#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>

#ifndef M_PI  /* usually defined in math.h, but not in the ANSI standard */
#define M_PI 3.14159265358979323846
#endif

int main()
{
    int i, j;
    extern double drunkard(int nsteps);

    srand(time(NULL));

    for (i = 0; i <= 10; i++) {
        double total = 0;
        for (j = 0; j < 100; j++)
            total += drunkard(i);
        printf("%d\t%g\n", i, total / 100);
    }

    return 0;
}


double drunkard(int nsteps)  /* returns ending distance from origin */
{
    int i;
    double x, y;  /* current position */
    extern double randangle();

    x = y = 0;  /* start at (0,0) */
    for (i = 0; i < nsteps; i++) {
        double r = randangle();
        /* sin(r) is y distance (perhaps negative), cos(r) is x distance */
        y += sin(r);
        x += cos(r);
    }

    /* return cartesian distance to origin */
    return sqrt(x * x + y * y);
}


double randangle()  /* return a random angle in radians */
{
    return rand() / (RAND_MAX + 1.0) * 2 * M_PI;
}