





import heapq
import sys

import numpy as np

snake_case								=							tuple[int, int]





class 					A_					:







       """simple docstring"""





       def __init__(     self						:						List[Any]	)    ->       List[Any]:
         _lowercase						    =			[]
         _lowercase						    =			set()







       def  __UpperCAmelCase			(     self						:						List[str]	)    ->       Optional[int]:
         if not self.empty():
           return self.elements[0][0]
         else:
           return float('inf'	)







       def  __UpperCAmelCase			(     self						:						List[str]	)    ->       Union[str, Any]:
         return len(self.elements	) == 0







       def  __UpperCAmelCase			(     self						:						str    ,__A						:						Any    ,__A						:						Any	)    ->       int:
         if item not in self.set:
           heapq.heappush(self.elements    ,(priority, item)	)
           self.set.add(__A	)
         else:
           # update
           # print("update", item)
           _lowercase						    =			[]
           ((_lowercase)    ,		(_lowercase))						    =			heapq.heappop(self.elements	)
           while x != item:
             temp.append((pri, x)	)
             ((_lowercase)    ,		(_lowercase))						    =			heapq.heappop(self.elements	)
           temp.append((priority, item)	)
           for pro, xxx in temp:
             heapq.heappush(self.elements    ,(pro, xxx)	)







       def  __UpperCAmelCase			(     self						:						List[str]    ,__A						:						Optional[Any]	)    ->       Dict:
         if item in self.set:
           self.set.remove(__A	)
           _lowercase						    =			[]
           ((_lowercase)    ,		(_lowercase))						    =			heapq.heappop(self.elements	)
           while x != item:
             temp.append((pro, x)	)
             ((_lowercase)    ,		(_lowercase))						    =			heapq.heappop(self.elements	)
           for prito, yyy in temp:
             heapq.heappush(self.elements    ,(prito, yyy)	)







       def  __UpperCAmelCase			(     self						:						List[str]	)    ->       Any:
         return self.elements[0][1]







       def  __UpperCAmelCase			(     self						:						Any	)    ->       Any:
         ((_lowercase)    ,		(_lowercase))						    =			heapq.heappop(self.elements	)
         self.set.remove(__A	)
         return (priority, item)

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:TPos      ,				snake_case__	:TPos  )   ->    Tuple:
  # euclidean distance
  _lowercase						    =			np.array(snake_case__  )
  _lowercase						    =			np.array(snake_case__  )
  return np.linalg.norm(a - b  )

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:TPos      ,				snake_case__	:TPos  )   ->    str:
  # integer division by time variable
  return consistent_heuristic(snake_case__      ,				snake_case__  ) // t

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:TPos      ,				snake_case__	:TPos  )   ->    Any:
  # manhattan distance
  return abs(p[0] - goal[0]  ) + abs(p[1] - goal[1]  )

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:TPos      ,				snake_case__	:int      ,				snake_case__	:TPos      ,				snake_case__	:dict[TPos, float]  )   ->    str:
  _lowercase						    =			g_function[start] + Wa * heuristics[i](snake_case__      ,				snake_case__  )
  return ans

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:Union[str, Any]      ,				snake_case__	:List[str]      ,				snake_case__	:Optional[int]  )   ->    int:
  _lowercase						    =			np.chararray((n, n)  )
  for i in range(snake_case__  ):
    for j in range(snake_case__  ):
      _lowercase						    =			'*'

  for i in range(snake_case__  ):
    for j in range(snake_case__  ):
      if (j, (n - 1) - i) in blocks:
        _lowercase						    =			'#'

  _lowercase						    =			'-'
  _lowercase						    =			back_pointer[goal]
  while x != start:
    ((_lowercase)    ,		(_lowercase))						    =			x
    # print(x)
    _lowercase						    =			'-'
    _lowercase						    =			back_pointer[x]
  _lowercase						    =			'-'

  for i in range(snake_case__  ):
    for j in range(snake_case__  ):
      if (i, j) == (0, n - 1):
        print(grid[i][j]      ,				end=' '  )
        print('<-- End position'      ,				end=' '  )
      else:
        print(grid[i][j]      ,				end=' '  )
    print()
  print('^'  )
  print('Start position'  )
  print()
  print('# is an obstacle'  )
  print('- is the path taken by algorithm'  )
  print('PATH TAKEN BY THE ALGORITHM IS:-'  )
  _lowercase						    =			back_pointer[goal]
  while x != start:
    print(snake_case__      ,				end=' '  )
    _lowercase						    =			back_pointer[x]
  print(snake_case__  )
  sys.exit()

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:TPos  )   ->    str:
  if p[0] < 0 or p[0] > n - 1:
    return False
  if p[1] < 0 or p[1] > n - 1:
    return False
  return True

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:str      ,				snake_case__	:Tuple      ,				snake_case__	:Optional[int]      ,				snake_case__	:str      ,				snake_case__	:Optional[int]      ,				snake_case__	:int      ,				snake_case__	:Tuple      ,				snake_case__	:str      ,				)   ->    Any:
  for itera in range(snake_case__  ):
    open_list[itera].remove_element(snake_case__  )
  # print("s", s)
  # print("j", j)
  ((_lowercase)    ,		(_lowercase))						    =			s
  _lowercase						    =			(x - 1, y)
  _lowercase						    =			(x + 1, y)
  _lowercase						    =			(x, y + 1)
  _lowercase						    =			(x, y - 1)

  for neighbours in [left, right, up, down]:
    if neighbours not in blocks:
      if valid(snake_case__  ) and neighbours not in visited:
        # print("neighbour", neighbours)
        visited.add(snake_case__  )
        _lowercase						    =			-1
        _lowercase						    =			float('inf'  )

      if valid(snake_case__  ) and g_function[neighbours] > g_function[s] + 1:
        _lowercase						    =			g_function[s] + 1
        _lowercase						    =			s
        if neighbours not in close_list_anchor:
          open_list[0].put(snake_case__      ,				key(snake_case__      ,				0      ,				snake_case__      ,				snake_case__  )  )
          if neighbours not in close_list_inad:
            for var in range(1      ,				snake_case__  ):
              if key(snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__  ) <= Wa * key(
                  snake_case__      ,				0      ,				snake_case__      ,				snake_case__  ):
                open_list[j].put(
                    snake_case__      ,				key(snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__  )  )

def 				SCREAMING_SNAKE_CASE__							(	)   ->    str:
  _lowercase						    =			[]
  for x in range(1      ,				5  ):
    for y in range(1      ,				6  ):
      some_list.append((x, y)  )

  for x in range(15      ,				20  ):
    some_list.append((x, 17)  )

  for x in range(10      ,				19  ):
    for y in range(1      ,				15  ):
      some_list.append((x, y)  )

    # L block
  for x in range(1      ,				4  ):
    for y in range(12      ,				19  ):
      some_list.append((x, y)  )
  for x in range(3      ,				13  ):
    for y in range(16      ,				19  ):
      some_list.append((x, y)  )
  return some_list


snake_case								=							{0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

snake_case								=							[
    (0, 1),
    (1, 1),
    (2, 1),
    (3, 1),
    (4, 1),
    (5, 1),
    (6, 1),
    (7, 1),
    (8, 1),
    (9, 1),
    (1_0, 1),
    (1_1, 1),
    (1_2, 1),
    (1_3, 1),
    (1_4, 1),
    (1_5, 1),
    (1_6, 1),
    (1_7, 1),
    (1_8, 1),
    (1_9, 1),
]
snake_case								=							make_common_ground()


snake_case								=							blocks_blk
# hyper parameters
snake_case								=							1
snake_case								=							1
snake_case								=							2_0
snake_case								=							3  # one consistent and two other inconsistent

# start and end destination
snake_case								=							(0, 0)
snake_case								=							(n - 1, n - 1)

snake_case								=							1

def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:TPos      ,				snake_case__	:TPos      ,				snake_case__	:int  )   ->    Any:
  _lowercase						    =			{start: 0, goal: float('inf'  )}
  _lowercase						    =			{start: -1, goal: -1}
  _lowercase						    =			[]
  _lowercase						    =			set()

  for i in range(snake_case__  ):
    open_list.append(PriorityQueue()  )
    open_list[i].put(snake_case__      ,				key(snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__  )  )

  _lowercase						    =			[]
  _lowercase						    =			[]
  while open_list[0].minkey() < float('inf'  ):
    for i in range(1      ,				snake_case__  ):
      # print(open_list[0].minkey(), open_list[i].minkey())
      if open_list[i].minkey() <= Wa * open_list[0].minkey():
        global t
        t += 1
        if g_function[goal] <= open_list[i].minkey():
          if g_function[goal] < float('inf'  ):
            do_something(snake_case__      ,				snake_case__      ,				snake_case__  )
        else:
          _lowercase    ,		_lowercase						    =			open_list[i].top_show()
          visited.add(snake_case__  )
          expand_state(
              snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				)
          close_list_inad.append(snake_case__  )
      else:
        if g_function[goal] <= open_list[0].minkey():
          if g_function[goal] < float('inf'  ):
            do_something(snake_case__      ,				snake_case__      ,				snake_case__  )
        else:
          _lowercase						    =			open_list[0].top_show()
          visited.add(snake_case__  )
          expand_state(
              snake_case__      ,				0      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				snake_case__      ,				)
          close_list_anchor.append(snake_case__  )
  print('No path found to goal'  )
  print()
  for i in range(n - 1      ,				-1      ,				-1  ):
    for j in range(snake_case__  ):
      if (j, i) in blocks:
        print('#'      ,				end=' '  )
      elif (j, i) in back_pointer:
        if (j, i) == (n - 1, n - 1):
          print('*'      ,				end=' '  )
        else:
          print('-'      ,				end=' '  )
      else:
        print('*'      ,				end=' '  )
      if (j, i) == (n - 1, n - 1):
        print('<-- End position'      ,				end=' '  )
    print()
  print('^'  )
  print('Start position'  )
  print()
  print('# is an obstacle'  )
  print('- is the path taken by algorithm'  )


if __name__ == "__main__":
      multi_a_star(start, goal, n_heuristic)


def 							_lowerCamelCase   (			SCREAMING_SNAKE_CASE		,				SCREAMING_SNAKE_CASE   ):
      '''simple docstring'''







      A_							       =		len(SCREAMING_SNAKE_CASE   )
      A_							       =		len(SCREAMING_SNAKE_CASE   )
      A_							       =		(
          first_str_length if first_str_length > second_str_length else second_str_length
      )
      A_							       =		[]
      for char_count in range(SCREAMING_SNAKE_CASE   ):
            if char_count < first_str_length:
                  output_list.append(first_str[char_count]   )
            if char_count < second_str_length:
                  output_list.append(second_str[char_count]   )
      return "".join(SCREAMING_SNAKE_CASE   )


if __name__ == "__main__":
      print(alternative_string_arrange("""AB""", """XYZ"""), end=""" """)





