#include <cstdlib>
#include <cmath>
#include <iostream>

//QUADRATIC APPROX

//accuracy is a parameter that tells us when algorithm will stop.
//If difference between in x after another algorithm step is less than that accuracy algorithm will be stopped
#define ACCURACY 0.01
//a is left border of area where we look for answer and b is right
double a = -1;
double b = 1;

//our function in which we are trying to find minimum in range [-1,1]
double function1(double x){
    double s = sin(2*x+1)+2;
    return 1 / (1 + exp(s));
}

double function2(double x){
    return -sin(x+1);
}

//this function calculates next x (x2) using quadratic approximation (check lab pdf for more info)
//it takes as parameters pointer to function we calculate and previous x (x1)
double qudratApprox(double x1, double(*func)(double)){
    double x2;
    x2 = (func(a)*(pow(b,2) - pow(x1,2)) + func(x1)*(pow(a,2) - pow(b,2)) + func(b)*(pow(x1,2) - pow(a,2)))/
        (func(a)*(b-x1) + func(x1)*(a-b) + func(b)*(x1-a));
    x2 *= 0.5;

    //x2 has to be beetween left and right border otherwise more advanced implementation of the algorithm has to be used
    if(a < x2 && b > x2){

        return x2;
    }else{
        std::cout<< "ERROR HAS OCCURED\n";
    }
    return x2;
}


int main(){

    //for the beggining we put x in the middle of our range
    double x = 0;

    //variable for storing next x
    double x2;

    //check internet to find out what is do while loop
    do{
        //first we calculate our next x
        x2 = qudratApprox(x,function1);
        //std::cout << x2 << std::endl;

        //now we are comparing which in which point function is bigger
        //(check lab pdf why we do that, that is the essential of this algorithm)
        if(function1(x) > function1(x2)){
            //this and below if statements are for swiping,
            //we will shrink our range from left or right side depending on what side are x and x2
            if(x < x2)  a = x;
            else b = x;
        }else{
            if(x < x2)  a = x2;
            else b = x2;
        }
        //again we put our x in the middle of the new shrinken range
        x = (a+b)/2;
        std::cout << "x = " << x << std::endl;

    //we repeat these steps until difference between two steps is smaller than predefined accuracy
    }while(abs(x-x2) >= ACCURACY);

    //finally we print out our result
    std::cout << "xmin = " << x << std::endl;
    std::cout << "f(xmin) = " << function1(x) << std::endl;

    return 1;
}