// Lagrangeuv interpolacni polynom

#include <iostream>

#include <stdlib.h>

//#include <conio.h>

const int N=50;

using namespace std;



int  main()

{

	double x[N],y[N];    // tabulka funkce

	double x0,fx0,cit,jm;   // x0 -> bod, v nemz urcujeme funkcni hodnotu

	int i,n,p;

	cout<<endl<<"       Lagrangeuv interpolacni polynom."<<endl;

	cout <<endl<< "   Zadejte pocet vstupnich bodu (max. 50):"<<endl;

	cout<<"   Pocet bodu:  "; cin >> n; cout<<endl;



	cout << "   Zadejte tabulku:"<<endl;

	for(i=0;i<n;i++)

        {cout<<"   x["<<i<<"]= "; cin >>x[i];

         cout<<"   y["<<i<<"]= "; cin >>y[i];}

	cout << endl<<"   Zadejte hodnotu x0, pro niz chceme urcit y=f(x0)"<<endl;

	 cout<<"   x0 = "; cin >> x0;  cout<<endl;

	for (i=0;i<n;i++){cout<<"  x["<<i<<"]="<<x[i]<<"   y["<<i<<"]="<<y[i]<<endl;}

	// vlastni vypocet

        fx0=0;  for( int i=0; i<n;  i++)

      { cit=1; jm= 1; if (i==0) {for ( p=1; p<n;p++)

                                 {cit *=(x0-x[p]); jm *=(x[i] - x[p]);

                                 }

                                }

                          else  if (i<(n-1))

                       { for ( p=0; p<(i);p++)

                              {cit *=(x0-x[p]); jm *=(x[i] - x[p]);

                              }

                                 for(p=(i+1); p<n;p++)

                                     {cit *=(x0-x[p]); jm *=(x[i] - x[p]);

                                     }

                       }

                         else     { for(p=0; p<(n-1);p++)

                                   {cit *=(x0-x[p]); jm *=(x[i] - x[p]);

                                   }

                                  }

                                    fx0 +=((cit/jm)*y[i]);

      }



    cout<<endl<<"  f("<<x0<<") = "<<fx0<<endl;

    	return 0;

}