Problem
In a drunkard's walk, the drunkard starts out at a random point. At each time unit, the drunkard takes one step in a randomly chosen direction. The question is, how far will the drunkard travel after a given number of steps? Of course, the distance traveled will depend on the particular path that the drunkard takes, so we should really ask, what is the average distance traveled by a drunkard after a given number of steps. To investigate this question, you will run a large number of drunkard's walk experiments and compute the average distance traveled.
To keep things simple, we will assume that the drunkard's position is given by two int values, x and y. At each step, the drunkard can move in one of eight directions, chosen at random. This will change the values of x and y as shown in the diagram at the right.