





'''simple docstring'''






# Author: OMKAR PATHAK, Nwachukwu Chidiebere

# Use a Python dictionary to construct the graph.
from __future__ import annotations

from pprint import pformat
from typing import Generic, TypeVar

A__							:  str    =TypeVar('''T''')




class 					UpperCAmelCase	(     Generic[T]  ):




      def __init__(     self     :					Union[str, Any]     ,     __snake_case     :					bool = True    )							-> None:
            _lowerCAmelCase					=				{}  # dictionary of lists
            _lowerCAmelCase					=				directed




      def 							lowercase__       (     self     :					str     ,     __snake_case     :					T     ,     __snake_case     :					T    )							-> GraphAdjacencyList[T]:

            if not self.directed:  # For undirected graphs
                  # if both source vertex and destination vertex are both present in the
                  # adjacency list, add destination vertex to source vertex list of adjacent
                  # vertices and add source vertex to destination vertex list of adjacent
                  # vertices.
                  if source_vertex in self.adj_list and destination_vertex in self.adj_list:
                        self.adj_list[source_vertex].append(__snake_case    )
                        self.adj_list[destination_vertex].append(__snake_case    )
                  # if only source vertex is present in adjacency list, add destination vertex
                  # to source vertex list of adjacent vertices, then create a new vertex with
                  # destination vertex as key and assign a list containing the source vertex
                  # as it's first adjacent vertex.
                  elif source_vertex in self.adj_list:
                        self.adj_list[source_vertex].append(__snake_case    )
                        _lowerCAmelCase					=				[source_vertex]
                  # if only destination vertex is present in adjacency list, add source vertex
                  # to destination vertex list of adjacent vertices, then create a new vertex
                  # with source vertex as key and assign a list containing the source vertex
                  # as it's first adjacent vertex.
                  elif destination_vertex in self.adj_list:
                        self.adj_list[destination_vertex].append(__snake_case    )
                        _lowerCAmelCase					=				[destination_vertex]
                  # if both source vertex and destination vertex are not present in adjacency
                  # list, create a new vertex with source vertex as key and assign a list
                  # containing the destination vertex as it's first adjacent vertex also
                  # create a new vertex with destination vertex as key and assign a list
                  # containing the source vertex as it's first adjacent vertex.
                  else:
                        _lowerCAmelCase					=				[destination_vertex]
                        _lowerCAmelCase					=				[source_vertex]
            else:  # For directed graphs
                  # if both source vertex and destination vertex are present in adjacency
                  # list, add destination vertex to source vertex list of adjacent vertices.
                  if source_vertex in self.adj_list and destination_vertex in self.adj_list:
                        self.adj_list[source_vertex].append(__snake_case    )
                  # if only source vertex is present in adjacency list, add destination
                  # vertex to source vertex list of adjacent vertices and create a new vertex
                  # with destination vertex as key, which has no adjacent vertex
                  elif source_vertex in self.adj_list:
                        self.adj_list[source_vertex].append(__snake_case    )
                        _lowerCAmelCase					=				[]
                  # if only destination vertex is present in adjacency list, create a new
                  # vertex with source vertex as key and assign a list containing destination
                  # vertex as first adjacent vertex
                  elif destination_vertex in self.adj_list:
                        _lowerCAmelCase					=				[destination_vertex]
                  # if both source vertex and destination vertex are not present in adjacency
                  # list, create a new vertex with source vertex as key and a list containing
                  # destination vertex as it's first adjacent vertex. Then create a new vertex
                  # with destination vertex as key, which has no adjacent vertex
                  else:
                        _lowerCAmelCase					=				[destination_vertex]
                        _lowerCAmelCase					=				[]

            return self




      def __repr__(     self     :					Tuple    )							-> str:
            return pformat(self.adj_list    )













'''simple docstring'''






from __future__ import annotations

import numpy as np
def   UpperCamelCase__ (						lowerCAmelCase    ):





      """simple docstring"""


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

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()






