/*	Koen Noens
*	september 2003
*
*	multopler choice tool; probability calculation,
*
*	what is the probability to achieve a given score by randomly answering
*	a given number of questions, each with a given number of multiple choice
*	answers.
*
*/


/* TO DO
	check casting and/or find a way to use larger numbers
*/

#include  <iostream.h>

//functies
void showLogo();
void showIntro();
void doBlankLines(unsigned char n);
void getInitData(unsigned int &n, unsigned int  &a, unsigned int &p, unsigned int &t, float &f);
unsigned int NumberCorrectAnswersNeeded(unsigned int n, unsigned int p, unsigned int t, float f);
float FairPunishment(unsigned int t, unsigned int a);
long double power(float a, unsigned int b);
long frac(unsigned int a);
long frac(unsigned int a, unsigned int b);
long combinations(unsigned int set, unsigned int subset);
long double cumulprob(unsigned int n, unsigned int k, unsigned int a);
long double binomialprob(unsigned int n, unsigned int k, unsigned int a);
void getDecision(unsigned char &c);

void main()
{ 
		//variables
		unsigned int n=0; //number of questions
		unsigned int a=0; //number of options per question (multiple choice)
		unsigned int p=0; //points needed to pass te test
		unsigned int t=0; //points to be earned with a correct answer
		float f=0; //points to subtract for a wrong answer
		unsigned int c=0; //number of correct answers given by student
		unsigned int w=0; //number of wrong answers given by student
		unsigned int k=0; //number of questions that need to be answered correctly in order to pass this test
		unsigned char decision = 'Y' ;	//decision to continue or not
		

		while(decision == 'Y')
		{
			cout << "decision : "<< decision << endl;
			showLogo(); 
			getInitData(n,a,p,t,f);

			k=NumberCorrectAnswersNeeded(n, p, t, f);
			cout << "gambling student needs to guess at least "<< k <<" questions correctly\n";
		
			cout <<"\n\nThere is a probability of " << (float) cumulprob(n,k,a) << " % " << endl 
				<< " to pass this test on pure guess work" << endl << endl
				<< " wanna risk it ... ?" << endl << endl;
		
			//continue?
			doBlankLines(4);
			getDecision(decision);
		};

		//wait to exit
		cin.get();
};


long combinations(unsigned int set, unsigned int subset)
{/*	number of combinations of a subset in a set 
 */
	//return ( frac(set) / ( frac(subset) * frac(set - subset) ) ) ;
	return frac(set, subset);
}

long double binomprob(unsigned int n, unsigned int k, unsigned int a)
{//binomial probabolity, result in  %
	long double result;
	long double bpcoeff;
	long double p;
	long double q;

	bpcoeff = frac(n) / ( frac(k) * frac(n-k) ) ;
	
	p = float(1)/a; 
	q = (float)(a-1)/a;

	p = power(p,k);
	q = power(q,(n-k));

	result = bpcoeff * p * q * 100;	// resultaat in %
	return result;

}
long double cumulprob(unsigned int n, unsigned int k, unsigned int a)
{
	/* calculate  of combinations of a subset in a set
	*	given that for  set choose subset, 
	*	set choose subset+1, subset+2 etc need to be considered as well, 
	*	until subset+n = set
	*/
	long double result = 0.0;
	while (k <= n)
	{
		result = result + binomprob (n, k, a ) ;
		k++;
	};
	return result;
}

unsigned int NumberCorrectAnswersNeeded(unsigned int n, unsigned int p, unsigned int t, float f)
{//calculate how many correct answers you need in order to pass this test,

	float temp;
	unsigned  int result;

	temp = (p + (n*f)) / (t + f);
	result = int(temp);

	//round up, but only if there are decimals
	if((temp - result)!=0)
	{
		result += 1;
	}
	return result;
}

float FairPunishment(unsigned int t, unsigned int a)
{
	return ( (float)t /(a-1) );
}

void getInitData(unsigned int &n, unsigned int  &a, unsigned int &p, unsigned int &t, float &f)
{
	do {
			cout <<"number of questions : ";
			cin >> n;
			if(n>15) //frac functie overflow when > 15
			{
				cout << "this number may be too large for the program to function correctly.\n Try a number smaller than 16\n";
			}
		}
	while(n>15);

	cout << "multiple choice : how many answers to a question ? : ";
	cin >> a;

	cout <<"points earned by correct answer : ";
	cin >> t;

	cout << "total points for this test : " << n*t << endl;

	cout <<"points needed to pass : ";
	cin >> p;

	cout <<"points subtracted per wrong answer (suggestion : " <<FairPunishment(t,a)<<") : ";
	cin >> f;

	//random solutions
	cout << "\nThis test has  " << (long)power((float)a,n) << "  possible solutions.\n\n";
	

}


long double power(float a, unsigned int b)
{//returns a ^ b. no negative exponents allowed

	long double result=1;

	//unsigned power
	for(unsigned int i=0; i<b;i++)
	{
		result *= a;
	};
	if(b=0){ result = 1; };	//by definition
	return result;
}


long frac(unsigned int a)
{/*	returns fractional of a
  *			frac(a) = a! = 1 * 2 * 3 * 4 * ... * a
  */
	long result = 1;
	for(unsigned int i = 1; i<=a;i++)
	{
		result = result*i;
	}
	if(a=0)
	{
		result = 1;
	}
	return result;
}

long frac(unsigned int a, unsigned int b)
{/*	returns 
  *			frac(a)/frac(b) = a!/b! = a  * (a-1) * ... b
  */
	long result = 1;
	for(unsigned int i = b; b<=a;b++)
	{
		result = result*i;
	}
	if(a=0)
	{
		result = 1;
	}
	return result;
}

void getDecision(unsigned char &c)
{
	cout << "calculate new situation ?" << endl;
	
	do
	{
		cin >> c;
		//uppercase A-Z only : ascii 65-90
		if(c>90)
		{
			c -=32;		//from a = 97 to A = 65 etc.
		};
		if(c<65 || c>90)
		{
			cout << "invalid choice. Choose Y / N \n";
		};
	}while(c<65 || c>90);

	//screen layout
	doBlankLines(65);
}

void showIntro()
{
	cout << "Multiple Choice Tool\n\nCalculate the probability of passing a test by answering randomly to a given number of multiple choice questions\n\n" ;
}

void showLogo()
{
	cout <<"\n\n\t\t\tSilly Software Productions\n\n\t\t\t\t-=oOo=-\n\n";
	showIntro();
}

void doBlankLines(unsigned char n)
{
	// do n blank lines
	for(int i = 0;i<=n;i++)
	{cout << "\n";
	}
}