我正在尝试编写 Python 代码来查看平均需要掷多少次硬币才能连续出现 N 个正面朝上的序列。
让我感到困惑的是,我的代码生成的答案与在线给出的答案不匹配,例如这里(和许多其他地方)https://math.stackexchange.com/questions/364038/expected-number-of-coin-tosses-to-get-five-consecutive-heads
据此,我需要连续获得各种正面朝上的预期 throw 次数为:E(1) = 2, E(2) = 6, E(3) = 14, E( 4) = 30, E(5) = 62。但我没有得到这些答案!例如,我得到 E(3) = 8,而不是 14。运行下面的代码给出该答案,但您可以更改 n 以测试连续出现正面的其他目标数量。
出了什么问题?大概我的代码逻辑有问题,但我承认我无法弄清楚它是什么。
您可以在此处查看、运行和制作我的代码的修改副本:https://trinket.io/python/17154b2cbd
下面是代码本身,位于可运行的 trinket.io 页面之外。如果您能帮助找出问题所在,我们将不胜感激!
非常感谢,
拉杰 附言我能找到的最接近的相关问题是这个:Monte-Carlo Simulation of expected tosses for two consecutive heads in python 然而,据我所知,该问题中的代码实际上并没有测试两个 连续 头,而是测试一个以头开始的序列,然后在稍后的某个时间,可能是非连续,时间得到另一个头。
# Click here to run and/or modify this code:
# https://trinket.io/python/17154b2cbd
import random
# n is the target number of heads in a row
# Change the value of n, for different target heads-sequences
n = 3
possible_tosses = [ 'h', 't' ]
num_trials = 1000
target_seq = ['h' for i in range(0,n)]
toss_sequence = []
seq_lengths_rec = []
for trial_num in range(0,num_trials):
if (trial_num % 100) == 0:
print 'Trial num', trial_num, 'out of', num_trials
# (The free version of trinket.io uses Python2)
target_reached = 0
toss_num = 0
while target_reached == 0:
toss_num += 1
random.shuffle(possible_tosses)
this_toss = possible_tosses[0]
#print([toss_num, this_toss])
toss_sequence.append(this_toss)
last_n_tosses = toss_sequence[-n:]
#print(last_n_tosses)
if last_n_tosses == target_seq:
#print('Reached target at toss', toss_num)
target_reached = 1
seq_lengths_rec.append(toss_num)
print 'Average', sum(seq_lengths_rec) / len(seq_lengths_rec)
最佳答案
您不需要为每个实验重新初始化 toss_sequence
,因此您使用预先存在的正面序列开始每个实验,有二分之一的机会在第一次击中目标序列尝试每个新实验。
在外循环中初始化 toss_sequence
将解决您的问题:
import random
# n is the target number of heads in a row
# Change the value of n, for different target heads-sequences
n = 4
possible_tosses = [ 'h', 't' ]
num_trials = 1000
target_seq = ['h' for i in range(0,n)]
seq_lengths_rec = []
for trial_num in range(0,num_trials):
if (trial_num % 100) == 0:
print('Trial num {} out of {}'.format(trial_num, num_trials))
# (The free version of trinket.io uses Python2)
target_reached = 0
toss_num = 0
toss_sequence = []
while target_reached == 0:
toss_num += 1
random.shuffle(possible_tosses)
this_toss = possible_tosses[0]
#print([toss_num, this_toss])
toss_sequence.append(this_toss)
last_n_tosses = toss_sequence[-n:]
#print(last_n_tosses)
if last_n_tosses == target_seq:
#print('Reached target at toss', toss_num)
target_reached = 1
seq_lengths_rec.append(toss_num)
print(sum(seq_lengths_rec) / len(seq_lengths_rec))
您可以稍微简化您的代码,使其不易出错:
import random
# n is the target number of heads in a row
# Change the value of n, for different target heads-sequences
n = 3
possible_tosses = [ 'h', 't' ]
num_trials = 1000
seq_lengths_rec = []
for trial_num in range(0, num_trials):
if (trial_num % 100) == 0:
print('Trial num {} out of {}'.format(trial_num, num_trials))
# (The free version of trinket.io uses Python2)
heads_counter = 0
toss_counter = 0
while heads_counter < n:
toss_counter += 1
this_toss = random.choice(possible_tosses)
if this_toss == 'h':
heads_counter += 1
else:
heads_counter = 0
seq_lengths_rec.append(toss_counter)
print(sum(seq_lengths_rec) / len(seq_lengths_rec))
关于python - Python 中的 Q : Expected number of coin tosses to get N heads in a row,。我的代码给出的答案与已发布的正确答案不匹配,但不确定原因,我们在Stack Overflow上找到一个类似的问题: https://stackoverflow.com/questions/55377700/