;
float fact(float x)
{if(x==1)
return 1;
else
return x*fact(x-1);
}
 
 int main()
 {
 	cout<<"newton forward @developed by mayank timbal"<<endl;
 	cout<<"enter all value in only integer or float do not enter alphanumeric symbols or characters"<<endl;
 int n,i,j;
 cout.precision(5);
 block:
 cout<<"enter how many values you have for function"<<endl;

while(!(cin >> n))
{ cin.clear();
 cin.ignore(INT_MAX,'\n');
	cout<<"it is char enter valid input try again "<<endl;
}
if(n<=0)
{
	cout<<"its negative"<<endl;
	goto block;
}

 float y[n][n];
 float x[n];
 cout<<"enter x[0] value=";
 cin>>x[0];
 
 float h;
 cout<<"enter h for table=";
 cin>>h;
 
 for(i=1;i<n;i++)
 {
 x[i]=h+x[i-1];
 }
 
 for(i=0;i<n;i++)
{
cout<<"enter your y["<<i<<"]"<<"for"<< "x["<<i<<"]"<<endl;
cin>>y[0][i];
}

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];
}
}

float temp,r;
cout<<"enter at which point you want to find value x="<<endl;
float f;
cin>>f;

r=(f-x[0])/h;
float sum=0;

for(i=0;i<n;i++)
{
temp=1;
temp=temp*y[i][0];
for(int k=0;k<i;k++)
{temp=(temp*(r-k));
}
if(i!=0)
{temp=temp/fact(i);
}
sum=sum+temp;
}
cout<<"answer is ="<<sum;

 return 0;
}