
"""simple docstring"""

class      _UpperCAmelCase							:




						def __init__(							self   ,       lowercase_   ,       lowercase_=None   ,       lowercase_=None							)						->					List[str]:
										UpperCAmelCase									=					data
										UpperCAmelCase									=					previous
										UpperCAmelCase									=					next_node




						def __str__(							self							)						->					str:
										return F"{self.data}"




						def     a_      (							self							)						->					int:
										return self.data




						def     a_      (							self							)						->					Optional[Any]:
										return self.next




						def     a_      (							self							)						->					Any:
										return self.previous

class      _UpperCAmelCase							:




						def __init__(							self   ,       lowercase_							)						->					Tuple:
										UpperCAmelCase									=					head




						def __iter__(							self							)						->					str:
										return self




						def     a_      (							self							)						->					Any:
										if not self.current:
														raise StopIteration
										else:
														UpperCAmelCase									=					self.current.get_data()
														UpperCAmelCase									=					self.current.get_next()
														return value

class      _UpperCAmelCase							:




						def __init__(							self							)						->					Union[str, Any]:
										UpperCAmelCase									=					None  # First node in list
										UpperCAmelCase									=					None  # Last node in list




						def __str__(							self							)						->					Optional[Any]:
										UpperCAmelCase									=					self.head
										UpperCAmelCase									=					[]
										while current is not None:
														nodes.append(current.get_data()							)
														UpperCAmelCase									=					current.get_next()
										return " ".join(str(lowercase_							) for node in nodes							)




						def __contains__(							self   ,       lowercase_							)						->					List[str]:
										UpperCAmelCase									=					self.head
										while current:
														if current.get_data() == value:
																		return True
														UpperCAmelCase									=					current.get_next()
										return False




						def __iter__(							self							)						->					Tuple:
										return LinkedListIterator(self.head							)




						def     a_      (							self							)						->					Tuple:
										if self.head:
														return self.head.get_data()
										return None




						def     a_      (							self							)						->					Union[str, Any]:
										if self.tail:
														return self.tail.get_data()
										return None




						def     a_      (							self   ,       lowercase_							)						->					None:
										if self.head is None:
														UpperCAmelCase									=					node
														UpperCAmelCase									=					node
										else:
														self.insert_before_node(self.head   ,       lowercase_							)




						def     a_      (							self   ,       lowercase_							)						->					None:
										if self.head is None:
														self.set_head(lowercase_							)
										else:
														self.insert_after_node(self.tail   ,       lowercase_							)




						def     a_      (							self   ,       lowercase_							)						->					None:
										UpperCAmelCase									=					Node(lowercase_							)
										if self.head is None:
														self.set_head(lowercase_							)
										else:
														self.set_tail(lowercase_							)




						def     a_      (							self   ,       lowercase_   ,       lowercase_							)						->					None:
										UpperCAmelCase									=					node
										UpperCAmelCase									=					node.previous

										if node.get_previous() is None:
														UpperCAmelCase									=					node_to_insert
										else:
														UpperCAmelCase									=					node_to_insert

										UpperCAmelCase									=					node_to_insert




						def     a_      (							self   ,       lowercase_   ,       lowercase_							)						->					None:
										UpperCAmelCase									=					node
										UpperCAmelCase									=					node.next

										if node.get_next() is None:
														UpperCAmelCase									=					node_to_insert
										else:
														UpperCAmelCase									=					node_to_insert

										UpperCAmelCase									=					node_to_insert




						def     a_      (							self   ,       lowercase_   ,       lowercase_							)						->					None:
										UpperCAmelCase									=					1
										UpperCAmelCase									=					Node(lowercase_							)
										UpperCAmelCase									=					self.head
										while node:
														if current_position == position:
																		self.insert_before_node(lowercase_   ,       lowercase_							)
																		return
														current_position += 1
														UpperCAmelCase									=					node.next
										self.insert_after_node(self.tail   ,       lowercase_							)




						def     a_      (							self   ,       lowercase_							)						->					Node:
										UpperCAmelCase									=					self.head
										while node:
														if node.get_data() == item:
																		return node
														UpperCAmelCase									=					node.get_next()
										raise Exception('Node not found'							)




						def     a_      (							self   ,       lowercase_							)						->					Tuple:
										if (node := self.get_node(lowercase_							)) is not None:
														if node == self.head:
																		UpperCAmelCase									=					self.head.get_next()

														if node == self.tail:
																		UpperCAmelCase									=					self.tail.get_previous()

														self.remove_node_pointers(lowercase_							)




						@staticmethod
						def     a_      (							lowercase_							)						->					None:
										if node.get_next():
														UpperCAmelCase									=					node.previous

										if node.get_previous():
														UpperCAmelCase									=					node.next

										UpperCAmelCase									=					None
										UpperCAmelCase									=					None




						def     a_      (							self							)						->					Any:
										return self.head is None




def     lowercase__						(					) ->      int:






				"""simple docstring"""








if __name__ == "__main__":
			import doctest

			doctest.testmod()





"""simple docstring"""

def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      int:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )
    if n == 0:
        return 0
    UpperCAmelCase									=					float('-inf' )
    for i in range(1 ,				n + 1 ):
        UpperCAmelCase									=					max(
            lowerCAmelCase ,				prices[i - 1] + naive_cut_rod_recursive(n - i ,				lowerCAmelCase ) )

    return max_revue




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Dict:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					[float('-inf' ) for _ in range(n + 1 )]
    return _top_down_cut_rod_recursive(lowerCAmelCase ,				lowerCAmelCase ,				lowerCAmelCase )




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ,				lowerCAmelCase				:					list ) ->      int:






    """simple docstring"""




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

        UpperCAmelCase									=					max_revenue

    return max_rev[n]




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Optional[int]:






    """simple docstring"""




    _enforce_args(lowerCAmelCase ,				lowerCAmelCase )

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

    for i in range(1 ,				n + 1 ):
        UpperCAmelCase									=					max_rev[i]
        for j in range(1 ,				i + 1 ):
            UpperCAmelCase									=					max(lowerCAmelCase ,				prices[j - 1] + max_rev[i - j] )

        UpperCAmelCase									=					max_revenue_i

    return max_rev[n]




def     lowercase__						(					lowerCAmelCase				:					int ,				lowerCAmelCase				:					list ) ->      Union[str, Any]:






    """simple docstring"""




    if n < 0:
        UpperCAmelCase									=					F"n must be greater than or equal to 0. Got n = {n}"
        raise ValueError(lowerCAmelCase )

    if n > len(lowerCAmelCase ):
        UpperCAmelCase									=					(
            'Each integral piece of rod must have a corresponding price. '
            F"Got n = {n} but length of prices = {len(lowerCAmelCase )}"
        )
        raise ValueError(lowerCAmelCase )




def     lowercase__						(					) ->      Optional[int]:






    """simple docstring"""




    UpperCAmelCase									=					[6, 10, 12, 15, 20, 23]
    UpperCAmelCase									=					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.
    UpperCAmelCase									=					36

    UpperCAmelCase									=					top_down_cut_rod(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					bottom_up_cut_rod(lowerCAmelCase ,				lowerCAmelCase )
    UpperCAmelCase									=					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()



