#include "stdstuff.h"
#include "odds.h"

// Here's a solution to the "food for thought" part of the assignment.

int _count = 0; 

double probabilityOfState (int AWins, int GWins) {

  double result;

  if (AWins+GWins>7) { result = 0.0; return result; }

  if ((AWins == 0) && (GWins == 0)) {

    result = 1.0; 
    _count++; // count every time we get to here

  } else  if ((AWins == 0) || (GWins == 4)) {

    result = probabilityOfState (AWins, GWins - 1) *
             (1 - probabilityOfAngelVictory (AWins, GWins - 1));

  } else if ((GWins == 0) || (AWins == 4)) {

    result = probabilityOfState (AWins - 1, GWins) *
             probabilityOfAngelVictory (AWins - 1, GWins);

  } else {

    result =
      ( probabilityOfState (AWins, GWins - 1) *
        (1 - probabilityOfAngelVictory (AWins, GWins - 1)) ) +
      ( probabilityOfState (AWins - 1, GWins) *
        probabilityOfAngelVictory (AWins - 1, GWins) );
  }

  return result;

}


void realMain () {

  int i, j;
  double P, AngelsP = 0, GiantsP = 0;

  cout << setiosflags (ios::fixed | ios::showpoint) << setprecision(6);

  // Let's create a new table where probOFIJ[i][j] represents the probability that at 
  // some point in the series, the Angels have won i games and the Giants have won j.  
  // Note that we calculate this using probabilityOfState.

  double probOfIJ [5][5];

  for (i=0; i<=4; i++) {
	  for (j=0; j<=4; j++) {
		  probOfIJ[i][j]=probabilityOfState(i,j);
	  }
  }

  // Let's now print out the table, so we can have a look at it.

  cout << "\nHere's the new probOfIJ table (i, j, and value):\n";

  for (i=0; i<=4; i++) {
	  for (j=0; j<=4; j++) {
		  cout << "\n" << i << " "<< j << " " << probOfIJ[i][j];
	  }
  }

  cout << "\n\nHere are the old calculations:\n";

  for (i = 0; i <= 3; i++) {
    P = probabilityOfState (4, i);
    cout << "The probability of the Angels winning in " << (4 + i)
         << " games is " << P << ".\n";
    AngelsP += P;
    P = probabilityOfState (i, 4);
    cout << "The probability of the Giants winning in " << (4 + i)
         << " games is " << P << ".\n";
    GiantsP += P;
  }

  cout << "\nThe probability of the Angels winning the series is "
       << AngelsP << ".\n";
  cout << "The probability of the Giants winning the series is "
       << GiantsP << ".\n";

  cout << "\nThe sum of all of the probabilities is "
       << (AngelsP + GiantsP) << ".\n";

  cout << "\nNow let's see how many times probabilityOfAngelVictory is called ";
  cout << "\nwhen calculating the probability of the Angels winning in 7 games:\n";

  _count = 0;

  P = probabilityOfState(4,3);
  cout << "\nThe probability of the Angels winning in 7 games is " <<  P << ".\n";

  cout << "The number of times the recursive function was called for (0,0) is "
       << _count << ".\n";

  cout << "\nNow let's do the calculations using probOfIJ instead:\n";

  AngelsP = GiantsP = 0;

  for (i = 0; i <= 3; i++) {
    P = probOfIJ[4][i];
    cout << "The probability of the Angels winning in " << (4 + i)
         << " games is " << P << ".\n";
    AngelsP += P;
    P = probOfIJ[i][4];
    cout << "The probability of the Giants winning in " << (4 + i)
         << " games is " << P << ".\n";
    GiantsP += P;
  }

  cout << "\nThe probability of the Angels winning the series is "
       << AngelsP << ".\n";
  cout << "The probability of the Giants winning the series is "
       << GiantsP << ".\n";

  cout << "\nThe sum of all of the probabilities is "
       << (AngelsP + GiantsP) << ".\n";

  P = probOfIJ[4][3];
  cout << "\nThe probability of the Angels winning in 7 games is " <<  P << ".\n";

  cout << "Note that we don't have any recursive calls this time!\n\n";

}


int main () {

  try {

    realMain ();

  }
  catch (exception &e) { // catches all uncaught exceptions

    cout << "\nException <" << e.what() << "> occurred.\n";

  }

  pause ();
  return 0;

}