mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 09:10:16 +00:00
110 lines
3.0 KiB
Python
110 lines
3.0 KiB
Python
import math
|
|
from collections.abc import Generator
|
|
|
|
|
|
def slow_primes(max_n: int) -> Generator[int, None, None]:
|
|
"""
|
|
Return a list of all primes numbers up to max.
|
|
>>> list(slow_primes(0))
|
|
[]
|
|
>>> list(slow_primes(-1))
|
|
[]
|
|
>>> list(slow_primes(-10))
|
|
[]
|
|
>>> list(slow_primes(25))
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23]
|
|
>>> list(slow_primes(11))
|
|
[2, 3, 5, 7, 11]
|
|
>>> list(slow_primes(33))
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
|
|
>>> list(slow_primes(1000))[-1]
|
|
997
|
|
"""
|
|
numbers: Generator = (i for i in range(1, (max_n + 1)))
|
|
for i in (n for n in numbers if n > 1):
|
|
for j in range(2, i):
|
|
if (i % j) == 0:
|
|
break
|
|
else:
|
|
yield i
|
|
|
|
|
|
def primes(max_n: int) -> Generator[int, None, None]:
|
|
"""
|
|
Return a list of all primes numbers up to max.
|
|
>>> list(primes(0))
|
|
[]
|
|
>>> list(primes(-1))
|
|
[]
|
|
>>> list(primes(-10))
|
|
[]
|
|
>>> list(primes(25))
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23]
|
|
>>> list(primes(11))
|
|
[2, 3, 5, 7, 11]
|
|
>>> list(primes(33))
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
|
|
>>> list(primes(1000))[-1]
|
|
997
|
|
"""
|
|
numbers: Generator = (i for i in range(1, (max_n + 1)))
|
|
for i in (n for n in numbers if n > 1):
|
|
# only need to check for factors up to sqrt(i)
|
|
bound = int(math.sqrt(i)) + 1
|
|
for j in range(2, bound):
|
|
if (i % j) == 0:
|
|
break
|
|
else:
|
|
yield i
|
|
|
|
|
|
def fast_primes(max_n: int) -> Generator[int, None, None]:
|
|
"""
|
|
Return a list of all primes numbers up to max.
|
|
>>> list(fast_primes(0))
|
|
[]
|
|
>>> list(fast_primes(-1))
|
|
[]
|
|
>>> list(fast_primes(-10))
|
|
[]
|
|
>>> list(fast_primes(25))
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23]
|
|
>>> list(fast_primes(11))
|
|
[2, 3, 5, 7, 11]
|
|
>>> list(fast_primes(33))
|
|
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
|
|
>>> list(fast_primes(1000))[-1]
|
|
997
|
|
"""
|
|
numbers: Generator = (i for i in range(1, (max_n + 1), 2))
|
|
# It's useless to test even numbers as they will not be prime
|
|
if max_n > 2:
|
|
yield 2 # Because 2 will not be tested, it's necessary to yield it now
|
|
for i in (n for n in numbers if n > 1):
|
|
bound = int(math.sqrt(i)) + 1
|
|
for j in range(3, bound, 2):
|
|
# As we removed the even numbers, we don't need them now
|
|
if (i % j) == 0:
|
|
break
|
|
else:
|
|
yield i
|
|
|
|
|
|
def benchmark():
|
|
"""
|
|
Let's benchmark our functions side-by-side...
|
|
"""
|
|
from timeit import timeit
|
|
|
|
setup = "from __main__ import slow_primes, primes, fast_primes"
|
|
print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
|
|
print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
|
|
print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
number = int(input("Calculate primes up to:\n>> ").strip())
|
|
for ret in primes(number):
|
|
print(ret)
|
|
benchmark()
|