

import heapq
import sys

import numpy as np

__lowercase  :   List[str]						      =tuple[int, int]

class      A       :



      def __init__(	self:						Optional[int]       )						->    Dict:
         '''simple docstring'''

         UpperCAmelCase_											=[]
         UpperCAmelCase_											=set()



      def 	lowerCAmelCase__    (	self:						int       )						->    List[Any]:
         '''simple docstring'''

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



      def 	lowerCAmelCase__    (	self:						Dict       )						->    Optional[Any]:
         '''simple docstring'''

         return len(self.elements       ) == 0



      def 	lowerCAmelCase__    (	self:						str		,  _lowerCAmelCase:						Union[str, Any]		,  _lowerCAmelCase:						Optional[Any]       )						->    Dict:
         '''simple docstring'''

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



      def 	lowerCAmelCase__    (	self:						List[str]		,  _lowerCAmelCase:						Optional[Any]       )						->    Dict:
         '''simple docstring'''

         if item in self.set:
            self.set.remove(_lowerCAmelCase       )
            UpperCAmelCase_											=[]
            ((UpperCAmelCase_)						,       (UpperCAmelCase_))											=heapq.heappop(self.elements       )
            while x != item:
               temp.append((pro, x)       )
               ((UpperCAmelCase_)						,       (UpperCAmelCase_))											=heapq.heappop(self.elements       )
            for prito, yyy in temp:
               heapq.heappush(self.elements		,  (prito, yyy)       )



      def 	lowerCAmelCase__    (	self:						Any       )						->    List[Any]:
         '''simple docstring'''

         return self.elements[0][1]






      def 	lowerCAmelCase__    (	self:						Optional[int]       )						->    List[Any]:
         '''simple docstring'''

         ((UpperCAmelCase_)						,       (UpperCAmelCase_))											=heapq.heappop(self.elements       )
         self.set.remove(_lowerCAmelCase       )
         return (priority, item)




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=np.array(lowercase__  )
   UpperCAmelCase_											=np.array(lowercase__  )
   return np.linalg.norm(a - b  )




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   return consistent_heuristic(lowercase__  ,    lowercase__  ) // t




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






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




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=g_function[start] + Wa * heuristics[i](lowercase__  ,    lowercase__  )
   return ans




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=np.chararray((n, n)  )
   for i in range(lowercase__  ):
      for j in range(lowercase__  ):
         UpperCAmelCase_											="*"

   for i in range(lowercase__  ):
      for j in range(lowercase__  ):
         if (j, (n - 1) - i) in blocks:
            UpperCAmelCase_											="#"

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

   for i in range(lowercase__  ):
      for j in range(lowercase__  ):
         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:-"  )
   UpperCAmelCase_											=back_pointer[goal]
   while x != start:
      print(lowercase__  ,    end=" "  )
      UpperCAmelCase_											=back_pointer[x]
   print(lowercase__  )
   sys.exit()




def     a__ (					lowercase__  ):






   '''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     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    ):






   '''simple docstring'''






   for itera in range(lowercase__  ):
      open_list[itera].remove_element(lowercase__  )
   # print("s", s)
   # print("j", j)
   ((UpperCAmelCase_)						,       (UpperCAmelCase_))											=s
   UpperCAmelCase_											=(x - 1, y)
   UpperCAmelCase_											=(x + 1, y)
   UpperCAmelCase_											=(x, y + 1)
   UpperCAmelCase_											=(x, y - 1)

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

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




def     a__ (					):






   '''simple docstring'''






   UpperCAmelCase_											=[]
   for x in range(1  ,    5  ):
      for y in range(1  ,    6  ):
         some_list.append((x, y)  )

   for x in range(1_5  ,    2_0  ):
      some_list.append((x, 1_7)  )

   for x in range(1_0  ,    1_9  ):
      for y in range(1  ,    1_5  ):
         some_list.append((x, y)  )

    # L block
   for x in range(1  ,    4  ):
      for y in range(1_2  ,    1_9  ):
         some_list.append((x, y)  )
   for x in range(3  ,    1_3  ):
      for y in range(1_6  ,    1_9  ):
         some_list.append((x, y)  )
   return some_list


__lowercase  :   Optional[int]						      ={0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

__lowercase  :   Optional[Any]						      =[
    (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),
]
__lowercase  :   Optional[Any]						      =make_common_ground()


__lowercase  :   Dict						      =blocks_blk
# hyper parameters
__lowercase  :   Union[str, Any]						      =1
__lowercase  :   Union[str, Any]						      =1
__lowercase  :   Optional[int]						      =20
__lowercase  :   List[str]						      =3  # one consistent and two other inconsistent

# start and end destination
__lowercase  :   str						      =(0, 0)
__lowercase  :   str						      =(n - 1, n - 1)

__lowercase  :   Optional[Any]						      =1




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											={start: 0, goal: float("inf"  )}
   UpperCAmelCase_											={start: -1, goal: -1}
   UpperCAmelCase_											=[]
   UpperCAmelCase_											=set()

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

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











import sys
import turtle




def     a__ (					lowercase__  ,    lowercase__  ):






   '''simple docstring'''






   return (pa[0] + pa[0]) / 2, (pa[1] + pa[1]) / 2




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    ):






   '''simple docstring'''






   my_pen.up()
   my_pen.goto(vertexa[0]  ,    vertexa[1]  )
   my_pen.down()
   my_pen.goto(vertexa[0]  ,    vertexa[1]  )
   my_pen.goto(vertexa[0]  ,    vertexa[1]  )
   my_pen.goto(vertexa[0]  ,    vertexa[1]  )

   if depth == 0:
      return

   triangle(lowercase__  ,    get_mid(lowercase__  ,    lowercase__  )  ,    get_mid(lowercase__  ,    lowercase__  )  ,    depth - 1  )
   triangle(lowercase__  ,    get_mid(lowercase__  ,    lowercase__  )  ,    get_mid(lowercase__  ,    lowercase__  )  ,    depth - 1  )
   triangle(lowercase__  ,    get_mid(lowercase__  ,    lowercase__  )  ,    get_mid(lowercase__  ,    lowercase__  )  ,    depth - 1  )


if __name__ == "__main__":
     if len(sys.argv) != 2:
          raise ValueError(
              """Correct format for using this script: """
              """python fractals.py <int:depth_for_fractal>"""
          )
     __lowercase  :   Any						      =turtle.Turtle()
     my_pen.ht()
     my_pen.speed(5)
     my_pen.pencolor("""red""")

     __lowercase  :   str						      =[(-175, -125), (0, 175), (175, -125)]  # vertices of triangle
     triangle(vertices[0], vertices[1], vertices[2], int(sys.argv[1]))




