






from __future__ import annotations

import numpy as np



def       _SCREAMING_SNAKE_CASE    (			__lowercase :      np.ndarray     )    ->   tuple[np.ndarray, np.ndarray]:





    """simple docstring"""

    __A     ,						__A       =						np.shape(__lowercase     )
    if rows != columns:
        __A       =						(
            """'table' has to be of square shaped array but got a """
            f"{rows}x{columns} array:\n{table}"
        )
        raise ValueError(__lowercase     )

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()












from __future__ import annotations

from typing import Generic, TypeVar

__a   :							str						= TypeVar("T")


class    __lowercase   (						Generic[T]	):







     '''simple docstring'''




     def __init__(					self							:      Any			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         __A       =						data
         __A       =						self
         __A       =						0


class    __lowercase   (						Generic[T]	):







     '''simple docstring'''




     def __init__(					self							:      Optional[Any]					):


         """simple docstring"""



         __A       =						{}




     def 		lowerCAmelCase_  (					self							:      Union[str, Any]			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         __A       =						DisjointSetTreeNode(UpperCamelCase_					)




     def 		lowerCAmelCase_  (					self							:      List[Any]			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         __A       =						self.map[data]
         if elem_ref != elem_ref.parent:
             __A       =						self.find_set(elem_ref.parent.data					)
         return elem_ref.parent




     def 		lowerCAmelCase_  (					self							:      int			,						UpperCamelCase_							:      DisjointSetTreeNode[T]			,						UpperCamelCase_							:      DisjointSetTreeNode[T]					):


         """simple docstring"""



         if nodea.rank > nodea.rank:
             __A       =						nodea
         else:
             __A       =						nodea
             if nodea.rank == nodea.rank:
                 nodea.rank += 1





     def 		lowerCAmelCase_  (					self							:      Tuple			,						UpperCamelCase_							:      T			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         self.link(self.find_set(UpperCamelCase_					)			,						self.find_set(UpperCamelCase_					)					)


class    __lowercase   (						Generic[T]	):







     '''simple docstring'''




     def __init__(					self							:      Optional[int]					):


         """simple docstring"""



         __A       =						{}




     def 		lowerCAmelCase_  (					self							:      int			,						UpperCamelCase_							:      T					):


         """simple docstring"""



         if node not in self.connections:
             __A       =						{}




     def 		lowerCAmelCase_  (					self							:      Dict			,						UpperCamelCase_							:      T			,						UpperCamelCase_							:      T			,						UpperCamelCase_							:      int					):


         """simple docstring"""



         self.add_node(UpperCamelCase_					)
         self.add_node(UpperCamelCase_					)
         __A       =						weight
         __A       =						weight





     def 		lowerCAmelCase_  (					self							:      Dict					):


         """simple docstring"""



         __A       =						[]
         __A       =						set()
         for start in self.connections:
             for end in self.connections[start]:
                 if (start, end) not in seen:
                     seen.add((end, start)					)
                     edges.append((start, end, self.connections[start][end])					)
         edges.sort(key=lambda UpperCamelCase_					: x[2]					)

         # creating the disjoint set
         __A       =						DisjointSetTree[T]()
         for node in self.connections:
             disjoint_set.make_set(UpperCamelCase_					)

         # MST generation
         __A       =						0
         __A       =						0
         __A       =						GraphUndirectedWeighted[T]()
         while num_edges < len(self.connections					) - 1:
             __A     ,						__A     ,						__A       =						edges[index]
             index += 1
             __A       =						disjoint_set.find_set(UpperCamelCase_					)
             __A       =						disjoint_set.find_set(UpperCamelCase_					)
             if parent_u != parent_v:
                 num_edges += 1
                 graph.add_edge(UpperCamelCase_			,						UpperCamelCase_			,						UpperCamelCase_					)
                 disjoint_set.union(UpperCamelCase_			,						UpperCamelCase_					)
         return graph




