"""simple docstring"""







def     lowercase__( __SCREAMING_SNAKE_CASE							:  list[list[int]]  ,    __SCREAMING_SNAKE_CASE							:  int  ,    __SCREAMING_SNAKE_CASE							:  int  ,    __SCREAMING_SNAKE_CASE							:  list[int]   ):

     # 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     lowercase__( __SCREAMING_SNAKE_CASE							:  list[list[int]]  ,    __SCREAMING_SNAKE_CASE							:  list[int]  ,    __SCREAMING_SNAKE_CASE							:  int   ):

     # Base Case
     if curr_ind == len(__SCREAMING_SNAKE_CASE   ):
          # 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(__SCREAMING_SNAKE_CASE   )   ):
          if valid_connection(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   ):
               # Insert current vertex  into path as next transition
               lowercase_			:       Any									=			next_ver
               # Validate created path
               if util_hamilton_cycle(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE  ,    curr_ind + 1   ):
                    return True
               # Backtrack
               lowercase_			:       str									=			-1
     return False







def     lowercase__( __SCREAMING_SNAKE_CASE							:  list[list[int]]  ,    __SCREAMING_SNAKE_CASE							:  int = 0   ):
     lowercase_			:       List[str]									=			[-1] * (len(__SCREAMING_SNAKE_CASE   ) + 1)
     # initialize start and end of path with starting index
     lowercase_			:       str									=			start_index
     # evaluate and if we find answer return path either return empty array
     return path if util_hamilton_cycle(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE  ,    1   ) else []


"""simple docstring"""







__SCREAMING_SNAKE_CASE								={
    "Pillow": "Pillow",
    "accelerate": "accelerate>=0.11.0",
    "compel": "compel==0.1.8",
    "black": "black~=23.1",
    "datasets": "datasets",
    "filelock": "filelock",
    "flax": "flax>=0.4.1",
    "hf-doc-builder": "hf-doc-builder>=0.3.0",
    "huggingface-hub": "huggingface-hub>=0.13.2",
    "requests-mock": "requests-mock==1.10.0",
    "importlib_metadata": "importlib_metadata",
    "invisible-watermark": "invisible-watermark",
    "isort": "isort>=5.5.4",
    "jax": "jax>=0.2.8,!=0.3.2",
    "jaxlib": "jaxlib>=0.1.65",
    "Jinja2": "Jinja2",
    "k-diffusion": "k-diffusion>=0.0.12",
    "torchsde": "torchsde",
    "note_seq": "note_seq",
    "librosa": "librosa",
    "numpy": "numpy",
    "omegaconf": "omegaconf",
    "parameterized": "parameterized",
    "protobuf": "protobuf>=3.20.3,<4",
    "pytest": "pytest",
    "pytest-timeout": "pytest-timeout",
    "pytest-xdist": "pytest-xdist",
    "ruff": "ruff>=0.0.241",
    "safetensors": "safetensors",
    "sentencepiece": "sentencepiece>=0.1.91,!=0.1.92",
    "scipy": "scipy",
    "onnx": "onnx",
    "regex": "regex!=2019.12.17",
    "requests": "requests",
    "tensorboard": "tensorboard",
    "torch": "torch>=1.4",
    "torchvision": "torchvision",
    "transformers": "transformers>=4.25.1",
    "urllib3": "urllib3<=2.0.0",
}

