Lagrange interpolation

#include<stdio.h>
#include<stdlib.h>

void viete(int,double*,double*);
double horner(int,double*,double,double*);
void lagrange(int,double*,double*,double*);

int main(){
FILE* in;
FILE* out;
double *x,*y,*l;
int i,n;
if((in=fopen("in.txt","r"))==NULL){
printf("Nie mozna otworzyc pliku do czytania \n");
exit(1);
}
if((out=fopen("out.txt","w"))==NULL){
printf("Nie mozna otworzyc pliku do pisania \n");
exit(1);
}
while(!feof(in)){
fscanf(in,"%d",&n);
x=(double*)malloc((n+1)*sizeof(double));
y=(double*)malloc((n+1)*sizeof(double));
l=(double*)malloc(n*sizeof(double));
for(i=1;i<=n;i++)
fscanf(in,"%lf",&x[i]);
for(i=1;i<=n;i++)
fscanf(in,"%lf",&y[i]);
lagrange(n,x,y,l);
for(i=0;i<=n-1;i++)
fprintf(out,"l[%d]=%.15lf\n",i,l[i]);
fprintf(out,"\n");
free(x);
free(y);
free(l);
}
fclose(in);
fclose(out);
return 0;
}

void viete(int n,double* x,double* a){
     int i,j,e;
     double t;
     a[0]=1.0;
     for(i=1;i<=n;i++)
     a[i]=0.0;
     for(i=1;i<=n;i++)
       for(j=i;j>=1;j--)
         a[j]+=a[j-1]*x[i];
         e=n;
         for(i=0;i<(n+1)/2;i++){
         t=a[i];
         a[i]=a[e];
         a[e]=t;
         e--;
         }
       for(i=0;i<=n;i++)
       if((n-i)%2==1) a[i]=-a[i];
     }

double horner(int n,double* a,double c,double* b){
     int i;
     double r;
     r=a[n];
     for(i=n-1;i>=0;i--){
     b[i]=r;
     r=r*c+a[i];
     }
     return r;
     }

void lagrange(int n,double* x,double* y,double* l){
     int i,j;
     double* a;
     double* b;
     double d;
     a=(double*)malloc((n+1)*sizeof(double));
     b=(double*)malloc(n*sizeof(double));
     for(i=0;i<=n-1;i++)
     l[i]=0.0;
     viete(n,x,a);
     for(i=1;i<=n;i++){
     horner(n,a,x[i],b);
     d=1.0;
     for(j=1;j<=n;j++)
     if(j!=i) d*=(x[i]-x[j]);
     for(j=0;j<=n-1;j++)
     l[j]+=(double)(y[i]/d)*b[j];
     }
     free(a);
     free(b);
     }