#include <iostream.h>
#include <math.h>


const double g = 9.8; // metres/sec


double compute_distance (double angle /* in degrees */,
                         double initial_velocity /* in m/s */,
                         double height /* in m */ ) {

  double angle_radians = angle * (M_PI / 180.0),
         vel_v, vel_h; // vertical and horizontal components of initial velocity

  vel_v = sin(angle_radians) * initial_velocity;
  vel_h = cos(angle_radians) * initial_velocity;

  return ( ( vel_v + sqrt ((vel_v * vel_v) + (2 * g * height)) ) / g ) * vel_h;

}


void compute_and_output (double min_velocity, double max_velocity,
                         double height, double angle, double distance) {

  double low, high, mid, computed_distance;

  // make sure that we can hit the target
  if (distance < compute_distance (angle, min_velocity, height)) {
    cout << "\nTarget is too close to be hit.\n";
    return;
  }
  if (distance > compute_distance (angle, max_velocity, height)) {
    cout << "\nTarget is too far away to be hit.\n";
    return;
  }

  low = min_velocity; high = max_velocity;

  for (;;) {

    mid = (high + low) / 2;

    if ((high - low) < 0.0002) {
      // velocity is within 0.0001 of the correct answer
      cout << "\nA velocity of " << mid << " m/s should work fine.\n"
           << "This velocity is within 0.0001 of the theoretical value.\n";
      return;
    }

    computed_distance = compute_distance (angle, mid, height);

    if (fabs(computed_distance - distance) < 0.001) {
      // distance within 0.01 of desired distance
      cout << "\nA velocity of " << mid << " m/s will do nicely.\n"
           << "This will put you within 0.001 m of the target.\n";
      return;
    }

    if (computed_distance > distance) {
      high = mid;
    } else {
      low = mid;
    }

  }

}


void main (void) {

  double angle, min_velocity, max_velocity, launch_height,
         target_height, distance;

  cout << "Welcome to the CAT-1 artillery control system!\n"
       << "\nPlease enter your minium and maximum launch velocities: (in m/s): ";
  cin >> min_velocity >> max_velocity;

  cout << "Please enter height of release point (in m): ";
  cin >> launch_height;

  cout << "Please enter release angle (in degrees from the horizontal: ";
  cin >> angle;

  cout << "\nThank you - the system is now calibrated for your installation.\n";

  for (;;) {

    cout << "\nEnter distance to target and target height (zeroes to stop): ";
    cin >> distance >> target_height;

    if ((distance == 0) && (target_height == 0)) {
      return;
    }
    
    if (distance <= 0) {

      cout << "\nSorry - distance must be > 0.\n";

    } else if (target_height > launch_height) {

      cout << "Sorry - target height must be <= the launch height.\n";

    } else {

      compute_and_output (min_velocity, max_velocity,
                          launch_height - target_height, angle, distance);

    }

  }

}