



"""simple docstring"""





import heapq
import sys

import numpy as np

lowerCamelCase  			=		tuple[int, int]
class  lowercase__  :







       '''simple docstring'''


       def __init__(				self     :    List[str]       )					->		List[Any]:


             '''simple docstring'''




             UpperCAmelCase_     					=				[]
             UpperCAmelCase_     					=				set()



       def 	lowercase__							(				self     :    Any       )					->		Tuple:


             '''simple docstring'''




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



       def 	lowercase__							(				self     :    Any       )					->		Optional[int]:


             '''simple docstring'''




             return len(self.elements       ) == 0



       def 	lowercase__							(				self     :    Optional[int]						,							_UpperCAmelCase     :    str						,							_UpperCAmelCase     :    Any       )					->		Optional[Any]:


             '''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 	lowercase__							(				self     :    List[Any]						,							_UpperCAmelCase     :    Dict       )					->		Any:


             '''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 	lowercase__							(				self     :    List[str]       )					->		Dict:


             '''simple docstring'''




             return self.elements[0][1]







       def 	lowercase__							(				self     :    Union[str, Any]       )					->		Union[str, Any]:


             '''simple docstring'''




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



def   a__      ( lowerCAmelCase__      ,     lowerCAmelCase__ ):
      # euclidean distance
      UpperCAmelCase_     					=				np.array(lowerCAmelCase__ )
      UpperCAmelCase_     					=				np.array(lowerCAmelCase__ )
      return np.linalg.norm(a - b )
def   a__      ( lowerCAmelCase__      ,     lowerCAmelCase__ ):
      # integer division by time variable
      return consistent_heuristic(lowerCAmelCase__      ,     lowerCAmelCase__ ) // t
def   a__      ( lowerCAmelCase__      ,     lowerCAmelCase__ ):
      # manhattan distance
      return abs(p[0] - goal[0] ) + abs(p[1] - goal[1] )
def   a__      ( lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__ ):
      UpperCAmelCase_     					=				g_function[start] + Wa * heuristics[i](lowerCAmelCase__      ,     lowerCAmelCase__ )
      return ans
def   a__      ( lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__ ):
      UpperCAmelCase_     					=				np.chararray((n, n) )
      for i in range(lowerCAmelCase__ ):
            for j in range(lowerCAmelCase__ ):
                  UpperCAmelCase_     					=				"*"

      for i in range(lowerCAmelCase__ ):
            for j in range(lowerCAmelCase__ ):
                  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(lowerCAmelCase__ ):
            for j in range(lowerCAmelCase__ ):
                  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(lowerCAmelCase__      ,     end=" " )
            UpperCAmelCase_     					=				back_pointer[x]
      print(lowerCAmelCase__ )
      sys.exit()
def   a__      ( lowerCAmelCase__ ):
      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__      ( lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     ):
      for itera in range(lowerCAmelCase__ ):
            open_list[itera].remove_element(lowerCAmelCase__ )
      # 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(lowerCAmelCase__ ) and neighbours not in visited:
                        # print("neighbour", neighbours)
                        visited.add(lowerCAmelCase__ )
                        UpperCAmelCase_     					=				-1
                        UpperCAmelCase_     					=				float("inf" )

                  if valid(lowerCAmelCase__ ) 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(lowerCAmelCase__      ,     key(lowerCAmelCase__      ,     0      ,     lowerCAmelCase__      ,     lowerCAmelCase__ ) )
                              if neighbours not in close_list_inad:
                                    for var in range(1      ,     lowerCAmelCase__ ):
                                          if key(lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__ ) <= Wa * key(
                                              lowerCAmelCase__      ,     0      ,     lowerCAmelCase__      ,     lowerCAmelCase__ ):
                                                open_list[j].put(
                                                    lowerCAmelCase__      ,     key(lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__      ,     lowerCAmelCase__ ) )
def   a__      ( ):
      UpperCAmelCase_     					=				[]
      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


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

lowerCamelCase  			=		[
    (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),
]
lowerCamelCase  			=		make_common_ground()


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

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

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

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

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











from math import factorial



def  SCREAMING_SNAKE_CASE				(      snake_case						,   snake_case							)		->    int:

		# If either of the conditions are true, the function is being asked
		# to calculate a factorial of a negative number, which is not possible
		if n < k or k < 0:
				raise ValueError('Please enter positive integers for n and k where n >= k'							)
		return factorial(snake_case							) // (factorial(snake_case							) * factorial(n - k							))


if __name__ == "__main__":
		print(
		    '''The number of five-card hands possible from a standard''',
		    F"""fifty-two card deck is: {combinations(52, 5)}\n""",
		)

		print(
		    '''If a class of 40 students must be arranged into groups of''',
		    F"""4 for group projects, there are {combinations(40, 4)} ways""",
		    '''to arrange them.\n''',
		)

		print(
		    '''If 10 teams are competing in a Formula One race, there''',
		    F"""are {combinations(10, 3)} ways that first, second and""",
		    '''third place can be awarded.''',
		)




