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

void dif_dividides(double *x, double *y,int n){
    double *cs=malloc(sizeof(double)*n);
    int i;
    for(i=1;i<n;i++){
        int j;
        for(j=0;j<n-i;j++){
            y[j]=(y[j+1]-y[j])/(x[j+i]-x[j]);
        }
        cs[i]=y[0];
    }

    for(i=0;i<n;i++){
        y[i]=cs[i];
    }
    free(cs);

}

double aval(double *x,double *c, int n, double t){
    double r=0;
    int i;
    for(i=0;i<n;i++){
        double p=c[i];
        int j;
        for(j=0;j<i;j++){
            p=p*(t-x[j]);
        }
        r=r+p;
    }
    return r;
}

void imprimirArray(double *a, int n){
    int i;
    for(i=0;i<n;i++){
        printf("%e,",a[i]);
    }
    printf("\n");
}

double f(double t){
    return exp(sin(t)+cos(t));
}

int main(int argc,char *argv[]){
    if(argc>0){
        char *aux;
        int n=(int)strtol(argv[0],&aux,10);
        double *x=malloc(sizeof(double)*(n+1));
        double *y=malloc(sizeof(double)*(n+1));

        double inc=2*M_PI/n;
        double d=0;
        int i=0;
        while(d<=2*M_PI){
            x[i]=d;
            y[i]=f(d);
            d=d+inc;
            i++;
        }


        dif_dividides(x,y,n+1);

        char *nomArxiu="interp0";
        char cn='0'+n;
        aux=strcat(nomArxiu,&cn);
        aux=strcat(nomArxiu,".res");
        FILE *file=fopen(nomArxiu,"w");
        d=0.f;
        inc=2*M_PI/1000;
        double exacte=f(d);
        double aproximat=aval(x,y,n+1,d);
        double errorRelatiu=abs((exacte-aproximat)/exacte);
        for(i=0;i<1000;i++){
            fprintf(f,"%e %e %e %e",d,exacte,aproximat,errorRelatiu);
            d=d+inc;
        }
        fclose(file);
    }
    exit(0);
}