


from __future__ import annotations

A      :    Optional[int]		=					list[tuple[int, int]]

A      :    List[str]		=					[
    [0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0],
    [1, 0, 1, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 1, 0, 0],
]

A      :    Dict		=					([-1, 0], [0, -1], [1, 0], [0, 1])  # up, left, down, right







class 			_lowercase :


       """simple docstring"""




       def __init__(   self							:			Dict					,      __lowerCamelCase							:			int					,      __lowerCamelCase							:			int					,      __lowerCamelCase							:			int					,      __lowerCamelCase							:			int					,      __lowerCamelCase							:			float					,      __lowerCamelCase							:			Node | None					,      ):


             '''simple docstring'''



             lowerCamelCase__		:				int    =  pos_x
             lowerCamelCase__		:				List[str]    =  pos_y
             lowerCamelCase__		:				Union[str, Any]    =  (pos_y, pos_x)
             lowerCamelCase__		:				Optional[Any]    =  goal_x
             lowerCamelCase__		:				List[Any]    =  goal_y
             lowerCamelCase__		:				List[Any]    =  g_cost
             lowerCamelCase__		:				int    =  parent
             lowerCamelCase__		:				int    =  self.calculate_heuristic()





       def 						lowerCAmelCase     (   self							:			int       ):


             '''simple docstring'''



             lowerCamelCase__		:				List[str]    =  abs(self.pos_x - self.goal_x       )
             lowerCamelCase__		:				Optional[int]    =  abs(self.pos_y - self.goal_y       )
             return dx + dy





       def __lt__(   self							:			int					,      __lowerCamelCase							:			Dict       ):


             '''simple docstring'''



             return self.f_cost < other.f_cost







class 			_lowercase :


       """simple docstring"""




       def __init__(   self							:			List[Any]					,      __lowerCamelCase							:			tuple[int, int]					,      __lowerCamelCase							:			tuple[int, int]       ):


             '''simple docstring'''



             lowerCamelCase__		:				List[Any]    =  Node(start[1]					,      start[0]					,      goal[1]					,      goal[0]					,      0					,      __lowerCamelCase       )
             lowerCamelCase__		:				Optional[Any]    =  Node(goal[1]					,      goal[0]					,      goal[1]					,      goal[0]					,      99999					,      __lowerCamelCase       )

             lowerCamelCase__		:				str    =  [self.start]
             lowerCamelCase__		:				list[Node]    =  []

             lowerCamelCase__		:				Tuple    =  False





       def 						lowerCAmelCase     (   self							:			Any       ):


             '''simple docstring'''



             while self.open_nodes:
                   # Open Nodes are sorted using __lt__
                   self.open_nodes.sort()
                   lowerCamelCase__		:				Any    =  self.open_nodes.pop(0       )

                   if current_node.pos == self.target.pos:
                         lowerCamelCase__		:				Tuple    =  True
                         return self.retrace_path(__lowerCamelCase       )

                   self.closed_nodes.append(__lowerCamelCase       )
                   lowerCamelCase__		:				Union[str, Any]    =  self.get_successors(__lowerCamelCase       )

                   for child_node in successors:
                         if child_node in self.closed_nodes:
                               continue

                         if child_node not in self.open_nodes:
                               self.open_nodes.append(__lowerCamelCase       )
                         else:
                               # retrieve the best current path
                               lowerCamelCase__		:				Optional[Any]    =  self.open_nodes.pop(self.open_nodes.index(__lowerCamelCase       )       )

                               if child_node.g_cost < better_node.g_cost:
                                     self.open_nodes.append(__lowerCamelCase       )
                               else:
                                     self.open_nodes.append(__lowerCamelCase       )

             if not self.reached:
                   return [self.start.pos]
             return None





       def 						lowerCAmelCase     (   self							:			Optional[int]					,      __lowerCamelCase							:			Node       ):


             '''simple docstring'''



             lowerCamelCase__		:				List[str]    =  []
             for action in delta:
                   lowerCamelCase__		:				Tuple    =  parent.pos_x + action[1]
                   lowerCamelCase__		:				List[str]    =  parent.pos_y + action[0]

                   if not (0 <= pos_x <= len(grid[0]       ) - 1 and 0 <= pos_y <= len(__lowerCamelCase       ) - 1):
                         continue

                   if grid[pos_y][pos_x] != 0:
                         continue

                   successors.append(
                       Node(
                           __lowerCamelCase					,      __lowerCamelCase					,      self.target.pos_y					,      self.target.pos_x					,      parent.g_cost + 1					,      __lowerCamelCase					,      )       )
             return successors





       def 						lowerCAmelCase     (   self							:			Optional[Any]					,      __lowerCamelCase							:			Node | None       ):


             '''simple docstring'''



             lowerCamelCase__		:				Tuple    =  node
             lowerCamelCase__		:				Any    =  []
             while current_node is not None:
                   path.append((current_node.pos_y, current_node.pos_x)       )
                   lowerCamelCase__		:				Tuple    =  current_node.parent
             path.reverse()
             return path


if __name__ == "__main__":
    A      :    Optional[Any]		=					(0, 0)
    A      :    Tuple		=					(len(grid) - 1, len(grid[0]) - 1)
    for elem in grid:
        print(elem)

    print("------")

    A      :    List[Any]		=					GreedyBestFirst(init, goal)
    A      :    List[Any]		=					greedy_bf.search()
    if path:
        for pos_x, pos_y in path:
            A      :    Optional[int]		=					2

        for elem in grid:
            print(elem)






def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




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

      return max_revue

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      _enforce_args(_A    ,					_A						)
      lowerCamelCase__		:				int    =  [float("-inf"						) for _ in range(n + 1						)]
      return _top_down_cut_rod_recursive(_A    ,					_A    ,					_A						)

def       lowercase_		(		_A			:    int    ,					_A			:    list    ,					_A			:    list						):

      """simple docstring"""




      if max_rev[n] >= 0:
            return max_rev[n]
      elif n == 0:
            return 0
      else:
            lowerCamelCase__		:				Dict    =  float("-inf"						)
            for i in range(1    ,					n + 1						):
                  lowerCamelCase__		:				int    =  max(
                      _A    ,					prices[i - 1] + _top_down_cut_rod_recursive(n - i    ,					_A    ,					_A						)    ,					)

            lowerCamelCase__		:				List[Any]    =  max_revenue

      return max_rev[n]

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      _enforce_args(_A    ,					_A						)

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

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

            lowerCamelCase__		:				Any    =  max_revenue_i

      return max_rev[n]

def       lowercase_		(		_A			:    int    ,					_A			:    list						):

      """simple docstring"""




      if n < 0:
            lowerCamelCase__		:				Optional[int]    =  F"n must be greater than or equal to 0. Got n = {n}"
            raise ValueError(_A						)

      if n > len(_A						):
            lowerCamelCase__		:				Optional[int]    =  (
                "Each integral piece of rod must have a corresponding price. "
                F"Got n = {n} but length of prices = {len(_A						)}"
            )
            raise ValueError(_A						)

def       lowercase_		(		):

      """simple docstring"""




      lowerCamelCase__		:				Optional[Any]    =  [6, 10, 12, 15, 20, 23]
      lowerCamelCase__		:				Dict    =  len(_A						)

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

      lowerCamelCase__		:				List[Any]    =  top_down_cut_rod(_A    ,					_A						)
      lowerCamelCase__		:				List[Any]    =  bottom_up_cut_rod(_A    ,					_A						)
      lowerCamelCase__		:				List[Any]    =  naive_cut_rod_recursive(_A    ,					_A						)

      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()


