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

FILE *logfile;
FILE *logfile2;
double func1(double x);
double grid_search(double f(double), double start, double end, double tol);
double dihotomie(double f(double), double start, double end, double tol);
double raportAur(double f(double), double start, double end, double tol);

int main()
{
    logfile = fopen("log.csv","w");
    logfile2 = fopen("log2.csv", "w");
    if(logfile == NULL) return 1;
    double op = grid_search( func1, 0, 2*acos(-1), 0.001);
    double op2 = dihotomie( func1, 0, 2*acos(-1), 0.001);
    double op3 = raportAur( func1, 0, 2*acos(-1), 0.001);
    printf("Optimum: %f ,%f \n", op, func1(op));
    printf("Optimum: %f ,%f \n", op2, func1(op2));
    printf("Optimum: %f ,%f \n", op3, func1(op2));
    return 0;
}

double grid_search(double f(double), double start, double end, double tol)
{
 double min = 32000;
 double i;
 double poz;
 for(i = start ; i < end ; i+=tol)
 {
    fprintf(logfile, "%f , %f , %f , %f  \n", i, f(i), poz ,min);
    if(f(i) < min)
    {
        min = f(i);
        poz = i;
    }
 }
 return poz;
}

double dihotomie(double f(double), double start, double end, double tol)
{
    //a = start , b = end
    double eps = tol/3;

    while(end - start > tol)
    {
        double c = ((start + end)/2) - eps;
        double d = ((start + end)/2) + eps;

        if(f(c) > f(d))
            start = c;
        else
            end = d;

        fprintf(logfile2, "%f , %f , %f , %f  \n", start, f(start), end ,f(end));
    }
    return start;
}

double raportAur(double f(double), double start, double end, double tol)
{
    double R = ((1+sqrt(5))/2);

    double a = start;
    double b = end;

    double c = b - ((b-a)/R);
    double d = a + ((b-a)/R);

    while(b-a > tol)
    {
    if(f(c) > f(d))
    {
        a = c;
        c = d;
        d = a + (b-a)/R;
    }
    else
    {
        b = d;
        d = c;
        c = b - (b-a)/R;
    }
    }
    return b;
}

double vertex(double f(double), double x1, double x2, double x3)
{
    double y1 = f(x1), y2 = f(x2), y3 = f(x3);
    double denom = (x1-x2)*(x1-x3)*(x2-x3);
    double A = (x3*(y2-y1)+x2*(y1-y3)+x1*(y3-y2))/denom;
    double B = (x3*x3*(y1-y2)+x2*x2*(y1-y3)+x1*x1*(y2-y3))/denom;
    return -B/(2*A);
}

double interpolareParabolica(double f(double), double start, double end, double tol)
{
    double a = start;
    double b = end;

    double c = (a+b)/2;

    while(b-a > tol)
    {
        double d = vertex(f, a , b, c);

        if(d < c)
        {
            double aux;
            aux = c;
            c = d;
            d = aux;
        }
        if(f(c) > f(d))
        {
            a = c;
            c = d;
        }
        else
        {
            b = d;
        }
    }
}


double func1(double x)
{
    return sin(x);
}