선형 합동 의사 난수 생성기
O (1) 메모리
O (k) 작업
이 문제는 간단한 선형 합동 생성기 로 해결할 수 있습니다. . 이를 위해서는 일정한 메모리 오버 헤드 (8 개의 정수)와 최대 2 * (시퀀스 길이) 계산이 필요합니다.
다른 모든 솔루션은 더 많은 메모리와 더 많은 컴퓨팅을 사용합니다! 무작위 시퀀스가 몇 개만 필요한 경우이 방법이 훨씬 저렴합니다. size 범위의 N경우 N고유 k시퀀스 이상의 순서로 생성하려는 경우 속도를 위해 파이썬 에서 최적화되었으므로 기본 제공 방법 random.sample(range(N),k)을 사용하여 허용되는 솔루션을 권장합니다 .
암호
# Return a randomized "range" using a Linear Congruential Generator
# to produce the number sequence. Parameters are the same as for
# python builtin "range".
# Memory -- storage for 8 integers, regardless of parameters.
# Compute -- at most 2*"maximum" steps required to generate sequence.
#
def random_range(start, stop=None, step=None):
import random, math
# Set a default values the same way "range" does.
if (stop == None): start, stop = 0, start
if (step == None): step = 1
# Use a mapping to convert a standard range into the desired range.
mapping = lambda i: (i*step) + start
# Compute the number of numbers in this range.
maximum = (stop - start) // step
# Seed range with a random integer.
value = random.randint(0,maximum)
#
# Construct an offset, multiplier, and modulus for a linear
# congruential generator. These generators are cyclic and
# non-repeating when they maintain the properties:
#
# 1) "modulus" and "offset" are relatively prime.
# 2) ["multiplier" - 1] is divisible by all prime factors of "modulus".
# 3) ["multiplier" - 1] is divisible by 4 if "modulus" is divisible by 4.
#
offset = random.randint(0,maximum) * 2 + 1 # Pick a random odd-valued offset.
multiplier = 4*(maximum//4) + 1 # Pick a multiplier 1 greater than a multiple of 4.
modulus = int(2**math.ceil(math.log2(maximum))) # Pick a modulus just big enough to generate all numbers (power of 2).
# Track how many random numbers have been returned.
found = 0
while found < maximum:
# If this is a valid value, yield it in generator fashion.
if value < maximum:
found += 1
yield mapping(value)
# Calculate the next value in the sequence.
value = (value*multiplier + offset) % modulus
용법
이 함수 "random_range"의 사용법은 모든 생성기 ( "range"와 같은)와 동일합니다. 예 :
# Show off random range.
print()
for v in range(3,6):
v = 2**v
l = list(random_range(v))
print("Need",v,"found",len(set(l)),"(min,max)",(min(l),max(l)))
print("",l)
print()
샘플 결과
Required 8 cycles to generate a sequence of 8 values.
Need 8 found 8 (min,max) (0, 7)
[1, 0, 7, 6, 5, 4, 3, 2]
Required 16 cycles to generate a sequence of 9 values.
Need 9 found 9 (min,max) (0, 8)
[3, 5, 8, 7, 2, 6, 0, 1, 4]
Required 16 cycles to generate a sequence of 16 values.
Need 16 found 16 (min,max) (0, 15)
[5, 14, 11, 8, 3, 2, 13, 1, 0, 6, 9, 4, 7, 12, 10, 15]
Required 32 cycles to generate a sequence of 17 values.
Need 17 found 17 (min,max) (0, 16)
[12, 6, 16, 15, 10, 3, 14, 5, 11, 13, 0, 1, 4, 8, 7, 2, ...]
Required 32 cycles to generate a sequence of 32 values.
Need 32 found 32 (min,max) (0, 31)
[19, 15, 1, 6, 10, 7, 0, 28, 23, 24, 31, 17, 22, 20, 9, ...]
Required 64 cycles to generate a sequence of 33 values.
Need 33 found 33 (min,max) (0, 32)
[11, 13, 0, 8, 2, 9, 27, 6, 29, 16, 15, 10, 3, 14, 5, 24, ...]