模拟随机行走，假设位于原点的人在直线上往左或者往右随机行走1步，同时存在一个整数n，障碍物在n或者-n处，人遇到障碍物的时候停下。求解一下平均需要行走多少步。做图描述随着n的变化，随机行走的平均步数是如何变化的。
首先我们学习一下random模块几个常用的函数，这在今天求解问题的时候会用到。
random.randint(a, b)： 返回一个整数N，并且满足a <= N <= b。
random.random()：返回一个浮点数，并且范围是[0.0, 1.0)。
random.uniform(a, b)：返回一个浮点数，并且满足若a <= b则a <= N <= b，若b 根据以往的思路，咱们还是把大问题简单化。题目要求的是随着n的变化，我们考察对于某一个特定的n，随机行走的平均步数是多少。 先考察行走一步的情况，产生一个随机数，0表示向左走，1表示向右走。看看走这一步的代码版本1： 然后咱们将问题变得复杂一些，考虑一次随机行走，遇到n或者-n则停止，版本2如下： 还有两个问题需要考虑，其一是对于特定的n需要求解多次随机行走的平均步数，其二是随着n的变化，随机行走的平均步数是如何变化的。 我们需要在版本1的基础上进行循环才能解决问题1，还需要另外一个循环才能解决问题2。 那么有什么使得代码更简洁易懂的方法呢？答案肯定是有的，那就是定义函数randomWalk，接收参数n并且返回一次随机行走的步数。函数的定义方法如下： def randomWalk( n ) 其中，def是Python的关键字，randomWalk是函数名，而n是参数。函数的最后通常会有返回值，在本例中返回的就是一次随机行走的步数，即return length。 函数定义即版本3的代码如下： 有了randomWalk这个函数，我们很容易求解一次随机行走的步数，即： 同理，对于多次随机行走平均步数的求解，代码也变得简单易读，如下代码是随机行走100次的平均步数： 然而，我们要考虑随着n的变化随机行走的平均步数，是还需要对上述代码进行循环。思考到这里，你是否有方法使得代码更简洁易懂？ 对，答案还是定义函数。函数获取两个参数，即n和随机行走的次数numRepititions，函数的定义版本4的代码如下： 最终，我们考察n=10,20，...，100的时候，随机行走100次的平均步数，主程序代码如下： 小编在电脑上运行了一下，结果是113，415，937，1501，2356，4066，4965，6358，8313，10468。当然不同的执行结果肯定不一样了，这也是随机函数的魅力了。用MATLAB软件画一下图，似乎是更是直观： 今天，你学会这种随机行走的奥秘了吗？跟你的想象有什么区别吗？配图几米的漫画是否让你想起了某段时光？学完之后，欣赏一下几米的漫画《向左走，向右走》吧。import random
# Programmer: Python那些事
# Date: April 16, 2017
# Version 1: moves the person one step, either left or right, at random
location = 0 # tracks the person's current location
step = random.randint(0, 1) # returns 0 or 1, each with prob. 1/2
# Adjusts the random number to be either -1 or +1
if step == 0:
step = -1
location = location + step # updates location
print(location)import random
# Programmer: Python那些事
# Date: April 16, 2017
# Version 2: moves at random, one step at a time, left or right
# until the person reaches a barrier n or -n. Outputs the number of steps
# it took to reach the barrier
location = 0 # tracks the person's current location
n = 10 # value of the barrier
length = 0 # tracks the length of the random walk
# This moves the person until she reaches the barrier at n or -n
while abs(location) < n:
step = random.randint(0, 1) # returns 0 or 1, each with prob. 1/2
# Adjusts the random number to be either -1 or +1
if step == 0:
step = -1
location = location + step # updates location
length = length + 1
print(length)import random
# Programmer: Python那些事
# Date: April 16, 2017
# Version 3: moves at random, one step at a time, left or right,
# until the person reaches a barrier n or -n. Outputs the number of steps
# it took to reach the barrier
# This function takes in the value of the barrier, simulates a random
# walk that terminates on reaching the barrier, and returns the length
# of the simulated random walk
def randomWalk(n):
location = 0 # tracks the person's current location
length = 0 # tracks the length of the random walk
# This moves the person until she reaches the barrier at n or -n
while abs(location) != n:
step = random.randint(0, 1) # returns 0 or 1, each with prob. 1/2
# Adjusts the random number to be either -1 or +1
if step == 0:
step = -1
location = location + step # updates location
length = length + 1
return lengthn = input("Enter a positive integer: ")
print(randomWalk(n))# This is the main part of the program (i.e., outside the function)
n = input("Enter the value of the barrier (a positive integer): ")
sum = 0 # track the total length of all simulated random walks
counter = 0
# The simulation is repeated 100 times
while counter < 100:
sum = sum + randomWalk(n)
counter = counter + 1
print(sum/100)# Simulates random walks with barrier n as many times as specified by
# numRepititions. Returns the average length of a walk.
def manyRandomWalks(n, numRepititions):
sum = 0 # tracks the total length of all simulated random walks
counter = 0 # tracks the number of walks being performed
while counter < numRepititions:
sum = sum + randomWalk(n)
counter = counter + 1
return sum/numRepititions# Main loop for generating various values of the barrier
# We use barrier values 10, 20, 30, 40,..., 100
n = 10
while n <= 100:
print manyRandomWalks(n, 100)
n = n + 10
