



"""simple docstring"""




def      __UpperCamelCase     (  _lowerCAmelCase				,					_lowerCAmelCase		)	->  List[str]:



    """simple docstring"""






    _enforce_args(_lowerCAmelCase				,					_lowerCAmelCase		)
    if n == 0:
        return 0
    A			:	Optional[Any]										=       float("""-inf"""		)
    for i in range(1				,					n + 1		):
        A			:	str										=       max(
            _lowerCAmelCase				,					prices[i - 1] + naive_cut_rod_recursive(n - i				,					_lowerCAmelCase		)		)

    return max_revue




def      __UpperCamelCase     (  _lowerCAmelCase				,					_lowerCAmelCase		)	->  Dict:



    """simple docstring"""






    _enforce_args(_lowerCAmelCase				,					_lowerCAmelCase		)
    A			:	str										=       [float("""-inf"""		) for _ in range(n + 1		)]
    return _top_down_cut_rod_recursive(_lowerCAmelCase				,					_lowerCAmelCase				,					_lowerCAmelCase		)




def      __UpperCamelCase     (  _lowerCAmelCase				,					_lowerCAmelCase				,					_lowerCAmelCase		)	->  int:



    """simple docstring"""






    if max_rev[n] >= 0:
        return max_rev[n]
    elif n == 0:
        return 0
    else:
        A			:	str										=       float("""-inf"""		)
        for i in range(1				,					n + 1		):
            A			:	Tuple										=       max(
                _lowerCAmelCase				,					prices[i - 1] + _top_down_cut_rod_recursive(n - i				,					_lowerCAmelCase				,					_lowerCAmelCase		)				,					)

        A			:	Dict										=       max_revenue

    return max_rev[n]




def      __UpperCamelCase     (  _lowerCAmelCase				,					_lowerCAmelCase		)	->  str:



    """simple docstring"""






    _enforce_args(_lowerCAmelCase				,					_lowerCAmelCase		)

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

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

        A			:	List[str]										=       max_revenue_i

    return max_rev[n]




def      __UpperCamelCase     (  _lowerCAmelCase				,					_lowerCAmelCase		)	->  Union[str, Any]:



    """simple docstring"""






    if n < 0:
        A			:	str										=       f'''n must be greater than or equal to 0. Got n = {n}'''
        raise ValueError(_lowerCAmelCase		)

    if n > len(_lowerCAmelCase		):
        A			:	Union[str, Any]										=       (
            """Each integral piece of rod must have a corresponding price. """
            f'''Got n = {n} but length of prices = {len(_lowerCAmelCase		)}'''
        )
        raise ValueError(_lowerCAmelCase		)




def      __UpperCamelCase     (  )	->  Dict:



    """simple docstring"""






    A			:	Optional[Any]										=       [6, 10, 12, 15, 20, 23]
    A			:	Optional[int]										=       len(_lowerCAmelCase		)

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

    A			:	str										=       top_down_cut_rod(_lowerCAmelCase				,					_lowerCAmelCase		)
    A			:	Optional[int]										=       bottom_up_cut_rod(_lowerCAmelCase				,					_lowerCAmelCase		)
    A			:	str										=       naive_cut_rod_recursive(_lowerCAmelCase				,					_lowerCAmelCase		)

    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()







from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst




def      __UpperCamelCase     (  )	->  Tuple:



    """simple docstring"""






    A					,							A			:	Tuple										=       9, 14  # noqa: F841
    A			:	Optional[int]										=       [
        [0, 1, 4],
        [0, 7, 8],
        [1, 2, 8],
        [7, 8, 7],
        [7, 6, 1],
        [2, 8, 2],
        [8, 6, 6],
        [2, 3, 7],
        [2, 5, 4],
        [6, 5, 2],
        [3, 5, 14],
        [3, 4, 9],
        [5, 4, 10],
        [1, 7, 11],
    ]

    A			:	int										=       defaultdict(_lowerCAmelCase		)
    for nodea, nodea, cost in edges:
        adjancency[nodea].append([nodea, cost]		)
        adjancency[nodea].append([nodea, cost]		)

    A			:	List[str]										=       mst(_lowerCAmelCase		)

    A			:	str										=       [
        [7, 6, 1],
        [2, 8, 2],
        [6, 5, 2],
        [0, 1, 4],
        [2, 5, 4],
        [2, 3, 7],
        [0, 7, 8],
        [3, 4, 9],
    ]

    for answer in expected:
        A			:	Dict										=       tuple(answer[:2]		)
        A			:	List[str]										=       tuple(edge[::-1]		)
        assert edge in result or reverse in result


