





from __future__ import annotations

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






def lowerCamelCase__    (							snake_case_	:  list[list[int]]       ,      snake_case_	:  list[int]       ,      snake_case_	:  list[int]       ,      snake_case_	:  int       ,      snake_case_	:  list[list[int]]       ,      )      ->				tuple[list[list[int]], list[list[int]]]:
   __snake_case							       =   [
       [0 for col in range(len(grid[0]       )       )] for row in range(len(snake_case_       )       )
   ]  # the reference grid
   __snake_case							       =   1
   __snake_case							       =   [
       [0 for col in range(len(grid[0]       )       )] for row in range(len(snake_case_       )       )
   ]  # the action grid

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

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

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

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

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


if __name__ == "__main__":
    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],
    ]

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

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

    snake_case_			,		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])








from __future__ import annotations






def lowerCamelCase__    (							snake_case_	:  list[int]       ,      snake_case_	:  int       )      ->				list[list[int]]:
   __snake_case							       =   []
   __snake_case							       =   []
   __snake_case							       =   0
   __snake_case							       =   sum(snake_case_       )
   create_state_space_tree(snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       ,      snake_case_       )
   return result






def lowerCamelCase__    (							snake_case_	:  list[int]       ,      snake_case_	:  int       ,      snake_case_	:  int       ,      snake_case_	:  list[int]       ,      snake_case_	:  list[list[int]]       ,      snake_case_	:  int       ,      )      ->				None:
   if sum(snake_case_       ) > max_sum or (remaining_nums_sum + sum(snake_case_       )) < max_sum:
      return
   if sum(snake_case_       ) == max_sum:
      result.append(snake_case_       )
      return
   for index in range(snake_case_       ,      len(snake_case_       )       ):
      create_state_space_tree(
          snake_case_       ,      snake_case_       ,      index + 1       ,      [*path, nums[index]]       ,      snake_case_       ,      remaining_nums_sum - nums[index]       ,      )
snake_case_				=			[3, 34, 4, 12, 5, 2]
snake_case_				=			9
snake_case_				=			generate_sum_of_subsets_soln(nums, max_sum)







print(*result)

