"""simple docstring"""







from __future__ import annotations

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


def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,):






							"""simple docstring"""





							_lowercase :    List[str]							=							[
							    [0 for col in range(len(grid[0]			)			)] for row in range(len(__UpperCAmelCase			)			)
							]  # the reference grid
							_lowercase :    Optional[Any]							=							1
							_lowercase :    Any							=							[
							    [0 for col in range(len(grid[0]			)			)] for row in range(len(__UpperCAmelCase			)			)
							]  # the action grid

							_lowercase :    List[Any]							=							init[0]
							_lowercase :    Optional[Any]							=							init[1]
							_lowercase :    Union[str, Any]							=							0
							_lowercase :    Union[str, Any]							=							g + heuristic[x][y]  # cost from starting cell to destination cell
							_lowercase :    Dict							=							[[f, g, x, y]]

							_lowercase :    Tuple							=							False  # flag that is set when search is complete
							_lowercase :    Tuple							=							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()
																					_lowercase :    List[Any]							=							cell.pop()
																					_lowercase :    Optional[Any]							=							next_cell[2]
																					_lowercase :    List[str]							=							next_cell[3]
																					_lowercase :    Optional[int]							=							next_cell[1]

																					if x == goal[0] and y == goal[1]:
																												_lowercase :    Optional[Any]							=							True
																					else:
																												for i in range(len(__UpperCAmelCase			)			):  # to try out different valid actions
																																			_lowercase :    Any							=							x + DIRECTIONS[i][0]
																																			_lowercase :    Union[str, Any]							=							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:
																																																	_lowercase :    int							=							g + cost
																																																	_lowercase :    List[str]							=							ga + heuristic[xa][ya]
																																																	cell.append([fa, ga, xa, ya]			)
																																																	_lowercase :    List[Any]							=							1
																																																	_lowercase :    Dict							=							i
							_lowercase :    Union[str, Any]							=							[]
							_lowercase :    Optional[int]							=							goal[0]
							_lowercase :    Any							=							goal[1]
							invpath.append([x, y]			)  # we get the reverse path from here
							while x != init[0] or y != init[1]:
														_lowercase :    str							=							x - DIRECTIONS[action[x][y]][0]
														_lowercase :    Any							=							y - DIRECTIONS[action[x][y]][1]
														_lowercase :    Dict							=							xa
														_lowercase :    Tuple							=							ya
														invpath.append([x, y]			)

							_lowercase :    List[str]							=							[]
							for i in range(len(__UpperCAmelCase			)			):
														path.append(invpath[len(__UpperCAmelCase			) - 1 - i]			)
							return path, action


if __name__ == "__main__":
						SCREAMING_SNAKE_CASE									=						[
						    [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],
						]

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

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

						SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE									=						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])




"""simple docstring"""







def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	return not any(
	    neighbour == 1 and colored_vertices[i] == color
	    for i, neighbour in enumerate(__UpperCAmelCase			)			)


def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	if index == len(__UpperCAmelCase			):
		return True

	# Recursive Step
	for i in range(__UpperCAmelCase			):
		if valid_coloring(graph[index]     ,__UpperCAmelCase     ,__UpperCAmelCase			):
			# Color current vertex
			_lowercase :    str							=							i
			# Validate coloring
			if util_color(__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,index + 1			):
				return True
			# Backtrack
			_lowercase :    List[str]							=							-1
	return False







def      __lowerCAmelCase(		__UpperCAmelCase     ,__UpperCAmelCase			):






	"""simple docstring"""





	_lowercase :    Any							=							[-1] * len(__UpperCAmelCase			)

	if util_color(__UpperCAmelCase     ,__UpperCAmelCase     ,__UpperCAmelCase     ,0			):
		return colored_vertices

	return []



