"""simple docstring"""





from __future__ import annotations

_UpperCamelCase     :		List[Any]											=					list[tuple[int, int]]

_UpperCamelCase     :		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],
]

_UpperCamelCase     :		Optional[Any]											=					([-1, 0], [0, -1], [1, 0], [0, 1])  # up, left, down, right


class   UpperCAmelCase_			:


      def __init__(     self	,    a	,    a	,    a	,    a	,    a	,    a	,    ) ->      int:
             lowercase__    :	Union[str, Any]     					=			pos_x
             lowercase__    :	Tuple     					=			pos_y
             lowercase__    :	str     					=			(pos_y, pos_x)
             lowercase__    :	Dict     					=			goal_x
             lowercase__    :	Any     					=			goal_y
             lowercase__    :	int     					=			g_cost
             lowercase__    :	Dict     					=			parent
             lowercase__    :	int     					=			self.calculate_heuristic()


      def 	_UpperCAmelCase (     self							) ->      float:
             lowercase__    :	Tuple     					=			abs(self.pos_x - self.goal_x							)
             lowercase__    :	Any     					=			abs(self.pos_y - self.goal_y							)
             return dx + dy


      def __lt__(     self	,    a							) ->      bool:
             return self.f_cost < other.f_cost





class   UpperCAmelCase_			:


      def __init__(     self	,    a	,    a							) ->      Optional[int]:
             lowercase__    :	Optional[Any]     					=			Node(start[1]	,    start[0]	,    goal[1]	,    goal[0]	,    0	,    a							)
             lowercase__    :	Any     					=			Node(goal[1]	,    goal[0]	,    goal[1]	,    goal[0]	,    9_9_9_9_9	,    a							)

             lowercase__    :	Dict     					=			[self.start]
             lowercase__    :	int     					=			[]

             lowercase__    :	List[Any]     					=			False


      def 	_UpperCAmelCase (     self							) ->      Path | None:
             while self.open_nodes:
                    # Open Nodes are sorted using __lt__
                    self.open_nodes.sort()
                    lowercase__    :	Tuple     					=			self.open_nodes.pop(0							)

                    if current_node.pos == self.target.pos:
                           lowercase__    :	List[str]     					=			True
                           return self.retrace_path(a							)

                    self.closed_nodes.append(a							)
                    lowercase__    :	str     					=			self.get_successors(a							)

                    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(a							)
                           else:
                                  # retrieve the best current path
                                  lowercase__    :	Any     					=			self.open_nodes.pop(self.open_nodes.index(a							)							)

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

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


      def 	_UpperCAmelCase (     self	,    a							) ->      list[Node]:
             lowercase__    :	Any     					=			[]
             for action in delta:
                    lowercase__    :	Optional[int]     					=			parent.pos_x + action[1]
                    lowercase__    :	Any     					=			parent.pos_y + action[0]

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

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

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


      def 	_UpperCAmelCase (     self	,    a							) ->      Path:
             lowercase__    :	Union[str, Any]     					=			node
             lowercase__    :	Dict     					=			[]
             while current_node is not None:
                    path.append((current_node.pos_y, current_node.pos_x)							)
                    lowercase__    :	Optional[int]     					=			current_node.parent
             path.reverse()
             return path


if __name__ == "__main__":
       _UpperCamelCase     :		Dict											=					(0, 0)
       _UpperCamelCase     :		Optional[int]											=					(len(grid) - 1, len(grid[0]) - 1)
       for elem in grid:
              print(elem)

       print("------")

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

              for elem in grid:
                     print(elem)


"""simple docstring"""





def        a_  (   _lowerCAmelCase						:				str  ):





       '''simple docstring'''

       lowercase__    :	Any     					=			[0] * len(_lowerCAmelCase  )

       for i in range(1     ,				len(_lowerCAmelCase  )  ):
              # use last results for better performance - dynamic programming
              lowercase__    :	List[str]     					=			prefix_result[i - 1]
              while j > 0 and input_string[i] != input_string[j]:
                     lowercase__    :	Dict     					=			prefix_result[j - 1]

              if input_string[i] == input_string[j]:
                     j += 1
              lowercase__    :	Union[str, Any]     					=			j

       return prefix_result





def        a_  (   _lowerCAmelCase						:				str  ):





       '''simple docstring'''

       return max(prefix_function(_lowerCAmelCase  )  )


if __name__ == "__main__":
       import doctest

       doctest.testmod()

