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lagrange interpolation method


///Bismillahir Rahmanir Rahim
///Author:Tanvir Ahmmad
///CSE,Islamic University,Bangladesh


///Dept.CSE,IU,Bangladesh

#include<iostream>
using namespace std;
typedef int in;
typedef double db;



int main()
{
    in n,fin;
    cout<<"Enter number of data point: ";
    cin>>n;
    in arr_x[n+3],arr_y[n+3];

    cout<<"Input these "<<n<<" points:"<<endl;

    for(in i=1; i<=n; i++) cin>>arr_x[i]>>arr_y[i];
    cout<<"After given values : "<<endl;
    for(in i=1; i<=n; i++)
        cout<<"x["<<i<<"] = "<<arr_x[i]<<"  "<<"y["<<i<<"] = "<<arr_y[i]<<endl;
    cout<<"Enter interpolation point: ";
    cin>>fin;
    db ans=0;

    for(in i=1; i<=n; i++)
    {
        db up=arr_y[i],down=1;
        for(in j=1; j<=n; j++)
        {
            if(j==i) continue;
            else up*=(fin-arr_x[j]),down*=(arr_x[i]-arr_x[j]);;
        }
        ans+=(up/down);
    }
    cout<<"Interpolated value of "<<fin<<" is "<<ans<<endl;
return 0;

}

///Alhamdulillah



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