#include <iostream>
#include <iomanip>
#include <cmath>
using namespace std;

double a,b,c,eps,c1, e, x, m, M,x1,y;
int i,n,k;
bool u;
double f (double x) {
    return pow(x,4)-2*pow(x,2)-3;
}

double f1(double x) {
    return 4*pow(x,3)-4*x;
}

void bis_apriori(double a,double b){
    n=trunc(log((b-a)/eps)/log(2))+1; u=true;
    for(int i=1;i<=n;i++){
        c=(a+b)/2;
        if(f(c)==0) {
        cout << " c : " << fixed << setprecision(15) << c << "  f(c) : " << f(c) << fixed << setprecision(15) << "  n : " << n << endl;
        u=false; break;}
        else{ if(f(a)*f(c)>0){
            a=c;}
            else{
                b=c;
            }
        }
    }
    if(u) cout << " c -> " << fixed << setprecision(15) << c << "  f(c) -> " << f(c) << fixed << setprecision(15) << "  n -> " << n << endl;

}
void bis_aposteriori(double a,double b){
    c=a; u=true;
    do{ c1=c; k++;
       c=(a+b)/2;
        if(f(c)==0) {
        cout << " c -> " << fixed << setprecision(15) << c << "  f(c) -> " << f(c) << fixed << setprecision(15) << "  n -> " << k << endl;
        u=false; break;}
        else{ if(f(a)*f(c)>0){
            a=c;}
            else{
                b=c;
            }
        }


    }while(2*abs(c-c1)>eps);
    if(u) cout << " c -> " << fixed << setprecision(15) << c << "  f(c) -> " << f(c) << fixed << setprecision(15) << "  n -> " << k << endl;

}



void secanta(double a, double b, double eps, double m1, double m2) {


   c=a-(f(a)/(f(b)-f(a)))*(b-a);
   if (f(c)*f(a)>0){ e=b;x=a;
                }
	else{
   	e=a;x=b;
     }

  int k2 = 0;
  do {
    x1=x;
    k2++;
     x = x1 - (f(x1) * (e - x1)) / (f(e) - f(x1));
  } while ((((m1-m2) * abs(x - x1)) / m2) > eps);

    cout << " c -> " << fixed << setprecision(15) << x << "  f(c) -> " << f(x) << fixed << setprecision(15) << "  n -> " << k2 << endl;

}

void coardaapos(double a, double b, double eps, double m1, double m2) {
  c = a;
  u = true;
  int k4 = 0;
  do {
    c1 = c;
    k4++;
    c = (a * f(b) - b * f(a)) / (f(b) - f(a));
    if (f(c) == 0) {
      cout << " c : " << fixed << setprecision(15) << c << "  f(c) : " << f(c) << fixed << setprecision(15) << "  n : " << k4 << endl;
      u = false;
      break;
    } else {
      if (f(c)*f(a) > 0) {
        a = c;
      } else {
        b = c;
      }
    }

  } while (((m1 * abs(c - c1)) / m2) > eps);
  if (u) {
    cout << " c : " << fixed << setprecision(15) << c << "  f(c) : " << f(c) << fixed << setprecision(15) << "  n : " << k4 << endl;
  }
}
void coardaapriori(double x1, double x2) {

  int 	k1 = trunc(log(eps/0.5) / (log(f1(x2) - f1(x1)) - log(f1(x2)))) + 1;
  c = a;
  for (int i = 1; i <= k1; i++) {

    c = c - (f(c) * (x2 - c)) / (f(x2) - f(c));
  }
  cout << " c : " << fixed << setprecision(15) << c << "  f(c) : " << fixed << setprecision(15) << f(c) << "  n : " << k1 << endl;

}
void tang(double a, double b, double eps, double m1, double m2) {
	int k5=0;double x,x1,c=0;
  c = (a * f(b) - b * f(a))/(f(b)-f(a));
	if (f(a)*f(c)>0) { x = b;
					   } else { x = a;
					                   }
	do {
	     x1=x;
	     x = x1 - f(x1)/f1(x1);
	     k5++;


  }while(((m1*pow((x-x1),2))/(2*m2))>=eps);
  cout << " c -> " << fixed << setprecision(15) << x << "  f(c) -> " << fixed << setprecision(15) << f(x) << "  n -> " << k5 << endl;


}
void mixt(double a,double b,double eps){

	int k6 = 0;double h=0; double x,y;
	h = (a * f(b) - b * f(a))/(f(b)-f(a));
	if (f(a)*f(h)>0) { x = b;
					   y = a; } else { x = a;
					                   y = b; }
	do {
	     y = y - (f(y) * (x-y))/(f(x)-f(y));
	     x = x - f(x)/f1(x);
	     k6++;


	}
	while (abs(x-y) >= eps);
    cout << " c -> " << fixed << setprecision(15) << x << "  f(c) -> " << fixed << setprecision(15) << f(x) << "  n -> " << k6 << endl;


}
int main(){
    a=1; b=2;
     m=abs(f1(a));
     M=abs(f1(b));

    cout<<"a -> "<<a<<" "<<"   b -> "<<b<<endl;
    cout<<"M -> "<<M<<" "<<"   m -> "<<m<<endl;
    m=pow(10,-15);
    cout<<"bisectia apriori"<<endl;
    eps=pow(10,-15);
    bisapriori(a,b);
    cout<<"bisectia aposteriori"<<endl;
    bisaposteriori(a,b);
    cout<<"secanta aposteriori"<<endl;
    secanta(a,b,eps,M,m);
    cout<<"coarde aposteriori"<<endl;
    coardaapos(a,b,eps,M,m);
    cout<<"coarde apriori"<<endl;
    eps=pow(10,-15);
    cout<<"nu putem aplica metoda f'(a)=0,ceea ce nu satisface conditiile metodei"<<endl;
    cout<<"dar daca a=1.5,putem aplica metoda(f e convexa,f e strict crescatoare,f'(a)>0,f e derivabila)"<<endl;


    coardaapriori(1.5,b);

    cout<<"tangenta aposteriori"<<endl;
    tang(1.5,b,eps,44,7.5);
    cout<<"mixta"<<endl;
     mixt(1.5,b,eps);

    return 0;
}