





def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase					)						->			bool:

 # 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 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase							,       _lowerCAmelCase					)						->			bool:

 # 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
   UpperCamelCase     : List[str]	     =       next_ver
   # Validate created path
   if util_hamilton_cycle(_lowerCAmelCase							,       _lowerCAmelCase							,       curr_ind + 1					):
    return True
   # Backtrack
   UpperCamelCase     : List[Any]	     =       -1
 return False



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase = 0					)						->			list[int]:
 UpperCamelCase     : Optional[Any]	     =       [-1] * (len(_lowerCAmelCase					) + 1)
 # initialize start and end of path with starting index
 UpperCamelCase     : 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 []









import sys

from .dependency_versions_table import deps
from .utils.versions import require_version, require_version_core


# define which module versions we always want to check at run time
# (usually the ones defined in `install_requires` in setup.py)
#
# order specific notes:
# - tqdm must be checked before tokenizers

__lowerCamelCase	:					Optional[int]			  =					"""python tqdm regex requests packaging filelock numpy tokenizers""".split()
if sys.version_info < (3, 7):
    pkgs_to_check_at_runtime.append("""dataclasses""")
if sys.version_info < (3, 8):
    pkgs_to_check_at_runtime.append("""importlib_metadata""")

for pkg in pkgs_to_check_at_runtime:
    if pkg in deps:
        if pkg == "tokenizers":
            # must be loaded here, or else tqdm check may fail
            from .utils import is_tokenizers_available

            if not is_tokenizers_available():
                continue  # not required, check version only if installed

        require_version_core(deps[pkg])
    else:
        raise ValueError(f"""can't find {pkg} in {deps.keys()}, check dependency_versions_table.py""")



def 		A_    (					_lowerCAmelCase							,       _lowerCAmelCase=None					)						->			Optional[Any]:
 require_version(deps[pkg]							,       _lowerCAmelCase					)
