Random number generator

Содержание:

Примеры использования модуля random.
Bookkeeping functions¶
Почему это очень плохо?
Real-valued distributions¶
Игра в кости с использованием модуля random в Python
Guide to Random Drawings
- Blog and Business Giveaways
- Audited Lotteries and Sweepstakes
Functions for sequences¶
Official iPhone and Android App
Choosing Order
Предыстория
Другие функции генерации распределений
Функции для получения целых «случайных» чисел – randint() и randrange()
Функции управления генератором
Where are random numbers useful?
Создание случайного пароля пользователя
Но ведь Unity заботится об объеме используемой ОЗУ
Метод sample(population, k) из модуля random

Примеры использования модуля random.

Базовое применение модуля:

>>> import random
# Случайное float:  0.0 <= x < 1.0
>>> random.random()
# 0.37444887175646646

# Случайное float:  2.5 <= x < 10.0
>>> random.uniform(2.5, 10.0)
# 3.1800146073117523

# Интервал между прибытием в среднем 5 секунд
>>> random.expovariate(1  5)
# 5.148957571865031

# Четное целое число от 0 до 100 включительно
>>> random.randrange(10)
# 7

# Even integer from 0 to 100 inclusive
>>> random.randrange(, 101, 2)
26

# Один случайный элемент из последовательности
>>> random.choice()
'draw'

>>> deck = 'ace two three four'.split()
# Перемешать список
>>> random.shuffle(deck)
>>> deck
'four', 'two', 'ace', 'three'

# Четыре образца без замены
>>> random.sample(, k=4)
#

Имитационные расчеты:

# Шесть вращений колеса рулетки (взвешенная выборка с заменой)
>>> choices(, 18, 18, 2], k=6)
# 

# Сдайте 20 карт без замены из колоды из 52 игральных карт
# и определите пропорцию карт с достоинством в: 
# десять, валет, дама или король.
>>> dealt = sample(, counts=16, 36], k=20)
>>> dealt.count('tens')  20
# 0.15

# Оценка вероятности получения 5 или более попаданий из 7 
# бросаний монеты, которая выпадает орлом в 60% случаев.
>>> def trial():
...     return choices('HT', cum_weights=(0.60, 1.00), k=7).count('H') >= 5
...
>>> sum(trial() for i in range(10_000))  10_000
# 0.4169

>>> # Вероятность того, что медиана из 5 выборок находится в средних двух квартилях
>>> def trial():
...     return 2_500 <= sorted(choices(range(10_000), k=5))[2 < 7_500
...
>>> sum(trial() for i in range(10_000))  10_000
# 0.7958

Пример статистической начальной загрузки с использованием повторной выборки с заменой для оценки доверительного интервала для среднего значения выборки:

# http://statistics.about.com/od/Applications/a/Example-Of-Bootstrapping.htm
from statistics import fmean as mean
from random import choices

data = 41, 50, 29, 37, 81, 30, 73, 63, 20, 35, 68, 22, 60, 31, 95
means = sorted(mean(choices(data, k=len(data))) for i in range(100))
print(f'The sample mean of {mean(data).1f} has a 90% confidence '
      f'interval from {means5.1f} to {means94.1f}')

Пример теста перестановки повторной выборки для определения статистической значимости или Р-значения наблюдаемой разницы между эффектами препарата и плацебо:

# Example from "Statistics is Easy" by Dennis Shasha and Manda Wilson
from statistics import fmean as mean
from random import shuffle

drug = 54, 73, 53, 70, 73, 68, 52, 65, 65
placebo = 54, 51, 58, 44, 55, 52, 42, 47, 58, 46
observed_diff = mean(drug) - mean(placebo)

n = 10_000
count = 
combined = drug + placebo
for i in range(n):
    shuffle(combined)
    new_diff = mean(combined) - mean(combinedlen(drug):])
    count += (new_diff >= observed_diff)

print(f'{n} label reshufflings produced only {count} instances with a difference')
print(f'at least as extreme as the observed difference of {observed_diff.1f}.')
print(f'The one-sided p-value of {count  n.4f} leads us to reject the null')
print(f'hypothesis that there is no difference between the drug and the placebo.')

Моделирование времени прибытия и доставки услуг для многосерверной очереди:

from heapq import heappush, heappop
from random import expovariate, gauss
from statistics import mean, median, stdev

average_arrival_interval = 5.6
average_service_time = 15.0
stdev_service_time = 3.5
num_servers = 3

waits = []
arrival_time = 0.0
servers = 0.0 * num_servers  # time when each server becomes available
for i in range(100_000):
    arrival_time += expovariate(1.0  average_arrival_interval)
    next_server_available = heappop(servers)
    wait = max(0.0, next_server_available - arrival_time)
    waits.append(wait)
    service_duration = gauss(average_service_time, stdev_service_time)
    service_completed = arrival_time + wait + service_duration
    heappush(servers, service_completed)

print(f'Mean wait: {mean(waits).1f}.  Stdev wait: {stdev(waits).1f}.')
print(f'Median wait: {median(waits).1f}.  Max wait: {max(waits).1f}.')

Bookkeeping functions¶

(a=None, version=2)

Модуль random на примерах

Initialize the random number generator.

If a is omitted or , the current system time is used. If
randomness sources are provided by the operating system, they are used
instead of the system time (see the function for details
on availability).

If a is an int, it is used directly.

With version 2 (the default), a , , or
object gets converted to an and all of its bits are used.

With version 1 (provided for reproducing random sequences from older versions
of Python), the algorithm for and generates a
narrower range of seeds.

Changed in version 3.2: Moved to the version 2 scheme which uses all of the bits in a string seed.

Deprecated since version 3.9: In the future, the seed must be one of the following types:
NoneType, , , ,
, or .

(): Return an object capturing the current internal state of the generator. This
object can be passed to to restore the state.

Почему это очень плохо?

Теория вероятностей на практике или знаете ли вы о random

Как минимум — игроки заметят и в дело вступит эффект отмены.

Как максимум, придется изобретать костыль, чтобы вернуть seed в предыдущее состояние после вызова метода . Если вернуть значение нельзя, потому что «случайные» значения постоянно используются, то придется перед каждым использование Random принудительно проставлять seed.

Это замечательный пример того, как неправильное использование статических классов. В результате мы получим:

Жесткую связность. Неявная завязка на реализацию одного конкретного класса. Он не передается через конструктор, не инжектится через свойство, а мы просто пишем
Каскадное изменение поведения там, где это не нужно, но где используется статическая зависимость.

Real-valued distributions¶

Как сгенерировать случайное число в java

The following functions generate specific real-valued distributions. Function
parameters are named after the corresponding variables in the distribution’s
equation, as used in common mathematical practice; most of these equations can
be found in any statistics text.

(): Return the next random floating point number in the range [0.0, 1.0).

(a, b)

Return a random floating point number N such that for
and for .

The end-point value may or may not be included in the range
depending on floating-point rounding in the equation .

(low, high, mode): Return a random floating point number N such that and
with the specified mode between those bounds. The low and high bounds
default to zero and one. The mode argument defaults to the midpoint
between the bounds, giving a symmetric distribution.

(alpha, beta): Beta distribution. Conditions on the parameters are and
. Returned values range between 0 and 1.

(lambd): Exponential distribution. lambd is 1.0 divided by the desired
mean. It should be nonzero. (The parameter would be called
“lambda”, but that is a reserved word in Python.) Returned values
range from 0 to positive infinity if lambd is positive, and from
negative infinity to 0 if lambd is negative.

(alpha, beta)

Gamma distribution. (Not the gamma function!) Conditions on the
parameters are and .

The probability distribution function is:

          x ** (alpha - 1) * math.exp(-x  beta)
pdf(x) =  --------------------------------------
            math.gamma(alpha) * beta ** alpha

(mu, sigma)

Gaussian distribution. mu is the mean, and sigma is the standard
deviation. This is slightly faster than the function
defined below.

Multithreading note: When two threads call this function
simultaneously, it is possible that they will receive the
same return value. This can be avoided in three ways.
1) Have each thread use a different instance of the random
number generator. 2) Put locks around all calls. 3) Use the
slower, but thread-safe function instead.

(mu, sigma): Log normal distribution. If you take the natural logarithm of this
distribution, you’ll get a normal distribution with mean mu and standard
deviation sigma. mu can have any value, and sigma must be greater than
zero.

(mu, sigma): Normal distribution. mu is the mean, and sigma is the standard deviation.

(mu, kappa): mu is the mean angle, expressed in radians between 0 and 2*pi, and kappa
is the concentration parameter, which must be greater than or equal to zero. If
kappa is equal to zero, this distribution reduces to a uniform random angle
over the range 0 to 2*pi.

(alpha): Pareto distribution. alpha is the shape parameter.

Игра в кости с использованием модуля random в Python

Далее представлен код простой игры в кости, которая поможет понять принцип работы функций модуля random. В игре два участника и два кубика.

Участники по очереди бросают кубики, предварительно встряхнув их;
Алгоритм высчитывает сумму значений кубиков каждого участника и добавляет полученный результат на доску с результатами;
Участник, у которого в результате большее количество очков, выигрывает.

Код программы для игры в кости Python:

Python

import random

PlayerOne = «Анна»
PlayerTwo = «Алекс»

AnnaScore = 0
AlexScore = 0

# У каждого кубика шесть возможных значений
diceOne =
diceTwo =

def playDiceGame():
«»»Оба участника, Анна и Алекс, бросают кубик, используя метод shuffle»»»

for i in range(5):
#оба кубика встряхиваются 5 раз
random.shuffle(diceOne)
random.shuffle(diceTwo)
firstNumber = random.choice(diceOne) # использование метода choice для выбора случайного значения
SecondNumber = random.choice(diceTwo)
return firstNumber + SecondNumber

print(«Игра в кости использует модуль random\n»)

#Давайте сыграем в кости три раза
for i in range(3):
# определим, кто будет бросать кости первым
AlexTossNumber = random.randint(1, 100) # генерация случайного числа от 1 до 100, включая 100
AnnaTossNumber = random.randrange(1, 101, 1) # генерация случайного числа от 1 до 100, не включая 101

if( AlexTossNumber > AnnaTossNumber):
print(«Алекс выиграл жеребьевку.»)
AlexScore = playDiceGame()
AnnaScore = playDiceGame()
else:
print(«Анна выиграла жеребьевку.»)
AnnaScore = playDiceGame()
AlexScore = playDiceGame()

if(AlexScore > AnnaScore):
print («Алекс выиграл игру в кости. Финальный счет Алекса:», AlexScore, «Финальный счет Анны:», AnnaScore, «\n»)
else:
print(«Анна выиграла игру в кости. Финальный счет Анны:», AnnaScore, «Финальный счет Алекса:», AlexScore, «\n»)

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importrandom

PlayerOne=»Анна»

PlayerTwo=»Алекс»

AnnaScore=

AlexScore=

# У каждого кубика шесть возможных значений

diceOne=1,2,3,4,5,6

diceTwo=1,2,3,4,5,6

defplayDiceGame()

«»»Оба участника, Анна и Алекс, бросают кубик, используя метод shuffle»»»

foriinrange(5)

#оба кубика встряхиваются 5 раз

random.shuffle(diceOne)

random.shuffle(diceTwo)

firstNumber=random.choice(diceOne)# использование метода choice для выбора случайного значения

SecondNumber=random.choice(diceTwo)

returnfirstNumber+SecondNumber

print(«Игра в кости использует модуль random\n»)

#Давайте сыграем в кости три раза

foriinrange(3)

# определим, кто будет бросать кости первым

AlexTossNumber=random.randint(1,100)# генерация случайного числа от 1 до 100, включая 100

AnnaTossNumber=random.randrange(1,101,1)# генерация случайного числа от 1 до 100, не включая 101

if(AlexTossNumber>AnnaTossNumber)

print(«Алекс выиграл жеребьевку.»)

AlexScore=playDiceGame()

AnnaScore=playDiceGame()

else

print(«Анна выиграла жеребьевку.»)

AnnaScore=playDiceGame()

AlexScore=playDiceGame()

if(AlexScore>AnnaScore)

print(«Алекс выиграл игру в кости. Финальный счет Алекса:»,AlexScore,»Финальный счет Анны:»,AnnaScore,»\n»)

else

print(«Анна выиграла игру в кости. Финальный счет Анны:»,AnnaScore,»Финальный счет Алекса:»,AlexScore,»\n»)

Вывод:

Shell

Игра в кости использует модуль random

Анна выиграла жеребьевку.
Анна выиграла игру в кости. Финальный счет Анны: 5 Финальный счет Алекса: 2

Анна выиграла жеребьевку.
Анна выиграла игру в кости. Финальный счет Анны: 10 Финальный счет Алекса: 2

Алекс выиграл жеребьевку.
Анна выиграла игру в кости. Финальный счет Анны: 10 Финальный счет Алекса: 8

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Игравкостииспользуетмодульrandom

Аннавыигралажеребьевку.

Аннавыигралаигрувкости.ФинальныйсчетАнны5ФинальныйсчетАлекса2

Аннавыигралажеребьевку.

Аннавыигралаигрувкости.ФинальныйсчетАнны10ФинальныйсчетАлекса2

Алексвыигралжеребьевку.

Аннавыигралаигрувкости.ФинальныйсчетАнны10ФинальныйсчетАлекса8

Вот и все. Оставить комментарии можете в секции ниже.

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Functions for sequences¶

(seq): Return a random element from the non-empty sequence seq. If seq is empty,
raises .

(population, weights=None, *, cum_weights=None, k=1)

Return a k sized list of elements chosen from the population with replacement.
If the population is empty, raises .

If a weights sequence is specified, selections are made according to the
relative weights. Alternatively, if a cum_weights sequence is given, the
selections are made according to the cumulative weights (perhaps computed
using ). For example, the relative weights
are equivalent to the cumulative weights
. Internally, the relative weights are converted to
cumulative weights before making selections, so supplying the cumulative
weights saves work.

If neither weights nor cum_weights are specified, selections are made
with equal probability. If a weights sequence is supplied, it must be
the same length as the population sequence. It is a
to specify both weights and cum_weights.

The weights or cum_weights can use any numeric type that interoperates
with the values returned by (that includes
integers, floats, and fractions but excludes decimals). Behavior is
undefined if any weight is negative. A is raised if all
weights are zero.

For a given seed, the function with equal weighting
typically produces a different sequence than repeated calls to
. The algorithm used by uses floating
point arithmetic for internal consistency and speed. The algorithm used
by defaults to integer arithmetic with repeated selections
to avoid small biases from round-off error.

New in version 3.6.

Changed in version 3.9: Raises a if all weights are zero.

(x, random)

Shuffle the sequence x in place.

The optional argument random is a 0-argument function returning a random
float in [0.0, 1.0); by default, this is the function .

To shuffle an immutable sequence and return a new shuffled list, use
instead.

Note that even for small , the total number of permutations of x
can quickly grow larger than the period of most random number generators.
This implies that most permutations of a long sequence can never be
generated. For example, a sequence of length 2080 is the largest that
can fit within the period of the Mersenne Twister random number generator.

Deprecated since version 3.9, will be removed in version 3.11: The optional parameter random.

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