/* ------------------------------------------------------------------- 
// Figure 14.24: A Monte Carlo approximation.                 
// Figure 14.26: Functions for the Monte Carlo simulation.    
// ------------------------------------------------------------------- 
*/
#include "tools.h" 

#define BOX_SIDE  2.0           /* Length of side of bounding box. */ 
typedef struct POINT { double x, y; } point_type ; 

bool inside( point_type p );
double simulate( int max, double box_side );

void main( void )                                                 
{  
    double area;    /* Approximate area of unit circle. */  
    int trials;     /* Loop limit. */          

    banner(); 
    puts( " Monte Carlo Approximation to Area of a Unit Circle" );
    srand( (unsigned)time( NULL ) );   /* seed random number generator */

    printf( " Number of random trials to use = " ); 
    scanf( "%i", &trials );
    
    area = simulate( trials, BOX_SIDE ); 
    printf( " With %i trials, estimate of circle area = %.4g\n", 
            trials, area ); 
    bye(); 
}

/* Is point p inside a unit circle? --------------------------------------- */
bool inside( point_type p ) 
{
    return sqrt( p.x * p.x + p.y * p.y ) < 1.0; 
}

/* Carry out the random trials -------------------------------------------- */
double simulate( int max, double box_side )
{ 
    point_type random;                      /* The point we select. */
    int k;                                  /* Loop counter. */
    int count = 0;                          /* Number of successful trials. */
    for (k = 0; k < max; ++k) {  
        /* Get random x and y coordinates for point. */
        random.x = (randy() -.5) * box_side;
        random.y = (randy() -.5) * box_side;    
        if (inside( random )) count += 1;   /* +1 if inside circle. */ 
    }  
    return box_side * box_side * ((double)count / max);
}