Python库 | pupy-2.11.0.tar.gz

# -*- coding: utf-8 -*- # ~ Jesse K. Rubin ~ Pretty Useful Python from collections import Counter from math import acos from math import factorial from math import pi from math import sqrt from operator import add from operator import floordiv from operator import methodcaller from operator import sub from operator import truediv from typing import Any from typing import Iterator from typing import List from typing import Optional from typing import Set from typing import Tuple from typing import Type from typing import Union from pupy.decorations import cash_it from pupy.foreign import iter_product def partitions_gen( numero: int, min_p: int = 1, max_p: Optional[int] = None ) -> Iterator[ Union[Tuple[int, int], Tuple[int, int, int], Tuple[int], Tuple[int, int, int, int]] ]: """Partitions generator Adapted from: code.activestate.com/recipes/218332-generator-for-integer-partitions/min_p :param numero: number for which to yield partiton tuples :type numero: int :param min_p: smallest part size (Default value = 1) :type min_p: int :param max_p: largest part size (Default value = None) :type max_p: int .. docstring::python >>> list(partitions_gen(4)) [(4,), (1, 3), (1, 1, 2), (1, 1, 1, 1), (2, 2)] >>> list(partitions_gen(4, min_p=1, max_p=2)) [(1, 1, 2), (1, 1, 1, 1), (2, 2)] """ if max_p is None or max_p >= numero: yield (numero,) for i in range(min_p, numero // 2 + 1): for p in partitions_gen(numero - i, i, max_p): yield (i,) + p @cash_it def rfactorial(n: int) -> int: """Recursive factorial function :param n: .. docstring::python >>> from math import factorial >>> rfactorial(1) == factorial(1) True >>> rfactorial(2) == factorial(2) True >>> rfactorial(3) == factorial(3) True >>> rfactorial(4) == factorial(4) True >>> rfactorial(5) == factorial(5) True >>> rfactorial(6) == factorial(6) True >>> rfactorial(7) == factorial(7) True >>> rfactorial(8) == factorial(8) True >>> rfactorial(9) == factorial(9) True """ if n == 1: return 1 else: return rfactorial(n - 1) * n def radians_2_degrees(rads: float) -> float: """Converts radians to degrees :param rads: .. doctest:: python >>> from math import pi >>> radians_2_degrees(2*pi) == 360.0 True >>> radians_2_degrees(2*pi) 360.0 """ return 180 * rads / pi def degrees_2_radians(degs: float) -> float: """Converts degrees to radians :param degs: .. doctest:: python >>> from math import pi >>> degrees_2_radians(360.0) == 2*pi True """ return degs * pi / 180 def power_mod(number: int, exponent: int, mod: int) -> int: """ :param number: :param exponent: :param mod: .. doctest:: python >>> power_mod(2, 4, 3) 2 >>> power_mod(12, 3, 4) 144 >>> power_mod(123, 2, 3) 123 >>> power_mod(120, 6, 10) 14400 >>> power_mod(120, 6, 1) 14400 """ if exponent > 0: if exponent % 2 == 0: return power_mod(number, floordiv(exponent, 2), mod) return power_mod(number, floordiv(exponent, 2), mod) * number else: return 1 def divisors_gen(n: int) -> Iterator[int]: """Divisors generator :param n: number w/ divisors to be generated :type n: int .. doctest:: python >>> list(divisors_gen(1)) [1] >>> list(divisors_gen(4)) [1, 2, 4] >>> list(divisors_gen(16)) [1, 2, 4, 8, 16] """ large_divisors = [] for i in range(1, int(sqrt(n) + 1)): if n % i == 0: yield i if i * i != n: large_divisors.append(n // i) for divisor in reversed(large_divisors): yield divisor def gcd_it(a: int, b: int) -> int: """iterative gcd :param a: :param b: >>> from pupy.maths import gcd_it >>> from pupy.maths import gcd_r >>> gcd_it(1, 4) == gcd_r(1, 4) True >>> gcd_it(2, 6) == gcd_r(2, 6) True >>> gcd_it(3, 14) == gcd_r(3, 14) True >>> gcd_it(4, 300) == gcd_r(4, 300) True """ while a: a, b = b % a, a return b @cash_it def gcd_r(a: int, b: int) -> int: """recursive greatest common divisor :param a: :param b: .. doctest:: python >>> from pupy.maths import gcd_it >>> from pupy.maths import gcd_r >>> gcd_it(1, 4) == gcd_r(1, 4) True >>> gcd_it(2, 6) == gcd_r(2, 6) True >>> gcd_it(3, 14) == gcd_r(3, 14) True >>> gcd_it(4, 300) == gcd_r(4, 300) True """ if b > a: return gcd_r(b, a) r = a % b if r == 0: return b return gcd_r(r, b) def reverse(n: int) -> int: """Reverses a number :param n: number to be reversed :type n: int :returns: reversed of a number :rtype: int .. doctest:: python >>> reverse(1) 1 >>> reverse(12345) 54321 >>> reverse(54321) 12345 >>> reverse(54321000) 12345 """ reversed = 0 while n > 0: reversed *= 10 reversed += n % 10 n //= 10 return reversed @cash_it def fib_r(n: int) -> int: """Recursively the nth fibonacci number :param n: nth fibonacci sequence number :type n: int :returns: the nth fibonacci number :rtype: int .. doctest:: python >>> fib_r(1) 1 >>> fib_r(2) 2 >>> fib_r(6) 13 """ return n if n < 3 else fib_r(n - 1) + fib_r(n - 2) def expo(d: int, n: int) -> int: """greatest exponent for a divisor of n :param d: divisor :type d: int :param n: number be divided :type n: int :returns: number of times a divisor divides n :rtype: int .. doctest:: python >>> expo(100, 2) 2 >>> expo(12, 5) 0 >>> expo(12, 2) 2 >>> expo(160, 4) 2 >>> expo(1000, 4) 1 """ if n < d: # flip d, n = n, d c = n divs = 0 while c % d == 0: c //= d divs += 1 return divs def pytriple_gen(max_c: int) -> Iterator[Tuple[int, int, int]]: """primative pythagorean triples generator special thanks to 3Blue1Brown's video on pythagorean triples https://www.youtube.com/watch?v=QJYmyhnaaek&t=300s :param max_c: max value of c to yeild triples up to :type max_c: int """ for real_pts in range(2, int(sqrt(max_c)) + 1, 1): for imag_pts in range(real_pts % 2 + 1, real_pts, 2): comp = complex(real_pts, imag_pts) sqrd = comp * comp real = int(sqrd.real) imag = int(sqrd.imag) if abs(real - imag) % 2 == 1 and gcd_it(imag, real) == 1: sea = int((comp * comp.conjugate()).real) if sea > max_c: break else: yield (imag, real, sea) if real > imag else (real, imag, sea) def n_permutations_with_replacements( it: Union[ Tuple[int, int, int, int], Tuple[int, int, int, int, int, int, int], Tuple[int, int, int, int, int], Tuple[int, int, int, int, int, int], ] ) -> int: """ .. doctest:: python >>> n_permutations_with_replacements((1, 2, 3, 4)) 24 >>> n_permutations_with_replacements((1, 2, 3, 4, 3)) 60 >>> n_permutations_with_replacements((1, 2, 3, 4, 3, 3)) 120 >>> n_permutations_with_replacements((1, 2, 3, 4, 3, 4, 4)) 420 """ c = Counter(n for n in it) a =