


from __future__ import annotations

__a     =			[
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]
def   _UpperCamelCase				(						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						)						->tuple[list[list[int]], list[list[int]]]:
   UpperCAmelCase							=     [
       [0 for col in range(len(grid[0]   )   )] for row in range(len(lowerCAmelCase_   )   )
   ]  # the reference grid
   UpperCAmelCase							=     1
   UpperCAmelCase							=     [
       [0 for col in range(len(grid[0]   )   )] for row in range(len(lowerCAmelCase_   )   )
   ]  # the action grid

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

   UpperCAmelCase							=     False  # flag that is set when search is complete
   UpperCAmelCase							=     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()
         UpperCAmelCase							=     cell.pop()
         UpperCAmelCase							=     next_cell[2]
         UpperCAmelCase							=     next_cell[3]
         UpperCAmelCase							=     next_cell[1]

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

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


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

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

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

 __a   ,					__a     =			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])







__a     =			[
    (1000, """M"""),
    (900, """CM"""),
    (500, """D"""),
    (400, """CD"""),
    (100, """C"""),
    (90, """XC"""),
    (50, """L"""),
    (40, """XL"""),
    (10, """X"""),
    (9, """IX"""),
    (5, """V"""),
    (4, """IV"""),
    (1, """I"""),
]
def   _UpperCamelCase				(						lowerCAmelCase_   )						->int:
   UpperCAmelCase							=     {"""I""": 1, """V""": 5, """X""": 1_0, """L""": 5_0, """C""": 1_0_0, """D""": 5_0_0, """M""": 1_0_0_0}
   UpperCAmelCase							=     0
   UpperCAmelCase							=     0
   while place < len(lowerCAmelCase_   ):
      if (place + 1 < len(lowerCAmelCase_   )) and (vals[roman[place]] < vals[roman[place + 1]]):
         total += vals[roman[place + 1]] - vals[roman[place]]
         place += 2
      else:
         total += vals[roman[place]]
         place += 1
   return total
def   _UpperCamelCase				(						lowerCAmelCase_   )						->str:
   UpperCAmelCase							=     []
   for arabic, roman in ROMAN:
      ((UpperCAmelCase)				,  (UpperCAmelCase))							=     divmod(lowerCAmelCase_  ,						lowerCAmelCase_   )
      result.append(roman * factor   )
      if number == 0:
         break
   return "".join(lowerCAmelCase_   )


if __name__ == "__main__":
 import doctest

 doctest.testmod()



