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Merged
merged 3 commits into from
Sep 14, 2022
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Itertools sieve() recipe #96813

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26943e7
Add sieve() recipe to demonstrate count, islice, and compress
rhettinger Sep 13, 2022
5669975
Group imports together and make arrow notation consistent
rhettinger Sep 13, 2022
17d2266
Change variable to "p" for "prime"
rhettinger Sep 13, 2022
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34 changes: 28 additions & 6 deletions Doc/library/itertools.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -314,7 +314,7 @@ loops that truncate the stream.

def count(start=0, step=1):
# count(10) --> 10 11 12 13 14 ...
# count(2.5, 0.5) -> 2.5 3.0 3.5 ...
# count(2.5, 0.5) --> 2.5 3.0 3.5 ...
n = start
while True:
yield n
Expand Down Expand Up @@ -739,7 +739,7 @@ which incur interpreter overhead.

def prepend(value, iterator):
"Prepend a single value in front of an iterator"
# prepend(1, [2, 3, 4]) -> 1 2 3 4
# prepend(1, [2, 3, 4]) --> 1 2 3 4
return chain([value], iterator)

def tabulate(function, start=0):
Expand Down Expand Up @@ -812,6 +812,16 @@ which incur interpreter overhead.
for k in range(len(roots) + 1)
]

def sieve(n):
"Primes less than n"
# sieve(30) --> 2 3 5 7 11 13 17 19 23 29
data = bytearray([1]) * n
data[:2] = 0, 0
limit = math.isqrt(n) + 1
for p in compress(count(), islice(data, limit)):
data[p+p : n : p] = bytearray(len(range(p+p, n, p)))
return compress(count(), data)

def flatten(list_of_lists):
"Flatten one level of nesting"
return chain.from_iterable(list_of_lists)
Expand Down Expand Up @@ -842,12 +852,12 @@ which incur interpreter overhead.

def triplewise(iterable):
"Return overlapping triplets from an iterable"
# triplewise('ABCDEFG') -> ABC BCD CDE DEF EFG
# triplewise('ABCDEFG') --> ABC BCD CDE DEF EFG
for (a, _), (b, c) in pairwise(pairwise(iterable)):
yield a, b, c

def sliding_window(iterable, n):
# sliding_window('ABCDEFG', 4) -> ABCD BCDE CDEF DEFG
# sliding_window('ABCDEFG', 4) --> ABCD BCDE CDEF DEFG
it = iter(iterable)
window = collections.deque(islice(it, n), maxlen=n)
if len(window) == n:
Expand Down Expand Up @@ -1079,6 +1089,7 @@ which incur interpreter overhead.
>>> import operator
>>> import collections
>>> import math
>>> import random

>>> take(10, count())
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
Expand Down Expand Up @@ -1128,7 +1139,6 @@ which incur interpreter overhead.
>>> list(repeatfunc(pow, 5, 2, 3))
[8, 8, 8, 8, 8]

>>> import random
>>> take(5, map(int, repeatfunc(random.random)))
[0, 0, 0, 0, 0]

Expand Down Expand Up @@ -1156,10 +1166,22 @@ which incur interpreter overhead.
>>> all(factored(x) == expanded(x) for x in range(-10, 11))
True

>>> list(sieve(30))
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
>>> len(list(sieve(100)))
25
>>> len(list(sieve(1_000)))
168
>>> len(list(sieve(10_000)))
1229
>>> len(list(sieve(100_000)))
9592
>>> len(list(sieve(1_000_000)))
78498

>>> list(flatten([('a', 'b'), (), ('c', 'd', 'e'), ('f',), ('g', 'h', 'i')]))
['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i']

>>> import random
>>> random.seed(85753098575309)
>>> list(repeatfunc(random.random, 3))
[0.16370491282496968, 0.45889608687313455, 0.3747076837820118]
Expand Down