




from __future__ import annotations

from typing import Generic, TypeVar

UpperCamelCase								=					TypeVar('T')





class 			__lowerCamelCase	(   Generic[T]   ):




    """simple docstring"""

    def __init__(	self					:					List[Any]       ,     SCREAMING_SNAKE_CASE__					:					T       )				->	None:
         lowerCAmelCase__          =			data
         lowerCAmelCase__          =			self
         lowerCAmelCase__          =			0






class 			__lowerCamelCase	(   Generic[T]   ):




    """simple docstring"""

    def __init__(	self					:					str       )				->	None:
         # map from node name to the node object
         lowerCAmelCase__          =			{}


    def        a				(	self					:					Any       ,     SCREAMING_SNAKE_CASE__					:					T       )				->	None:
         # create a new set with x as its member
         lowerCAmelCase__          =			DisjointSetTreeNode(SCREAMING_SNAKE_CASE__       )


    def        a				(	self					:					Optional[Any]       ,     SCREAMING_SNAKE_CASE__					:					T       )				->	DisjointSetTreeNode[T]:
         # find the set x belongs to (with path-compression)
         lowerCAmelCase__          =			self.map[data]
         if elem_ref != elem_ref.parent:
              lowerCAmelCase__          =			self.find_set(elem_ref.parent.data       )
         return elem_ref.parent


    def        a				(	self					:					Optional[Any]       ,     SCREAMING_SNAKE_CASE__					:					DisjointSetTreeNode[T]       ,     SCREAMING_SNAKE_CASE__					:					DisjointSetTreeNode[T]       )				->	None:
         # helper function for union operation
         if nodea.rank > nodea.rank:
              lowerCAmelCase__          =			nodea
         else:
              lowerCAmelCase__          =			nodea
              if nodea.rank == nodea.rank:
                   nodea.rank += 1


    def        a				(	self					:					Any       ,     SCREAMING_SNAKE_CASE__					:					T       ,     SCREAMING_SNAKE_CASE__					:					T       )				->	None:
         # merge 2 disjoint sets
         self.link(self.find_set(SCREAMING_SNAKE_CASE__       )       ,     self.find_set(SCREAMING_SNAKE_CASE__       )       )






class 			__lowerCamelCase	(   Generic[T]   ):




    """simple docstring"""

    def __init__(	self					:					List[str]       )				->	None:
         # connections: map from the node to the neighbouring nodes (with weights)
         lowerCAmelCase__          =			{}


    def        a				(	self					:					str       ,     SCREAMING_SNAKE_CASE__					:					T       )				->	None:
         # add a node ONLY if its not present in the graph
         if node not in self.connections:
              lowerCAmelCase__          =			{}


    def        a				(	self					:					Optional[int]       ,     SCREAMING_SNAKE_CASE__					:					T       ,     SCREAMING_SNAKE_CASE__					:					T       ,     SCREAMING_SNAKE_CASE__					:					int       )				->	None:
         # add an edge with the given weight
         self.add_node(SCREAMING_SNAKE_CASE__       )
         self.add_node(SCREAMING_SNAKE_CASE__       )
         lowerCAmelCase__          =			weight
         lowerCAmelCase__          =			weight


    def        a				(	self					:					Optional[Any]       )				->	GraphUndirectedWeighted[T]:
         lowerCAmelCase__          =			[]
         lowerCAmelCase__          =			set()
         for start in self.connections:
              for end in self.connections[start]:
                   if (start, end) not in seen:
                        seen.add((end, start)       )
                        edges.append((start, end, self.connections[start][end])       )
         edges.sort(key=lambda SCREAMING_SNAKE_CASE__       : x[2]       )

         # creating the disjoint set
         lowerCAmelCase__          =			DisjointSetTree[T]()
         for node in self.connections:
              disjoint_set.make_set(SCREAMING_SNAKE_CASE__       )

         # MST generation
         lowerCAmelCase__          =			0
         lowerCAmelCase__          =			0
         lowerCAmelCase__          =			GraphUndirectedWeighted[T]()
         while num_edges < len(self.connections       ) - 1:
              lowerCAmelCase__     ,		lowerCAmelCase__     ,		lowerCAmelCase__          =			edges[index]
              index += 1
              lowerCAmelCase__          =			disjoint_set.find_set(SCREAMING_SNAKE_CASE__       )
              lowerCAmelCase__          =			disjoint_set.find_set(SCREAMING_SNAKE_CASE__       )
              if parent_u != parent_v:
                   num_edges += 1
                   graph.add_edge(SCREAMING_SNAKE_CASE__       ,     SCREAMING_SNAKE_CASE__       ,     SCREAMING_SNAKE_CASE__       )
                   disjoint_set.union(SCREAMING_SNAKE_CASE__       ,     SCREAMING_SNAKE_CASE__       )
         return graph






from __future__ import annotations

UpperCamelCase								=					[
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]



def 							_A       (						lowerCAmelCase_					: list[list[int]]       ,    lowerCAmelCase_					: list[int]       ,    lowerCAmelCase_					: list[int]       ,    lowerCAmelCase_					: int       ,    lowerCAmelCase_					: list[list[int]]       ,    ):
     """simple docstring"""

     lowerCAmelCase__          =			[
         [0 for col in range(len(grid[0]      )      )] for row in range(len(lowerCAmelCase_      )      )
     ]  # the reference grid
     lowerCAmelCase__          =			1
     lowerCAmelCase__          =			[
         [0 for col in range(len(grid[0]      )      )] for row in range(len(lowerCAmelCase_      )      )
     ]  # the action grid

     lowerCAmelCase__          =			init[0]
     lowerCAmelCase__          =			init[1]
     lowerCAmelCase__          =			0
     lowerCAmelCase__          =			g + heuristic[x][y]  # cost from starting cell to destination cell
     lowerCAmelCase__          =			[[f, g, x, y]]

     lowerCAmelCase__          =			False  # flag that is set when search is complete
     lowerCAmelCase__          =			False  # flag set if we can't find expand

     while not found and not resign:
          if len(lowerCAmelCase_      ) == 0:
               raise ValueError("Algorithm is unable to find solution"      )
          else:  # to choose the least costliest action so as to move closer to the goal
               cell.sort()
               cell.reverse()
               lowerCAmelCase__          =			cell.pop()
               lowerCAmelCase__          =			next_cell[2]
               lowerCAmelCase__          =			next_cell[3]
               lowerCAmelCase__          =			next_cell[1]

               if x == goal[0] and y == goal[1]:
                    lowerCAmelCase__          =			True
               else:
                    for i in range(len(lowerCAmelCase_      )      ):  # to try out different valid actions
                         lowerCAmelCase__          =			x + DIRECTIONS[i][0]
                         lowerCAmelCase__          =			y + DIRECTIONS[i][1]
                         if xa >= 0 and xa < len(lowerCAmelCase_      ) and ya >= 0 and ya < len(grid[0]      ):
                              if closed[xa][ya] == 0 and grid[xa][ya] == 0:
                                   lowerCAmelCase__          =			g + cost
                                   lowerCAmelCase__          =			ga + heuristic[xa][ya]
                                   cell.append([fa, ga, xa, ya]      )
                                   lowerCAmelCase__          =			1
                                   lowerCAmelCase__          =			i
     lowerCAmelCase__          =			[]
     lowerCAmelCase__          =			goal[0]
     lowerCAmelCase__          =			goal[1]
     invpath.append([x, y]      )  # we get the reverse path from here
     while x != init[0] or y != init[1]:
          lowerCAmelCase__          =			x - DIRECTIONS[action[x][y]][0]
          lowerCAmelCase__          =			y - DIRECTIONS[action[x][y]][1]
          lowerCAmelCase__          =			xa
          lowerCAmelCase__          =			ya
          invpath.append([x, y]      )

     lowerCAmelCase__          =			[]
     for i in range(len(lowerCAmelCase_      )      ):
          path.append(invpath[len(lowerCAmelCase_      ) - 1 - i]      )
     return path, action


if __name__ == "__main__":
     UpperCamelCase								=					[
         [0, 1, 0, 0, 0, 0],
         [0, 1, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
         [0, 1, 0, 0, 0, 0],
         [0, 1, 0, 0, 1, 0],
         [0, 0, 0, 0, 1, 0],
     ]

     UpperCamelCase								=					[0, 0]
     # all coordinates are given in format [y,x]
     UpperCamelCase								=					[len(grid) - 1, len(grid[0]) - 1]
     UpperCamelCase								=					1

     # the cost map which pushes the path closer to the goal
     UpperCamelCase								=					[[0 for row in range(len(grid[0]))] for col in range(len(grid))]
     for i in range(len(grid)):
          for j in range(len(grid[0])):
               UpperCamelCase								=					abs(i - goal[0]) + abs(j - goal[1])
               if grid[i][j] == 1:
                    # added extra penalty in the heuristic map
                    UpperCamelCase								=					99

     UpperCamelCase						,  UpperCamelCase								=					search(grid, init, goal, cost, heuristic)

     print('ACTION MAP')
     for i in range(len(action)):
          print(action[i])

     for i in range(len(path)):
          print(path[i])
