


def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     ):

							# 1. Validate that path exists between current and next vertices
							if graph[path[curr_ind - 1]][next_ver] == 0:
														return False

							# 2. Validate that next vertex is not already in path
							return not any(vertex == next_ver for vertex in path     )







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase							,     __lowerCamelCase     ):

							# Base Case
							if curr_ind == len(UpperCAmelCase_     ):
														# return whether path exists between current and starting vertices
														return graph[path[curr_ind - 1]][path[0]] == 1

							# Recursive Step
							for next_ver in range(0							,     len(UpperCAmelCase_     )     ):
														if valid_connection(UpperCAmelCase_							,     UpperCAmelCase_							,     UpperCAmelCase_							,     UpperCAmelCase_     ):
																					# Insert current vertex  into path as next transition
																					__snake_case		:      Union[str, Any]										=       next_ver
																					# Validate created path
																					if util_hamilton_cycle(UpperCAmelCase_							,     UpperCAmelCase_							,     curr_ind + 1     ):
																												return True
																					# Backtrack
																					__snake_case		:      List[str]										=       -1
							return False







def     lowerCAmelCase_					( __lowerCamelCase							,     __lowerCamelCase = 0     ):
							__snake_case		:      Dict										=       [-1] * (len(UpperCAmelCase_     ) + 1)
							# initialize start and end of path with starting index
							__snake_case		:      Dict										=       start_index
							# evaluate and if we find answer return path either return empty array
							return path if util_hamilton_cycle(UpperCAmelCase_							,     UpperCAmelCase_							,     1     ) else []



from ..utils import DummyObject, requires_backends

class     a		(metaclass=_lowerCAmelCase				):




							"""simple docstring"""


							__UpperCAmelCase   :							int					  =  ["speech"]

							def __init__(							self	:  List[Any]   ,     *lowerCamelCase	:  List[Any]   ,     **lowerCamelCase	:  Optional[Any]    )     ->   Dict:
														requires_backends(self   ,     ["speech"]    )

class     a		(metaclass=_lowerCAmelCase				):




							"""simple docstring"""


							__UpperCAmelCase   :							Optional[Any]					  =  ["speech"]

							def __init__(							self	:  int   ,     *lowerCamelCase	:  List[Any]   ,     **lowerCamelCase	:  List[Any]    )     ->   Optional[int]:
														requires_backends(self   ,     ["speech"]    )

