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python factorizaion function
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import time | |
from functools import wraps | |
def timeit(f): | |
@wraps(f) | |
def inner(*x, **y): | |
a = time.monotonic() | |
r = f(*x, **y) | |
b = time.monotonic() | |
print(f"elapsed: {b-a:.3f}s") | |
return r | |
return inner | |
@timeit | |
def factorization(n: int) -> list[tuple[int, int]]: | |
res = [] | |
if n < 2: | |
return res | |
p = 2 | |
def helper(p: int) -> int: | |
if p < 6: | |
return (3, 5, 7)[(p - 1) // 2] | |
t = 1 if p % 3 == 1 else 0 | |
l = int(n ** 0.5 + 0.5) + 1 | |
while p < l: | |
p, t = p + (2, 4)[t], (t + 1) % 2 | |
if n % p == 0: | |
return p | |
return n | |
while n > 1: | |
e = 0 | |
while n % p == 0: | |
n, e = n // p, e + 1 | |
if e > 0: | |
res.append((p, e)) | |
p = helper(p) | |
return res | |
@timeit | |
def fac(n: int) -> list[tuple[int, int]]: | |
"enhanced version" | |
res = [] | |
if n < 2: | |
return res | |
i = 1 | |
def helper(k: int) -> int: | |
if k < 3: | |
return k + 1 | |
if k < 8: | |
return k + 2 | |
k = k + (4 if k % 3 == 1 else 2) | |
l = int(n ** 0.5 + 1.5) | |
while k < l: | |
if n % k == 0: | |
return k | |
if n % (k + 2) == 0: | |
return k + 2 | |
k += 6 | |
return n | |
while n > 1: | |
e = 0 | |
i = helper(i) | |
while n % i == 0: | |
n, e = n // i, e + 1 | |
if e > 0: | |
res.append((i, e)) | |
return res | |
if __name__ == "__main__": | |
ns = [3800651, 560411670, 10000128400406539] | |
for n in ns: | |
print(fac(n)) | |
print(factorization(n)) |
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