"""
 random walk problem, chapter 9 exercise 13

 two dimensions (x,y)
 

 in class, version 2 Thu Nov 10
"""

import random
from math import sqrt

def average(numbers):
    """ Return mean of a list of numbers.
        >>> average([1, 2, 3])
        2.0
        >>> average([])
        0.0
    """
    if len(numbers) == 0:
        return 0.0
    return float(sum(numbers))/len(numbers)

def random_walk_xy(n_steps):
    """ Return distance from start after random walk of n steps.
        in two dimensions.
        >>> distance = random_walk_xy(10)
        >>> 0 <= distance <= 10
        True
    """
    (x, y) = (0, 0)
    for i in range(n_steps):
        (dx, dy) = random.choice([(0,1), (1,0), (0,-1), (-1,0)])
        (x, y) = (x + dx, y + dy)
    return sqrt(x**2 + y**2)

def main():
    print "Finding average distance in 2D from random walk of n steps"
    steps = int(input("What is number of steps? "))
    iterations = 100
    distances = []
    for i in range(iterations):
        distances.append(random_walk_xy(steps))
    print "First few walks: %i, %i, %i" % \
        (distances[0], distances[1], distances[2])
    mean = average(distances)
    print "The mean of %i walks of %i steps is %.2f" % \
        (iterations, steps, mean)

if __name__ == "__main__":
    from doctest import testmod
    testmod()
    main()