/* Programa de Interpolacion_Lagrange */

#include <stdio.h>
#include <math.h>

  float  X[10];
  float  Fx[10];
  int    N;
  float  Xinc;
  int    k,j,i;
  float  Multi;
  float  Sum;

int Lee_Datos();

/* PROGRAMA PRINCIPAL */

int main(void)

{

  clrscr();
  printf("\n        METODO DE INTERPOLACIONDE LAGRANGE ");
  printf("\n==================================================");
  N=Lee_Datos();
  Sum =0;
  printf("\n Resultados del desarrollo:");
  printf("\n   i     Multi   Fx[i]");
  printf("\n--------------------------------");
  for (i = 0;i <= N ;i++)
    {
		Multi=1;
		for (j=0;j <= N; j++)
		  {
			 if (j != i)
					Multi = Multi * ( (Xinc - X[j]) / (X[i] - X[j]) );
		  }
		Sum += Multi * Fx[i];
		printf("\n%4d %10.4f %10.4f %10.4f",i,Multi,Fx[i],Multi*Fx[i]);
	 }
  printf("\n--------------------------------------");
  printf("\n Para X= %10.4f La Fx es =>%10.4f",Xinc,Sum);
  getche();
}


int Lee_Datos()

  {
	 printf("\n  Grado del Polinomio =");
	 scanf("%d",&N);
	 printf("\n  Valor a interpolar =>");
	 scanf("%f",&Xinc);
	 printf("\n");
	 printf("\n       Valores Tabulados ");
	 printf("\n--------------------------------");
	 printf("\n  i       X           Fx");
	 printf("\n--------------------------------");

	 X[0] = 20;     Fx[0]= 103;
	 X[1] = 25;     Fx[1]= 107;
	 X[2] = 30;     Fx[2]= 112;
	 X[3] = 35;     Fx[3]= 116;

	 for (k=0; k <=N ; k++)
		{
		  printf("\n%d  %10.4f   |  %10.4f",k,X[k],Fx[k]);
		}
	 printf("\n--------------------------------");
	 return N;
 }