random_walk.py

import random

def random_walk(n):
    """Return coordinates after 'n' block random walk."""
    x, y = 0, 0
    for i in range(n):
        #                           N       S      E       W
        (dx, dy) = random.choice([(0,1), (0,-1), (1,0), (-1,0)])
        x += dx
        y += dy
    return (x, y)

#for i in range(25):
#    walk = random_walk(10)
#    print(walk, "Distance from home = ", abs(walk[0]) + abs(walk[1]))

number_of_walks = 20000

for walk_length in range(1, 31):
    no_transport = 0 # Number of walks 4 or fewer blocks from home
    for i in range(number_of_walks):
        (x,y) = random_walk(walk_length)
        distance = abs(x) + abs(y)
        if distance <= 4:
            no_transport += 1
    no_transport_percentage = float(no_transport) / number_of_walks
    print("Walk size = ", walk_length,
          " / % of no transport = ", 100*no_transport_percentage)

# Challenge: Find the longest random walk which will, on average, leave you
# less than 5 blocks from home.