



"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					int							,	__lowerCamelCase       :					str							,	__lowerCamelCase       :					Union[str, Any]							,	__lowerCamelCase       :					int							,	__lowerCamelCase       :					Union[str, Any]							,	__lowerCamelCase       :					Optional[int]			):
			"""simple docstring"""
			if index == r:
						for j in range(__lowerCamelCase			):
									print(data[j]							,	end=''' '''			)
						print(''' '''			)
						return
			#  When no more elements are there to put in data[]
			if i >= n:
						return
			# current is included, put next at next location
			lowerCamelCase__	:	Any				=arr[i]
			combination_util(__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	index + 1							,	__lowerCamelCase							,	i + 1			)
			# current is excluded, replace it with
			# next (Note that i+1 is passed, but
			# index is not changed)
			combination_util(__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	i + 1			)
			# The main function that prints all combinations
			# of size r in arr[] of size n. This function
			# mainly uses combinationUtil()






def   snake_case__     (	__lowerCamelCase       :					Any							,	__lowerCamelCase       :					Any							,	__lowerCamelCase       :					Optional[int]			):
			"""simple docstring"""
			lowerCamelCase__	:	Optional[int]				=[0] * r
			# Print all combination using temporary array 'data[]'
			combination_util(__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	0							,	__lowerCamelCase							,	0			)


if __name__ == "__main__":
		# Driver code to check the function above
		_lowercase				:				List[Any]     =		[1_0, 2_0, 3_0, 4_0, 5_0]
		print_combination(arr, len(arr), 3)
		# This code is contributed by Ambuj sahu









"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					list[list[int]]							,	__lowerCamelCase       :					int							,	__lowerCamelCase       :					int							,	__lowerCamelCase       :					list[int]			):
			"""simple docstring"""

			# 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   snake_case__     (	__lowerCamelCase       :					list[list[int]]							,	__lowerCamelCase       :					list[int]							,	__lowerCamelCase       :					int			):
			"""simple docstring"""

			# Base Case
			if curr_ind == len(__lowerCamelCase			):
						# 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(__lowerCamelCase			)			):
						if valid_connection(__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase							,	__lowerCamelCase			):
									# Insert current vertex  into path as next transition
									lowerCamelCase__	:	Tuple				=next_ver
									# Validate created path
									if util_hamilton_cycle(__lowerCamelCase							,	__lowerCamelCase							,	curr_ind + 1			):
												return True
									# Backtrack
									lowerCamelCase__	:	int				=-1
			return False






def   snake_case__     (	__lowerCamelCase       :					list[list[int]]							,	__lowerCamelCase       :					int = 0			):
			"""simple docstring"""
			lowerCamelCase__	:	Tuple				=[-1] * (len(__lowerCamelCase			) + 1)
			# initialize start and end of path with starting index
			lowerCamelCase__	:	Union[str, Any]				=start_index
			# evaluate and if we find answer return path either return empty array
			return path if util_hamilton_cycle(__lowerCamelCase							,	__lowerCamelCase							,	1			) else []




