#include <cmath>
#include <iostream>
#include <iomanip>
 
using namespace std;
 
class Trap
{
 private:
 float sidea;//function of time
 float sideb;//function of time
 float width;//representation of time passed
 float area;//water discharged
 public:
 float Y(float);//calculates side lengths
 void Area(float);//durr
 void Width(float nwidth){width = nwidth;};//assings width for sep. runs
 float GetArea(){return area;};
};
 
 
int main()
{
 cout << "This program calculates the rate of flow from a 3107g tank\n";
 cout << "over 10000 seconds using the trapezoidal method.\n";
 cout << "The chart below displays the calculated total flow \n";
 cout << "based on 100, 1000, 10000, and 100000 trapezoids.\n\n";
 
 cout << " Trapezoids  Total Discharge(gallons) Tank Capacity(gallons)\n";
 
 Trap zoids[100000];
 float Traplimits[5] = {10, 100, 1000, 10000, 100000};
 
 int trapcount;
 float sum;
 
 //loops through the calculations with different numbers of trapezoids
 //being calculated for
 for(int i = 0; i < 5; i++)
   {
      trapcount = 0;
      sum = 0;
 
      //loops through array of trapezoids assigning new width
      //and then calculating area again
      for( int c = 0; c < Traplimits[i]; c++)
      {
           zoids[c].Width(10000/Traplimits[i]);
           zoids[c].Area(trapcount++);
 
      }
 
      //sums the areas of all calculated trapezoids in this run
      for( int p = 0; p < Traplimits[i]; p++)
           sum += zoids[p].GetArea();
 
      cout << fixed << showpoint << setprecision(2) << left;
      cout << setw(14) << Traplimits[i];
      cout << setw(27) << sum;
      cout << "3107\n";
 
   }
 
   cin.get();
   cin.get();
   return 0;
 
}
 
float Trap::Y(float time)
{
    return 200 * ( (2/(time + 1)) - exp(-0.693*(time + 1)) );
}
 
void Trap::Area(float tcount)
{
    // sidea  = Y(time passed until beginning of trapezoid
    sidea = Y(tcount++ * width);
 
    //sideb = Y(time passed up to end of trapezoid
    sideb = Y(tcount * width);
 
    //formula for area of a trapezoid
    area = 0.5 * (sidea + sideb) * width;
    cout << area << endl;
}