






def 				snake_case__							(							UpperCAmelCase							:  int    ,			UpperCAmelCase							:  int       ):
    while b:
        lowerCAmelCase__   :List[str]      							=				b, a % b
    return a


def 				snake_case__							(							UpperCAmelCase							:  int    ,			UpperCAmelCase							:  int       ):
    return a if b == 0 else euclidean_gcd_recursive(snake_case_    ,			a % b       )


def 				snake_case__							(							):
    print(F'''euclidean_gcd(3, 5) = {euclidean_gcd(3    ,			5       )}'''       )
    print(F'''euclidean_gcd(5, 3) = {euclidean_gcd(5    ,			3       )}'''       )
    print(F'''euclidean_gcd(1, 3) = {euclidean_gcd(1    ,			3       )}'''       )
    print(F'''euclidean_gcd(3, 6) = {euclidean_gcd(3    ,			6       )}'''       )
    print(F'''euclidean_gcd(6, 3) = {euclidean_gcd(6    ,			3       )}'''       )

    print(F'''euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3    ,			5       )}'''       )
    print(F'''euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5    ,			3       )}'''       )
    print(F'''euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1    ,			3       )}'''       )
    print(F'''euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3    ,			6       )}'''       )
    print(F'''euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6    ,			3       )}'''       )


if __name__ == "__main__":
 main()











from __future__ import annotations

import numpy as np


def 				snake_case__							(							UpperCAmelCase							:  np.ndarray       ):
    lowerCAmelCase__							,lowerCAmelCase__   :List[str]      							=				np.shape(UpperCAmelCase       )
    if rows != columns:
        lowerCAmelCase__   :Tuple      							=				(
            "'table' has to be of square shaped array but got a "
            F'''{rows}x{columns} array:\n{table}'''
        )
        raise ValueError(UpperCAmelCase       )

    lowerCAmelCase__   :Optional[Any]      							=				np.zeros((rows, columns)       )
    lowerCAmelCase__   :Tuple      							=				np.zeros((rows, columns)       )
    for i in range(UpperCAmelCase       ):
        for j in range(UpperCAmelCase       ):
            lowerCAmelCase__   :Any      							=				sum(lower[i][k] * upper[k][j] for k in range(UpperCAmelCase       )       )
            if upper[j][j] == 0:
                raise ArithmeticError("No LU decomposition exists"       )
            lowerCAmelCase__   :Any      							=				(table[i][j] - total) / upper[j][j]
        lowerCAmelCase__   :Tuple      							=				1
        for j in range(UpperCAmelCase    ,			UpperCAmelCase       ):
            lowerCAmelCase__   :Optional[Any]      							=				sum(lower[i][k] * upper[k][j] for k in range(UpperCAmelCase       )       )
            lowerCAmelCase__   :Dict      							=				table[i][j] - total
    return lower, upper


if __name__ == "__main__":
 import doctest

 doctest.testmod()



