




'''simple docstring'''





_SCREAMING_SNAKE_CASE							:   str      		= {
    "Pillow": "Pillow<10.0.0",
    "accelerate": "accelerate>=0.20.3",
    "av": "av==9.2.0",
    "beautifulsoup4": "beautifulsoup4",
    "black": "black~=23.1",
    "codecarbon": "codecarbon==1.2.0",
    "cookiecutter": "cookiecutter==1.7.3",
    "dataclasses": "dataclasses",
    "datasets": "datasets!=2.5.0",
    "decord": "decord==0.6.0",
    "deepspeed": "deepspeed>=0.9.3",
    "diffusers": "diffusers",
    "dill": "dill<0.3.5",
    "evaluate": "evaluate>=0.2.0",
    "fairscale": "fairscale>0.3",
    "faiss-cpu": "faiss-cpu",
    "fastapi": "fastapi",
    "filelock": "filelock",
    "flax": "flax>=0.4.1,<=0.7.0",
    "ftfy": "ftfy",
    "fugashi": "fugashi>=1.0",
    "GitPython": "GitPython<3.1.19",
    "hf-doc-builder": "hf-doc-builder>=0.3.0",
    "huggingface-hub": "huggingface-hub>=0.14.1,<1.0",
    "importlib_metadata": "importlib_metadata",
    "ipadic": "ipadic>=1.0.0,<2.0",
    "isort": "isort>=5.5.4",
    "jax": "jax>=0.2.8,!=0.3.2,<=0.4.13",
    "jaxlib": "jaxlib>=0.1.65,<=0.4.13",
    "jieba": "jieba",
    "kenlm": "kenlm",
    "keras-nlp": "keras-nlp>=0.3.1",
    "librosa": "librosa",
    "nltk": "nltk",
    "natten": "natten>=0.14.6",
    "numpy": "numpy>=1.17",
    "onnxconverter-common": "onnxconverter-common",
    "onnxruntime-tools": "onnxruntime-tools>=1.4.2",
    "onnxruntime": "onnxruntime>=1.4.0",
    "opencv-python": "opencv-python",
    "optuna": "optuna",
    "optax": "optax>=0.0.8,<=0.1.4",
    "packaging": "packaging>=20.0",
    "parameterized": "parameterized",
    "phonemizer": "phonemizer",
    "protobuf": "protobuf",
    "psutil": "psutil",
    "pyyaml": "pyyaml>=5.1",
    "pydantic": "pydantic<2",
    "pytest": "pytest>=7.2.0",
    "pytest-timeout": "pytest-timeout",
    "pytest-xdist": "pytest-xdist",
    "python": "python>=3.8.0",
    "ray[tune]": "ray[tune]",
    "regex": "regex!=2019.12.17",
    "requests": "requests",
    "rhoknp": "rhoknp>=1.1.0,<1.3.1",
    "rjieba": "rjieba",
    "rouge-score": "rouge-score!=0.0.7,!=0.0.8,!=0.1,!=0.1.1",
    "ruff": "ruff>=0.0.241,<=0.0.259",
    "sacrebleu": "sacrebleu>=1.4.12,<2.0.0",
    "sacremoses": "sacremoses",
    "safetensors": "safetensors>=0.3.1",
    "sagemaker": "sagemaker>=2.31.0",
    "scikit-learn": "scikit-learn",
    "sentencepiece": "sentencepiece>=0.1.91,!=0.1.92",
    "sigopt": "sigopt",
    "starlette": "starlette",
    "sudachipy": "sudachipy>=0.6.6",
    "sudachidict_core": "sudachidict_core>=20220729",
    "tensorflow-cpu": "tensorflow-cpu>=2.6,<2.14",
    "tensorflow": "tensorflow>=2.6,<2.14",
    "tensorflow-text": "tensorflow-text<2.14",
    "tf2onnx": "tf2onnx",
    "timeout-decorator": "timeout-decorator",
    "timm": "timm",
    "tokenizers": "tokenizers>=0.11.1,!=0.11.3,<0.14",
    "torch": "torch>=1.9,!=1.12.0",
    "torchaudio": "torchaudio",
    "torchvision": "torchvision",
    "pyctcdecode": "pyctcdecode>=0.4.0",
    "tqdm": "tqdm>=4.27",
    "unidic": "unidic>=1.0.2",
    "unidic_lite": "unidic_lite>=1.0.7",
    "urllib3": "urllib3<2.0.0",
    "uvicorn": "uvicorn",
}











"""simple docstring"""



def 		__lowercase     (   snake_case_  :  int				,snake_case_  :  list						)   ->Any:



    '''simple docstring'''







    _enforce_args(snake_case_				,snake_case_						)
    if n == 0:
        return 0
    __A    :						int						 =     float('''-inf'''						)
    for i in range(1				,n + 1						):
        __A    :						Union[str, Any]						 =     max(
            snake_case_				,prices[i - 1] + naive_cut_rod_recursive(n - i				,snake_case_						)						)

    return max_revue







def 		__lowercase     (   snake_case_  :  int				,snake_case_  :  list						)   ->int:



    '''simple docstring'''







    _enforce_args(snake_case_				,snake_case_						)
    __A    :						Dict						 =     [float('''-inf'''						) for _ in range(n + 1						)]
    return _top_down_cut_rod_recursive(snake_case_				,snake_case_				,snake_case_						)







def 		__lowercase     (   snake_case_  :  int				,snake_case_  :  list				,snake_case_  :  list						)   ->Any:



    '''simple docstring'''







    if max_rev[n] >= 0:
        return max_rev[n]
    elif n == 0:
        return 0
    else:
        __A    :						Any						 =     float('''-inf'''						)
        for i in range(1				,n + 1						):
            __A    :						Union[str, Any]						 =     max(
                snake_case_				,prices[i - 1] + _top_down_cut_rod_recursive(n - i				,snake_case_				,snake_case_						)				,)

        __A    :						Any						 =     max_revenue

    return max_rev[n]







def 		__lowercase     (   snake_case_  :  int				,snake_case_  :  list						)   ->Any:



    '''simple docstring'''







    _enforce_args(snake_case_				,snake_case_						)

    # length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
    # length 0.
    __A    :						Union[str, Any]						 =     [float('''-inf'''						) for _ in range(n + 1						)]
    __A    :						List[Any]						 =     0

    for i in range(1				,n + 1						):
        __A    :						Union[str, Any]						 =     max_rev[i]
        for j in range(1				,i + 1						):
            __A    :						str						 =     max(snake_case_				,prices[j - 1] + max_rev[i - j]						)

        __A    :						List[str]						 =     max_revenue_i

    return max_rev[n]







def 		__lowercase     (   snake_case_  :  int				,snake_case_  :  list						)   ->Union[str, Any]:



    '''simple docstring'''







    if n < 0:
        __A    :						Union[str, Any]						 =     F"""n must be greater than or equal to 0. Got n = {n}"""
        raise ValueError(snake_case_						)

    if n > len(snake_case_						):
        __A    :						List[Any]						 =     (
            '''Each integral piece of rod must have a corresponding price. '''
            F"""Got n = {n} but length of prices = {len(snake_case_						)}"""
        )
        raise ValueError(snake_case_						)







def 		__lowercase     (   )   ->str:



    '''simple docstring'''







    __A    :						Any						 =     [6, 10, 12, 15, 20, 23]
    __A    :						Union[str, Any]						 =     len(snake_case_						)

    # the best revenue comes from cutting the rod into 6 pieces, each
    # of length 1 resulting in a revenue of 6 * 6 = 36.
    __A    :						str						 =     36

    __A    :						Any						 =     top_down_cut_rod(snake_case_				,snake_case_						)
    __A    :						Any						 =     bottom_up_cut_rod(snake_case_				,snake_case_						)
    __A    :						Optional[Any]						 =     naive_cut_rod_recursive(snake_case_				,snake_case_						)

    assert expected_max_revenue == max_rev_top_down
    assert max_rev_top_down == max_rev_bottom_up
    assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
       main()




