






'''simple docstring'''
import heapq
import sys

import numpy as np

UpperCamelCase__ =			tuple[int, int]


class        _UpperCAmelCase						:




    def __init__(			self  :       Optional[int]			):






       '''simple docstring'''






       lowercase_	:    List[str]           =     []
       lowercase_	:    List[str]           =     set()




    def 				lowerCAmelCase__				(			self  :       List[str]			):






       '''simple docstring'''






       if not self.empty():
          return self.elements[0][0]
       else:
          return float("inf"			)




    def 				lowerCAmelCase__				(			self  :       Optional[Any]			):






       '''simple docstring'''






       return len(self.elements			) == 0




    def 				lowerCAmelCase__				(			self  :       Any  ,     a  :       List[Any]  ,     a  :       Tuple			):






       '''simple docstring'''






       if item not in self.set:
          heapq.heappush(self.elements  ,     (priority, item)			)
          self.set.add(a			)
       else:
          # update
          # print("update", item)
          lowercase_	:    int           =     []
          ((lowercase_)    ,		(lowercase_))	:    Any           =     heapq.heappop(self.elements			)
          while x != item:
             temp.append((pri, x)			)
             ((lowercase_)    ,		(lowercase_))	:    List[Any]           =     heapq.heappop(self.elements			)
          temp.append((priority, item)			)
          for pro, xxx in temp:
             heapq.heappush(self.elements  ,     (pro, xxx)			)




    def 				lowerCAmelCase__				(			self  :       Optional[int]  ,     a  :       List[str]			):






       '''simple docstring'''






       if item in self.set:
          self.set.remove(a			)
          lowercase_	:    Optional[Any]           =     []
          ((lowercase_)    ,		(lowercase_))	:    List[Any]           =     heapq.heappop(self.elements			)
          while x != item:
             temp.append((pro, x)			)
             ((lowercase_)    ,		(lowercase_))	:    Dict           =     heapq.heappop(self.elements			)
          for prito, yyy in temp:
             heapq.heappush(self.elements  ,     (prito, yyy)			)




    def 				lowerCAmelCase__				(			self  :       str			):






       '''simple docstring'''






       return self.elements[0][1]





    def 				lowerCAmelCase__				(			self  :       Optional[int]			):






       '''simple docstring'''






       ((lowercase_)    ,		(lowercase_))	:    Optional[Any]           =     heapq.heappop(self.elements			)
       self.set.remove(a			)
       return (priority, item)




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    int           =     np.array(_UpperCamelCase							)
   lowercase_	:    Optional[int]           =     np.array(_UpperCamelCase							)
   return np.linalg.norm(a - b							)




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   return consistent_heuristic(_UpperCamelCase						,		_UpperCamelCase							) // t




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   return abs(p[0] - goal[0]							) + abs(p[1] - goal[1]							)




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    List[Any]           =     g_function[start] + Wa * heuristics[i](_UpperCamelCase						,		_UpperCamelCase							)
   return ans




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    Dict           =     np.chararray((n, n)							)
   for i in range(_UpperCamelCase							):
      for j in range(_UpperCamelCase							):
         lowercase_	:    List[str]           =     "*"

   for i in range(_UpperCamelCase							):
      for j in range(_UpperCamelCase							):
         if (j, (n - 1) - i) in blocks:
            lowercase_	:    int           =     "#"

   lowercase_	:    Optional[int]           =     "-"
   lowercase_	:    List[Any]           =     back_pointer[goal]
   while x != start:
      ((lowercase_)    ,		(lowercase_))	:    Any           =     x
      # print(x)
      lowercase_	:    Dict           =     "-"
      lowercase_	:    str           =     back_pointer[x]
   lowercase_	:    Any           =     "-"

   for i in range(_UpperCamelCase							):
      for j in range(_UpperCamelCase							):
         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_	:    Dict           =     back_pointer[goal]
   while x != start:
      print(_UpperCamelCase						,		end=" "							)
      lowercase_	:    Dict           =     back_pointer[x]
   print(_UpperCamelCase							)
   sys.exit()




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase							):


   """simple docstring"""




   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					(  _UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		):


   """simple docstring"""




   for itera in range(_UpperCamelCase							):
      open_list[itera].remove_element(_UpperCamelCase							)
   # print("s", s)
   # print("j", j)
   ((lowercase_)    ,		(lowercase_))	:    Dict           =     s
   lowercase_	:    Union[str, Any]           =     (x - 1, y)
   lowercase_	:    Tuple           =     (x + 1, y)
   lowercase_	:    str           =     (x, y + 1)
   lowercase_	:    Dict           =     (x, y - 1)

   for neighbours in [left, right, up, down]:
      if neighbours not in blocks:
         if valid(_UpperCamelCase							) and neighbours not in visited:
            # print("neighbour", neighbours)
            visited.add(_UpperCamelCase							)
            lowercase_	:    Union[str, Any]           =     -1
            lowercase_	:    List[str]           =     float("inf"							)

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




def 		__SCREAMING_SNAKE_CASE					(  ):


   """simple docstring"""




   lowercase_	:    Any           =     []
   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


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

UpperCamelCase__ =			[
    (0, 1),
    (1, 1),
    (2, 1),
    (3, 1),
    (4, 1),
    (5, 1),
    (6, 1),
    (7, 1),
    (8, 1),
    (9, 1),
    (10, 1),
    (11, 1),
    (12, 1),
    (13, 1),
    (14, 1),
    (15, 1),
    (16, 1),
    (17, 1),
    (18, 1),
    (19, 1),
]
UpperCamelCase__ =			make_common_ground()


UpperCamelCase__ =			blocks_blk
# hyper parameters
UpperCamelCase__ =			1
UpperCamelCase__ =			1
UpperCamelCase__ =			20
UpperCamelCase__ =			3  # one consistent and two other inconsistent

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

UpperCamelCase__ =			1




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    List[str]           =     {start: 0, goal: float("inf"							)}
   lowercase_	:    Any           =     {start: -1, goal: -1}
   lowercase_	:    List[Any]           =     []
   lowercase_	:    Dict           =     set()

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

   lowercase_	:    list[int]           =     []
   lowercase_	:    list[int]           =     []
   while open_list[0].minkey() < float("inf"							):
      for i in range(1						,		_UpperCamelCase							):
         # 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(_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase							)
            else:
               lowercase_    ,		lowercase_	:    int           =     open_list[i].top_show()
               visited.add(_UpperCamelCase							)
               expand_state(
                   _UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		)
               close_list_inad.append(_UpperCamelCase							)
         else:
            if g_function[goal] <= open_list[0].minkey():
               if g_function[goal] < float("inf"							):
                  do_something(_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase							)
            else:
               lowercase_	:    List[str]           =     open_list[0].top_show()
               visited.add(_UpperCamelCase							)
               expand_state(
                   _UpperCamelCase						,		0						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		)
               close_list_anchor.append(_UpperCamelCase							)
   print("No path found to goal"							)
   print()
   for i in range(n - 1						,		-1						,		-1							):
      for j in range(_UpperCamelCase							):
         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)












'''simple docstring'''
def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase							):


   """simple docstring"""




   return [
       {
           0: [1, 2],
           1: [0, 2],
           2: [0, 1, 3, 5],
           3: [2, 4],
           4: [3],
           5: [2, 6, 8],
           6: [5, 7],
           7: [6, 8],
           8: [5, 7],
       },
       {
           0: [6],
           1: [9],
           2: [4, 5],
           3: [4],
           4: [2, 3],
           5: [2],
           6: [0, 7],
           7: [6],
           8: [],
           9: [1],
       },
       {
           0: [4],
           1: [6],
           2: [],
           3: [5, 6, 7],
           4: [0, 6],
           5: [3, 8, 9],
           6: [1, 3, 4, 7],
           7: [3, 6, 8, 9],
           8: [5, 7],
           9: [5, 7],
       },
       {
           0: [1, 3],
           1: [0, 2, 4],
           2: [1, 3, 4],
           3: [0, 2, 4],
           4: [1, 2, 3],
       },
   ][index]




def 		__SCREAMING_SNAKE_CASE					(  _UpperCamelCase							):


   """simple docstring"""




   lowercase_	:    Dict           =     0
   lowercase_	:    Optional[Any]           =     len(_UpperCamelCase							)  # No of vertices in graph
   lowercase_	:    Union[str, Any]           =     [0] * n
   lowercase_	:    Optional[int]           =     [False] * n

   def dfs(_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase							):
      lowercase_	:    Union[str, Any]           =     True
      lowercase_	:    Dict           =     id_
      id_ += 1
      for to in graph[at]:
         if to == parent:
            pass
         elif not visited[to]:
            dfs(_UpperCamelCase						,		_UpperCamelCase						,		_UpperCamelCase						,		id_							)
            lowercase_	:    str           =     min(low[at]						,		low[to]							)
            if id_ <= low[to]:
               bridges.append((at, to) if at < to else (to, at)							)
         else:
            # This edge is a back edge and cannot be a bridge
            lowercase_	:    Optional[int]           =     min(low[at]						,		low[to]							)

   lowercase_	:    list[tuple[int, int]]           =     []
   for i in range(_UpperCamelCase							):
      if not visited[i]:
         dfs(_UpperCamelCase						,		-1						,		_UpperCamelCase						,		id_							)
   return bridges


if __name__ == "__main__":
 import doctest

 doctest.testmod()




