






from __future__ import annotations

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


def 	lowerCamelCase__      (  lowercase    ,  lowercase    ,  lowercase    ,  lowercase    ,  lowercase    ,  ):

  """simple docstring"""






  SCREAMING_SNAKE_CASE							:   int						    =     [
      [0 for col in range(len(grid[0]					)					)] for row in range(len(lowercase					)					)
  ]  # the reference grid
  SCREAMING_SNAKE_CASE							:   Any						    =     1
  SCREAMING_SNAKE_CASE							:   int						    =     [
      [0 for col in range(len(grid[0]					)					)] for row in range(len(lowercase					)					)
  ]  # the action grid

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

  SCREAMING_SNAKE_CASE							:   Any						    =     False  # flag that is set when search is complete
  SCREAMING_SNAKE_CASE							:   List[Any]						    =     False  # flag set if we can't find expand

  while not found and not resign:
    if len(lowercase					) == 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()
      SCREAMING_SNAKE_CASE							:   Dict						    =     cell.pop()
      SCREAMING_SNAKE_CASE							:   str						    =     next_cell[2]
      SCREAMING_SNAKE_CASE							:   Dict						    =     next_cell[3]
      SCREAMING_SNAKE_CASE							:   Tuple						    =     next_cell[1]

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

  SCREAMING_SNAKE_CASE							:   Any						    =     []
  for i in range(len(lowercase					)					):
    path.append(invpath[len(lowercase					) - 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])










'''simple docstring'''
from __future__ import annotations

import math


def      a (     __a					,   __a					,   __a					,   __a					,   __a  )    ->      int:



					'''simple docstring'''






					if depth < 0:
										raise ValueError('''Depth cannot be less than 0'''  )

					if len(__a  ) == 0:
										raise ValueError('''Scores cannot be empty'''  )

					if depth == height:
										return scores[node_index]

					if is_max:
										return max(
										    minimax(depth + 1					,   node_index * 2					,   __a					,   __a					,   __a  )					,   minimax(depth + 1					,   node_index * 2 + 1					,   __a					,   __a					,   __a  )					,   )

					return min(
					    minimax(depth + 1					,   node_index * 2					,   __a					,   __a					,   __a  )					,   minimax(depth + 1					,   node_index * 2 + 1					,   __a					,   __a					,   __a  )					,   )


def      a (     )    ->      None:



					'''simple docstring'''






					UpperCamelCase__  :str				   =					[90, 23, 6, 33, 21, 65, 123, 34423]
					UpperCamelCase__  :List[Any]				   =					math.log(len(__a  )					,   2  )
					print('''Optimal value : '''					,   end=''''''  )
					print(minimax(0					,   0					,   __a					,   __a					,   __a  )  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()