// Prog: grader.cpp
// computes grade corresponding to number of points
#include <iostream>
#include <cassert>

class grader {
private:
  unsigned int p6; // 6.0 for at least p6 points
  unsigned int p4; // 4.0 for p4 points
  unsigned int p1; // 1.0 for at most p1 points

  // PRE:  hi yields grade g
  // POST: returns the smallest number of points which
  //       still yields grade g
  unsigned int from_here_to (unsigned int hi, double g)
  {			
    assert (grade (hi) == g);			
    unsigned int lo = hi;
    while (lo > 0 && grade (lo-1) == g) 
      --lo;
    return lo;
  }

public:
  // PRE:  top > pass > flop
  // POST: grader is initialized with the number of points
  //        - top (necessary to obtain grade 6.0)
  //        - pass (sufficient to obtain grade at least 4.0)
  //        - flop (up to this, grade 1.0 is obtained)
  grader (unsigned int top, unsigned int pass, unsigned int flop)
    : p6 (top), p4 (pass), p1 (flop)
  {
    assert (top > pass && pass > flop);
  }

  // POST: returns the grade obtained from p points, computed 
  //       through two different linear interpolations; one 
  //       between p_1 and p_4, and one between p_4 and p_6
  double grade (unsigned int p)
  {
    if (p >= p6) return 6.0;
    if (p <= p1) return 1.0;
    double ug; // unrounded grade
    if (p >= p4) 
      // p == p4 -> 4.0; p == p6 -> 6.0
      ug = 4.0 + 2.0 * (p - p4) / (p6 - p4);
    else
      // p == p1 -> 2.0; p == p4 -> 4.0
      ug = 1.0 + 3.0 * (p - p1) / (p4 - p1);
    // round down to next quarter grade
    unsigned int rg = 4 * ug;
    return 0.25 * rg;
  }
  
  // POST: prints the grading scale, where pm
  //       is the maximum number of points that
  //       can be achieved
  void print_grading_scale (unsigned int max)
  {
    double g = 6.0;
    unsigned int hi = max;
    for (;;) {
      // print range for grade g
      unsigned int lo = from_here_to (hi, g);
      std::cout << lo << " - " << hi << " : " << g << "\n";
      if (lo > 0) {
	hi = lo - 1;
	g = grade (hi);
      } else return;
    }
  }
};

int main() 
{
  const unsigned int max = 49;
  const unsigned int top = 46;
  const unsigned int pass = 27;
  const unsigned int flop = 5;

  grader g (top, pass, flop);
  g.print_grading_scale (max);

  return 0;
}