
from __future__ import annotations

from collections import Counter
from random import random

class __snake_case		:
    def __init__(  self				):



           '''simple docstring'''







           lowercase							:					Union[str, Any]	     =				{}
    def 				_SCREAMING_SNAKE_CASE	(  self		,snake_case				):



           '''simple docstring'''







           lowercase							:					List[str]	     =				{}
    def 				_SCREAMING_SNAKE_CASE	(  self		,snake_case		,snake_case		,snake_case				):



           '''simple docstring'''







           if nodea not in self.connections:
                  self.add_node(snake_case				)
           if nodea not in self.connections:
                  self.add_node(snake_case				)
           lowercase							:					Tuple	     =				probability
    def 				_SCREAMING_SNAKE_CASE	(  self				):



           '''simple docstring'''







           return list(self.connections				)
    def 				_SCREAMING_SNAKE_CASE	(  self		,snake_case				):



           '''simple docstring'''







           lowercase							:					Optional[Any]	     =				0
           lowercase							:					Optional[Any]	     =				random()

           for dest in self.connections[node]:
                  current_probability += self.connections[node][dest]
                  if current_probability > random_value:
                         return dest
           return ""







def 						_snake_case(  SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )			->   dict[str, int]:
       lowercase							:					List[str]	     =				MarkovChainGraphUndirectedUnweighted()

       for nodea, nodea, probability in transitions:
              graph.add_transition_probability(SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__ ,     SCREAMING_SNAKE_CASE__    )

       lowercase							:					Optional[int]	     =				Counter(graph.get_nodes()    )
       lowercase							:					Optional[int]	     =				start

       for _ in range(SCREAMING_SNAKE_CASE__    ):
              lowercase							:					List[Any]	     =				graph.transition(SCREAMING_SNAKE_CASE__    )
              visited[node] += 1

       return visited


if __name__ == "__main__":
  import doctest

  doctest.testmod()


from __future__ import annotations

import numpy as np







def 						_snake_case(  SCREAMING_SNAKE_CASE__    )			->   tuple[np.ndarray, np.ndarray]:
       lowercase     ,      lowercase							:					Dict	     =				np.shape(SCREAMING_SNAKE_CASE__    )
       if rows != columns:
              lowercase							:					str	     =				(
                  """'table' has to be of square shaped array but got a """
                  f"{rows}x{columns} array:\n{table}"
              )
              raise ValueError(SCREAMING_SNAKE_CASE__    )

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


if __name__ == "__main__":
  import doctest

  doctest.testmod()
