



'''simple docstring'''





from __future__ import annotations

from collections import Counter
from random import random







class     UpperCAmelCase_       :
    """simple docstring"""







    def __init__(    self					:     int						):
          snake_case__  :    Dict    						=      {}




    def lowerCamelCase       (    self					:     Union[str, Any] ,     snake_case_					:     str						):
          snake_case__  :    Union[str, Any]    						=      {}




    def lowerCamelCase       (    self					:     Optional[int] ,     snake_case_					:     str ,     snake_case_					:     str ,     snake_case_					:     float						):
          if nodea not in self.connections:
                self.add_node(snake_case_						)
          if nodea not in self.connections:
                self.add_node(snake_case_						)
          snake_case__  :    Optional[Any]    						=      probability




    def lowerCamelCase       (    self					:     List[str]						):
          return list(self.connections						)




    def lowerCamelCase       (    self					:     List[Any] ,     snake_case_					:     str						):
          snake_case__  :    Union[str, Any]    						=      0
          snake_case__  :    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(				_lowerCAmelCase     ,   _lowerCAmelCase     ,   _lowerCAmelCase		)		-> dict[str, int]:
      snake_case__  :    List[Any]    						=      MarkovChainGraphUndirectedUnweighted()

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

      snake_case__  :    Union[str, Any]    						=      Counter(graph.get_nodes()		)
      snake_case__  :    Optional[int]    						=      start

      for _ in range(_lowerCAmelCase		):
            snake_case__  :    Union[str, Any]    						=      graph.transition(_lowerCAmelCase		)
            visited[node] += 1

      return visited


if __name__ == "__main__":
       import doctest

       doctest.testmod()





'''simple docstring'''





def 						__snake_case(				_lowerCAmelCase     ,   _lowerCAmelCase     ,   _lowerCAmelCase		)		-> float:
      snake_case__  :    str    						=      (num_of_terms / 2) * (2 * first_term + (num_of_terms - 1) * common_diff)
      # formula for sum of series
      return total





def 						__snake_case(				)		-> List[str]:
      print(sum_of_series(1     ,   1     ,   10		)		)


if __name__ == "__main__":
       import doctest

       doctest.testmod()
