Page 17 problem in Introduction to Probability by Grinstead and Snell

randomWalks.py

import random

def SingleDimensionWalk(x,count):
    '''
    Write a program to simulate a random walk in one dimension starting at 0. 
    Have your program print out the lengths of the times between returns to the starting point (returns to 0).
    '''
    if random.randint(0,1):
        x+=1
    else:
        x-=1
    while x!= 0:
        count += 1
        if random.randint(0,1):
            x += 1
        else:
            x-=1
        #print(f"{x}")
    #print(f"{x}")
    return count


def TwoDimensionWalk(x,y,count):
    '''
    Write a program to simulate a random walk in two dimensions starting at (0,0).
    '''
    a = random.randint(0,3)
    if a == 0:
        x += 1 
    elif a == 1:
        x -= 1
    elif a == 2:
        y += 1
    else:
        #a == 3
        y -= 1
    while x!=0 or y!=0: #if either x or y are not equal to 0 keep going
        count += 1
        a = random.randint(0,3)
        if a == 0:
            x += 1 
        elif a == 1:
            x -= 1
        elif a == 2:
            y += 1
        else:
            #a == 3
            y -= 1
        #print(f"({x},{y})") 
    #print(f"({x},{y})") 
    return count
#TwoDimensionWalk(0,0,0)


walking_distances_2d = [] 
walking_distances = []       
for i in range(10):
    walking_distances.append(SingleDimensionWalk(0,0))
    walking_distances_2d.append(TwoDimensionWalk(0,0,0))
   
print(f"Max Walking Distance: {max(walking_distances)}")
print(f"Max Walking Distance 2D: {max(walking_distances_2d)}")