




'''simple docstring'''


from __future__ import annotations

_snake_case : List[str]  				=						[
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]
def 						snake_case_       (UpperCamelCase			:    list[list[int]]					,		UpperCamelCase			:    list[int]					,		UpperCamelCase			:    list[int]					,		UpperCamelCase			:    int					,		UpperCamelCase			:    list[list[int]]					,		):





							'''simple docstring'''


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

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

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

							while not found and not resign:
														if len(UpperCamelCase ) == 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()
																					_a      	=							cell.pop()
																					_a      	=							next_cell[2]
																					_a      	=							next_cell[3]
																					_a      	=							next_cell[1]

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

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


if __name__ == "__main__":
				_snake_case : str  				=						[
				    [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],
				]

				_snake_case : List[Any]  				=						[0, 0]
				# all coordinates are given in format [y,x]
				_snake_case : Optional[int]  				=						[len(grid) - 1, len(grid[0]) - 1]
				_snake_case : Tuple  				=						1

				# the cost map which pushes the path closer to the goal
				_snake_case : str  				=						[[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])):
												_snake_case : Optional[int]  				=						abs(i - goal[0]) + abs(j - goal[1])
												if grid[i][j] == 1:
																# added extra penalty in the heuristic map
																_snake_case : str  				=						99

				_snake_case				,							_snake_case : Any  				=						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])






from __future__ import annotations

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:dict	,   _snake_case	:str				)  ->     set[str]:
   _A  ,    _A      =       set(_snake_case				), [start]

   while stack:
      _A      =       stack.pop()
      explored.add(_snake_case				)
      # Differences from BFS:
      # 1) pop last element instead of first one
      # 2) add adjacent elements to stack without exploring them
      for adj in reversed(graph[v]				):
         if adj not in explored:
            stack.append(_snake_case				)
   return explored


UpperCAmelCase_		 =					{
    """A""": ["""B""", """C""", """D"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F"""],
    """D""": ["""B""", """D"""],
    """E""": ["""B""", """F"""],
    """F""": ["""C""", """E""", """G"""],
    """G""": ["""F"""],
}

if __name__ == "__main__":
   import doctest

   doctest.testmod()
   print(depth_first_search(G, """A"""))



