




"""simple docstring"""






lowercase__			=		{
    """A""": ["""B""", """C""", """E"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F""", """G"""],
    """D""": ["""B"""],
    """E""": ["""A""", """B""", """D"""],
    """F""": ["""C"""],
    """G""": ["""C"""],
}







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__						):
				_lowerCamelCase	:     int       =       set()
				# keep track of all the paths to be checked
				_lowerCamelCase	:     Union[str, Any]       =       [[start]]

				# return path if start is goal
				if start == goal:
								return [start]

				# keeps looping until all possible paths have been checked
				while queue:
								# pop the first path from the queue
								_lowerCamelCase	:     Optional[Any]       =       queue.pop(0						)
								# get the last node from the path
								_lowerCamelCase	:     Tuple       =       path[-1]
								if node not in explored:
												_lowerCamelCase	:     Any       =       graph[node]
												# go through all neighbour nodes, construct a new path and
												# push it into the queue
												for neighbour in neighbours:
																_lowerCamelCase	:     Optional[int]       =       list(lowercase__						)
																new_path.append(lowercase__						)
																queue.append(lowercase__						)
																# return path if neighbour is goal
																if neighbour == goal:
																				return new_path

            # mark node as explored
												explored.add(lowercase__						)

    # in case there's no path between the 2 nodes
				return []







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__						):
				if not graph or start not in graph or target not in graph:
								return -1
				if start == target:
								return 0
				_lowerCamelCase	:     int       =       [start]
				_lowerCamelCase	:     Dict       =       set(lowercase__						)
				# Keep tab on distances from `start` node.
				_lowerCamelCase	:     List[str]       =       {start: 0, target: -1}
				while queue:
								_lowerCamelCase	:     Tuple       =       queue.pop(0						)
								if node == target:
												_lowerCamelCase	:     Any       =       (
												    dist[node] if dist[target] == -1 else min(dist[target]				,       dist[node]						)
												)
								for adjacent in graph[node]:
												if adjacent not in visited:
																visited.add(lowercase__						)
																queue.append(lowercase__						)
																_lowerCamelCase	:     Any       =       dist[node] + 1
				return dist[target]


if __name__ == "__main__":
			print(bfs_shortest_path(demo_graph, """G""", """D"""))  # returns ['G', 'C', 'A', 'B', 'D']
			print(bfs_shortest_path_distance(demo_graph, """G""", """D"""))  # returns 4





"""simple docstring"""






from typing import Any







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       ):
				_validation(
				    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       )
				# Creates data structures and fill initial step
				_lowerCamelCase	:     dict       =       {}
				_lowerCamelCase	:     dict       =       {}
				for state in states_space:
								_lowerCamelCase	:     Optional[Any]       =       observations_space[0]
								_lowerCamelCase	:     int       =       (
								    initial_probabilities[state] * emission_probabilities[state][observation]
								)
								_lowerCamelCase	:     List[Any]       =       None

				# Fills the data structure with the probabilities of
				# different transitions and pointers to previous states
				for o in range(1				,       len(lowercase__						)						):
								_lowerCamelCase	:     List[str]       =       observations_space[o]
								_lowerCamelCase	:     str       =       observations_space[o - 1]
								for state in states_space:
												# Calculates the argmax for probability function
												_lowerCamelCase	:     Dict       =       ''
												_lowerCamelCase	:     int       =       -1
												for k_state in states_space:
																_lowerCamelCase	:     Any       =       (
																    probabilities[(k_state, prior_observation)]
																    * transition_probabilities[k_state][state]
																    * emission_probabilities[state][observation]
																)
																if probability > max_probability:
																				_lowerCamelCase	:     Dict       =       probability
																				_lowerCamelCase	:     int       =       k_state

            # Update probabilities and pointers dicts
												_lowerCamelCase	:     List[str]       =       (
												    probabilities[(arg_max, prior_observation)]
												    * transition_probabilities[arg_max][state]
												    * emission_probabilities[state][observation]
												)

												_lowerCamelCase	:     Union[str, Any]       =       arg_max

    # The final observation
				_lowerCamelCase	:     Tuple       =       observations_space[len(lowercase__						) - 1]

				# argmax for given final observation
				_lowerCamelCase	:     Optional[int]       =       ''
				_lowerCamelCase	:     str       =       -1
				for k_state in states_space:
								_lowerCamelCase	:     Optional[int]       =       probabilities[(k_state, final_observation)]
								if probability > max_probability:
												_lowerCamelCase	:     int       =       probability
												_lowerCamelCase	:     Optional[int]       =       k_state
				_lowerCamelCase	:     Any       =       arg_max

				# Process pointers backwards
				_lowerCamelCase	:     Optional[Any]       =       last_state
				_lowerCamelCase	:     Union[str, Any]       =       []
				for o in range(len(lowercase__						) - 1				,       -1				,       -1						):
								result.append(lowercase__						)
								_lowerCamelCase	:     Dict       =       pointers[previous, observations_space[o]]
				result.reverse()

				return result







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       ):
				_validate_not_empty(
				    lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       )
				_validate_lists(lowercase__				,       lowercase__						)
				_validate_dicts(
				    lowercase__				,       lowercase__				,       lowercase__						)







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       lowercase__				,       ):
				if not all(
				    [
				        observations_space,
				        states_space,
				        initial_probabilities,
				        transition_probabilities,
				        emission_probabilities,
				    ]						):
								raise ValueError('There\'s an empty parameter'						)







def 	_snake_case     (							lowercase__				,       lowercase__						):
				_validate_list(lowercase__				,       'observations_space'						)
				_validate_list(lowercase__				,       'states_space'						)







def 	_snake_case     (							lowercase__				,       lowercase__						):
				if not isinstance(_object				,       lowercase__						):
								_lowerCamelCase	:     Tuple       =       f'''{var_name} must be a list'''
								raise ValueError(lowercase__						)
				else:
								for x in _object:
												if not isinstance(lowercase__				,       lowercase__						):
																_lowerCamelCase	:     int       =       f'''{var_name} must be a list of strings'''
																raise ValueError(lowercase__						)







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__				,       ):
				_validate_dict(lowercase__				,       'initial_probabilities'				,       lowercase__						)
				_validate_nested_dict(lowercase__				,       'transition_probabilities'						)
				_validate_nested_dict(lowercase__				,       'emission_probabilities'						)







def 	_snake_case     (							lowercase__				,       lowercase__						):
				_validate_dict(_object				,       lowercase__				,       lowercase__						)
				for x in _object.values():
								_validate_dict(lowercase__				,       lowercase__				,       lowercase__				,       lowercase__						)







def 	_snake_case     (							lowercase__				,       lowercase__				,       lowercase__				,       lowercase__ = False						):
				if not isinstance(_object				,       lowercase__						):
								_lowerCamelCase	:     Tuple       =       f'''{var_name} must be a dict'''
								raise ValueError(lowercase__						)
				if not all(isinstance(lowercase__				,       lowercase__						) for x in _object						):
								_lowerCamelCase	:     Optional[int]       =       f'''{var_name} all keys must be strings'''
								raise ValueError(lowercase__						)
				if not all(isinstance(lowercase__				,       lowercase__						) for x in _object.values()						):
								_lowerCamelCase	:     Optional[int]       =       'nested dictionary ' if nested else ''
								_lowerCamelCase	:     Optional[Any]       =       f'''{var_name} {nested_text}all values must be {value_type.__name__}'''
								raise ValueError(lowercase__						)


if __name__ == "__main__":
			from doctest import testmod

			testmod()