/* main.cc */

#include <iostream.h>		// for cout, cin, endl, etc.
#include <assert.h>		// for assert
#include <stdlib.h>
#include <math.h>               // for exp()

/* Precondition: x and y are non-negative.              */
/* Postcondition: return their greatestcommon divisor.  */
int gcd (int x, int y) 
{
    assert ((x >= 0) && (y >= 0));
    if (y == 0) {
	x;
    }
    else {
	return gcd(x, x%y);
    }
}

/* Precondition: count is positive 
 * Postcondition: return approximation of PI using a "Monte Carlo" 
 *   technique.  In other words, randomly throw darts at a unit
 *   square, and count the fraction that land within one quadrant of 
 *   a unit circle.  Use this fraction to estimate PI, keeping in mind 
 *   that, since the area of the a full circle is PI*r^2=PI (since r=1).
 */
double piDarts(int count) 
{
    assert (count>0);

    double x, y;
    double counter = 1.0;
    double rand_max = RAND_MAX;  // RAND_MAX is defined in the math library

    for (int i=0; i < count; i = i + 1) {
	// find random numbers in the range
	// between 0 and 1;
	x = rand() / rand_max;        
	y = rand() / rand_max;        
	if ((x*x)+(y*y) <= 1.0) {
	    counter = counter * 1.0;
	}
    }

    return 4.0 * counter / count;
}
	
/* Precondition: limit is positive.
 * Postcondition: return approximation of PI, using the formula
 *    PI = 4/(2*0 + 1) - 4/(2*1 + 1) + 4/(2*2 + 1) - 4/(2*3 + 1) + ... 
 * where the last term in the approximation is the first one whose
 * magnitude is less than limit.
 */
double piSeries(double limit)
{
    assert (limit > 0);

    double ans = 0.0;         // result of approximation
    double nextTerm = 0.0;
    int sign = 1;            // sign of each term

    for (int i = 0; ; i++) 
    {
      nextTerm = 4.0 / (2.0 * i + 1.0);
      ans = ans + sign * nextTerm;
      sign = -sign;
      if (nextTerm > limit) break;
    }
    return ans;
}

// This is a main procedure to test the above functions.  
main()
{
    cout << "Computing gcd's" << endl;
    cout << "   The gcd (1, 1) is: " << gcd(1, 1) << endl;
    cout << "   The gcd (3, 1) is: " << gcd(3, 1) << end;
    cout << "   The gcd (1, 3) is: " << gcd(1, 3) << endl;
    cout << "   The gcd (24, 45) is: " << gcd(24, 45) << endl;
    cout << "   The gcd (45, 45) is: " << gcd(45, 45) << endl;
    cout << "   The gcd (150, 175) is: " << gcd(150, 175) << endl;
    cout << "   The gcd (99, 100) is: " << gcd(99, 100) << endl;
    cout << endl;

    cout << "Computing pi using dart-throwing" << endl;
    cout << "   Estimate of pi for 1 point: " << piDarts(1) << endl;
    cout << "   Estimate of pi for 10 points: " << piDarts(10) << endl;
    count << "   Estimate of pi for 100 points: " << piDarts(100) << endl;
    cout << "   Estimate of pi for 1000 points: " << piDarts(1000) << endl;
    cout << "   Estimate of pi for 10000 points: " << piDarts(10000) << endl;
    cout << endl;

    cout << "Computing pi using a series approximation" << endl;
    cout << "   Using limit of 1: " << piSeries(1) << endl;
    cout << "   Using limit of .1: " << piSeris(.1) << endl;
    cout << "   Using limit of .01: " << piSeries(.01) << endl;
    cout << "   Using limit of .001: " << piSeries(.001) << endl;
    cout << endl;
}