50 lines
1.2 KiB
Python
50 lines
1.2 KiB
Python
import random
|
|
|
|
# This class of problems is known as "resevoir sampling".
|
|
def choose_a(m, xs):
|
|
"""
|
|
Randomly choose `m` elements from `xs`.
|
|
This algorithm runs in linear time with respect to the size of `xs`.
|
|
"""
|
|
result = [None] * m
|
|
for i in range(len(xs)):
|
|
j = random.randint(0, i)
|
|
if j < m:
|
|
result[j] = xs[i]
|
|
return result
|
|
|
|
def choose_b(m, xs):
|
|
"""
|
|
This algorithm, which copies `xs`, which runs in linear time, and then
|
|
shuffles the copies, which also runs in linear time, achieves the same
|
|
result as `choose_a` and both run in linear time.
|
|
|
|
`choose_a` is still preferable since it has a coefficient of one, while this
|
|
version has a coefficient of two because it copies + shuffles.
|
|
"""
|
|
ys = xs[:]
|
|
random.shuffle(ys)
|
|
return ys[:m]
|
|
|
|
def choose_c(m, xs):
|
|
"""
|
|
This is one, possibly inefficient, way to randomly sample `m` elements from
|
|
`xs`.
|
|
"""
|
|
choices = set()
|
|
while len(choices) < m:
|
|
choices.add(random.randint(0, len(xs) - 1))
|
|
return [xs[i] for i in choices]
|
|
|
|
# ROYGBIV
|
|
xs = [
|
|
'red',
|
|
'orange',
|
|
'yellow',
|
|
'green',
|
|
'blue',
|
|
'indigo',
|
|
'violet',
|
|
]
|
|
print(choose_b(3, xs))
|
|
print(choose_c(3, xs))
|