




'''simple docstring'''




import heapq
import sys

import numpy as np

a_      :		Tuple							      =       tuple[int, int]


class   __UpperCamelCase       :






       def __init__(							self  ):



              """simple docstring"""







              lowerCamelCase_							=[]
              lowerCamelCase_							=set()






       def      lowercase__     (							self  ):



              """simple docstring"""







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






       def      lowercase__     (							self  ):



              """simple docstring"""







              return len(self.elements  ) == 0






       def      lowercase__     (							self,		lowerCAmelCase,		lowerCAmelCase  ):



              """simple docstring"""







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






       def      lowercase__     (							self,		lowerCAmelCase  ):



              """simple docstring"""







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






       def      lowercase__     (							self  ):



              """simple docstring"""







              return self.elements[0][1]






       def      lowercase__     (							self  ):



              """simple docstring"""







              ((lowerCamelCase_),      (lowerCamelCase_))							=heapq.heappop(self.elements  )
              self.set.remove(_UpperCamelCase  )
              return (priority, item)





def      a_							(      __snake_case							:			TPos   ,       __snake_case							:			TPos   )							->						Any:



       """simple docstring"""
       lowerCamelCase_							=np.array(__snake_case   )
       lowerCamelCase_							=np.array(__snake_case   )
       return np.linalg.norm(a - b   )





def      a_							(      __snake_case							:			TPos   ,       __snake_case							:			TPos   )							->						List[str]:



       """simple docstring"""
       return consistent_heuristic(__snake_case   ,       __snake_case   ) // t





def      a_							(      __snake_case							:			TPos   ,       __snake_case							:			TPos   )							->						Any:



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





def      a_							(      __snake_case							:			TPos   ,       __snake_case							:			int   ,       __snake_case							:			TPos   ,       __snake_case							:			dict[TPos, float]   )							->						Tuple:



       """simple docstring"""
       lowerCamelCase_							=g_function[start] + Wa * heuristics[i](__snake_case   ,       __snake_case   )
       return ans





def      a_							(      __snake_case							:			Tuple   ,       __snake_case							:			Optional[int]   ,       __snake_case							:			Optional[int]   )							->						Tuple:



       """simple docstring"""
       lowerCamelCase_							=np.chararray((n, n)   )
       for i in range(__snake_case   ):
              for j in range(__snake_case   ):
                     lowerCamelCase_							='''*'''

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

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

       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:-'''   )
       lowerCamelCase_							=back_pointer[goal]
       while x != start:
              print(__snake_case   ,       end=''' '''   )
              lowerCamelCase_							=back_pointer[x]
       print(__snake_case   )
       sys.exit()





def      a_							(      __snake_case							:			TPos   )							->						Optional[Any]:



       """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_							(      __snake_case							:			int   ,       __snake_case							:			Optional[int]   ,       __snake_case							:			Tuple   ,       __snake_case							:			Tuple   ,       __snake_case							:			Optional[int]   ,       __snake_case							:			str   ,       __snake_case							:			List[Any]   ,       __snake_case							:			Dict   ,       )							->						Dict:



       """simple docstring"""






       for itera in range(__snake_case   ):
              open_list[itera].remove_element(__snake_case   )
       # print("s", s)
       # print("j", j)
       ((lowerCamelCase_),      (lowerCamelCase_))							=s
       lowerCamelCase_							=(x - 1, y)
       lowerCamelCase_							=(x + 1, y)
       lowerCamelCase_							=(x, y + 1)
       lowerCamelCase_							=(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   )
                            lowerCamelCase_							=-1
                            lowerCamelCase_							=float('''inf'''   )

                     if valid(__snake_case   ) and g_function[neighbours] > g_function[s] + 1:
                            lowerCamelCase_							=g_function[s] + 1
                            lowerCamelCase_							=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      a_							(      )							->						str:



       """simple docstring"""
       lowerCamelCase_							=[]
       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


a_      :		Union[str, Any]							      =       {0: consistent_heuristic, 1: heuristic_a, 2: heuristic_a}

a_      :		List[str]							      =       [
    (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),
]
a_      :		List[str]							      =       make_common_ground()


a_      :		int							      =       blocks_blk
# hyper parameters
a_      :		Optional[int]							      =       1
a_      :		List[Any]							      =       1
a_      :		int							      =       20
a_      :		Optional[int]							      =       3  # one consistent and two other inconsistent

# start and end destination
a_      :		Tuple							      =       (0, 0)
a_      :		Any							      =       (n - 1, n - 1)

a_      :		List[Any]							      =       1





def      a_							(      __snake_case							:			TPos   ,       __snake_case							:			TPos   ,       __snake_case							:			int   )							->						Union[str, Any]:



       """simple docstring"""
       lowerCamelCase_							={start: 0, goal: float('''inf'''   )}
       lowerCamelCase_							={start: -1, goal: -1}
       lowerCamelCase_							=[]
       lowerCamelCase_							=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   )   )

       lowerCamelCase_							=[]
       lowerCamelCase_							=[]
       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:
                                   lowerCamelCase_,      lowerCamelCase_							=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:
                                   lowerCamelCase_							=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)











import numpy as np
from PIL import Image



def _a				(	lowerCamelCase:   np.ndarray					,				lowerCamelCase:   int					,				lowerCamelCase:   int )	->						np.ndarray:







      '''simple docstring'''






      __A          =				np.array(lowerCamelCase )
      if arr.shape[0] != arr.shape[1]:
            raise ValueError('''The input array is not a square matrix''' )
      __A          =				0
      __A          =				0
      __A          =				0
      __A          =				0

      # compute the shape of the output matrix
      __A          =				(arr.shape[0] - size) // stride + 1
      # initialize the output matrix with zeros of shape maxpool_shape
      __A          =				np.zeros((maxpool_shape, maxpool_shape) )

      while i < arr.shape[0]:
            if i + size > arr.shape[0]:
                  # if the end of the matrix is reached, break
                  break
            while j < arr.shape[1]:
                  # if the end of the matrix is reached, break
                  if j + size > arr.shape[1]:
                        break
                  # compute the maximum of the pooling matrix
                  __A          =				np.max(arr[i : i + size, j : j + size] )
                  # shift the pooling matrix by stride of column pixels
                  j += stride
                  mat_j += 1

            # shift the pooling matrix by stride of row pixels
            i += stride
            mat_i += 1

            # reset the column index to 0
            __A          =				0
            __A          =				0

      return updated_arr



def _a				(	lowerCamelCase:   np.ndarray					,				lowerCamelCase:   int					,				lowerCamelCase:   int )	->						np.ndarray:







      '''simple docstring'''






      __A          =				np.array(lowerCamelCase )
      if arr.shape[0] != arr.shape[1]:
            raise ValueError('''The input array is not a square matrix''' )
      __A          =				0
      __A          =				0
      __A          =				0
      __A          =				0

      # compute the shape of the output matrix
      __A          =				(arr.shape[0] - size) // stride + 1
      # initialize the output matrix with zeros of shape avgpool_shape
      __A          =				np.zeros((avgpool_shape, avgpool_shape) )

      while i < arr.shape[0]:
            # if the end of the matrix is reached, break
            if i + size > arr.shape[0]:
                  break
            while j < arr.shape[1]:
                  # if the end of the matrix is reached, break
                  if j + size > arr.shape[1]:
                        break
                  # compute the average of the pooling matrix
                  __A          =				int(np.average(arr[i : i + size, j : j + size] ) )
                  # shift the pooling matrix by stride of column pixels
                  j += stride
                  mat_j += 1

            # shift the pooling matrix by stride of row pixels
            i += stride
            mat_i += 1
            # reset the column index to 0
            __A          =				0
            __A          =				0

      return updated_arr


# Main Function
if __name__ == "__main__":
       from doctest import testmod

       testmod(name='avgpooling', verbose=True)

       # Loading the image
       snake_case__					:							Optional[Any]													=     Image.open('path_to_image')

       # Converting the image to numpy array and maxpooling, displaying the result
       # Ensure that the image is a square matrix

       Image.fromarray(maxpooling(np.array(image), size=3, stride=2)).show()

       # Converting the image to numpy array and averagepooling, displaying the result
       # Ensure that the image is a square matrix

       Image.fromarray(avgpooling(np.array(image), size=3, stride=2)).show()





