





"""simple docstring"""



from collections.abc import Callable






class 		__snake_case					:





 """simple docstring"""


 def __init__(    self					,						__lowerCamelCase = None  ):



     '''simple docstring'''




     __A    :						list						 =     []
     # Stores indexes of each item for supporting updates and deletion.
     __A    :						dict						 =     {}
     # Stores current size of heap.
     __A    :						str						 =     0
     # Stores function used to evaluate the score of an item on which basis ordering
     # will be done.
     __A    :						List[str]						 =     key or (lambda __lowerCamelCase  : x)

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     return int((i - 1) / 2  ) if i > 0 else None

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     __A    :						Optional[Any]						 =     int(2 * i + 1  )
     return left if 0 < left < self.size else None

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     __A    :						Any						 =     int(2 * i + 2  )
     return right if 0 < right < self.size else None

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase  ):



     '''simple docstring'''




     __A ,       __A    :						str						 =     (
         self.pos_map[self.arr[j][0]],
         self.pos_map[self.arr[i][0]],
     )
     # Then swap the items in the list.
     __A ,       __A    :						Optional[Any]						 =     self.arr[j], self.arr[i]

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase  ):



     '''simple docstring'''




     return self.arr[i][1] < self.arr[j][1]

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     __A    :						Optional[int]						 =     self._left(__lowerCamelCase  )
     __A    :						List[str]						 =     self._right(__lowerCamelCase  )
     __A    :						Dict						 =     i

     if left is not None and not self._cmp(__lowerCamelCase					,						__lowerCamelCase  ):
         __A    :						List[str]						 =     left
     if right is not None and not self._cmp(__lowerCamelCase					,						__lowerCamelCase  ):
         __A    :						int						 =     right

     return valid_parent

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     __A    :						Optional[Any]						 =     self._parent(__lowerCamelCase  )
     while parent is not None and not self._cmp(__lowerCamelCase					,						__lowerCamelCase  ):
         self._swap(__lowerCamelCase					,						__lowerCamelCase  )
         __A ,       __A    :						Any						 =     parent, self._parent(__lowerCamelCase  )

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     __A    :						Optional[int]						 =     self._get_valid_parent(__lowerCamelCase  )
     while valid_parent != index:
         self._swap(__lowerCamelCase					,						__lowerCamelCase  )
         __A ,       __A    :						Tuple						 =     valid_parent, self._get_valid_parent(__lowerCamelCase  )

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase  ):



     '''simple docstring'''




     if item not in self.pos_map:
         return
     __A    :						int						 =     self.pos_map[item]
     __A    :						Dict						 =     [item, self.key(__lowerCamelCase  )]
     # Make sure heap is right in both up and down direction.
     # Ideally only one of them will make any change.
     self._heapify_up(__lowerCamelCase  )
     self._heapify_down(__lowerCamelCase  )

 def 					UpperCamelCase__(    self					,						__lowerCamelCase  ):



     '''simple docstring'''




     if item not in self.pos_map:
         return
     __A    :						Optional[int]						 =     self.pos_map[item]
     del self.pos_map[item]
     __A    :						int						 =     self.arr[self.size - 1]
     __A    :						Optional[int]						 =     index
     self.size -= 1
     # Make sure heap is right in both up and down direction. Ideally only one
     # of them will make any change- so no performance loss in calling both.
     if self.size > index:
         self._heapify_up(__lowerCamelCase  )
         self._heapify_down(__lowerCamelCase  )

 def 					UpperCamelCase__(    self					,						__lowerCamelCase					,						__lowerCamelCase  ):



     '''simple docstring'''




     __A    :						Optional[Any]						 =     len(self.arr  )
     if arr_len == self.size:
         self.arr.append([item, self.key(__lowerCamelCase  )]  )
     else:
         __A    :						str						 =     [item, self.key(__lowerCamelCase  )]
     __A    :						int						 =     self.size
     self.size += 1
     self._heapify_up(self.size - 1  )

 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     return self.arr[0] if self.size else None







 def 					UpperCamelCase__(    self  ):



     '''simple docstring'''




     __A    :						int						 =     self.get_top()
     if top_item_tuple:
         self.delete_item(top_item_tuple[0]  )
     return top_item_tuple







def 		__lowercase     (   )   ->None:



    '''simple docstring'''









if __name__ == "__main__":
       import doctest

       doctest.testmod()











"""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()




