#include <iostream>
#include <cstdlib>
#include <ctime>
#include <cmath>
#include <iomanip>
using namespace std;
int main (){
 srand(time(NULL)); //Need this for rand #'s
 int rad;
 double bor;
 rad=(-1)*((rand()%11)+5);
 bor=(-1)*(rand()%(-1*rad));
 double x,y;
 double xint;
 double overhead;
 double launch;
 double crater;
 double a,h,k;
 int i = 0;

 while(i == 0 )
 {
  a=(-1)*((rand()%31)+20);
  h=((rand()%31)-20);
  k=(rand()&15)+5;

  cout<<"Radar range is "<<rad<<endl;
  cout<<"Our border is at "<<bor<<endl;
  cout<<"a= "<<a<<endl;
  cout<<"h= "<<h<<endl;
  cout<<"k= "<<k<<endl;

  if (h == 0) {

 h = h + .1;
}

  //y=((1/a)*(pow((x-h),2)+k));
   overhead = ((1/a)*(pow(h,2))+k);
    xint=sqrt((-1*k)*(a));
   launch=(-1*xint)+h;
   crater=(xint)+h;

   if(launch<=bor)
   {
    i++;
   }
}
double a1;
  a1 = 1/a;
  crater=(xint)+k;
  if ( h > 0) {

  cout <<setprecision (2) << "The equation of the rocket in vertex form is y = " << a1 << "(x-" << h << ")^2 + " << k << endl;
}
  if (h < 0) {
  	h = h * -1;
  	cout <<setprecision (2) << "The equation of the rocket in vertex form is y = " << a1 << "(x+" << h << ")^2 + " << k << endl;
  	h = h * -1;
  }



  double b ,c;

  b = -((2*h)/a);
  c = ((h*h)/a) + k;
  cout << setprecision (2) << "The equation of the rocket in standard form is y = (" <<a1<< ")x^2 + " << b << "x + " << c << endl << endl << endl;

  	x = 1;
 	double p1, p2, p3, p4;
 	double n[3];

 	cout << "CALCULATED VALUES" << endl ;
	cout << "We have observed the following points that the rocket has passed through: ";
	cout << endl << "The first point is (0," << c << ")" ;
for (int i = 0;i<3;i++)
 {

	 y=((1/a)*(pow(x,2)))+(b*x)+c;

	cout << setprecision(2) << endl << "Another point is ("  << x << "," << y <<")";

	x = x+2;
	n[i] = y;

}




	double m[3] = {1 , 3, 0};
	double temp1, temp2, num, den;

	temp1 = (n[1]-c);
	temp2 = (m[1]*m[1])*(n[0]-c);
	num = temp1 - temp2;
	den = (-(m[1]*m[1])+m[1]);
	b = num/den;
	a = (n[0] - c) - b;
	cout << endl << "a = " << a << endl;
	cout << "b = " << b <<endl;
	cout << "c = " << c <<endl;
	cout <<setprecision (2) << "The equation of the rocket in standard form is y = (" << a << ")x^2 + " << b << "x + " << c << endl;

 	h = -(b)/ (2*a);

 	k = (a*h*h) + (b*h) + c;


 	if ( h > 0) {
  		cout <<setprecision (2) << "The equation of the rocket in vertex form is y = " << a << "(x-" << h << ")^2 + " << k << endl;
}
  	if (h < 0) {
  		h = h * -1;
  		cout <<setprecision (2) <<  "The equation of the rocket in vertex form is y = " << a << "(x+" << h << ")^2 + " << k << endl;
  }
	if (h == 0)
 {

 	cout << endl << "The missle interception has failed. Take cover. ";
 	return 0;
}

 cout<<"overhead (y)= "<<overhead<<endl;
 cout<<"launch (x start)= "<<launch<<endl;
 cout<<"crater (x finish)= "<<crater<<endl;
   double whatis; //how far interceptor can make it
   double whatneedstobe; //how far rocket is from base
 double timeinterval = 0.001;


 for (x=rad;x<=crater;x=x+timeinterval){
  y=((1/a)*(pow((x-h),2))+k);
  whatneedstobe=sqrt((pow(x,2))+(pow(y,2)));

      double xveloc, yvelocnew, yvelocold, yveloc, rocketveloc;
      xveloc=(pow(x-(x-timeinterval),2));
      yvelocnew=((1/a)*(pow((x-h),2))+k);
      yvelocold=((1/a)*(pow(((x-timeinterval)-h),2))+k);
      yveloc=(yvelocnew-yvelocold)*(yvelocnew-yvelocold);
      rocketveloc=sqrt(xveloc+yveloc);


  if (x>bor){
   double time=x+(sqrt(rad*rad));
   double oops = (time-(abs(rad)-abs(bor)));
   whatis=5*oops;
   //cout<<"  #  "<<x<<"  #  "<<y<<"  #  "<<whatneedstobe<<"  #  "<<whatis<<"  #  "<<oops<< endl;
    if (whatneedstobe<=whatis){
     cout<<endl;
     cout<<"Interception at ( "<<x<<", "<<y<<")"<<endl;
     cout<<"Interception took "<<oops<<" seconds"<<endl;
     return 0;}
    if (x==crater){
     cout<<"Failure"<<endl;
     return 0;}
    //cout<<"whatis = "<<whatis<<" "<<"whatneedstobe = "<<whatneedstobe<<endl;



  }
  }
  }