
import heapq
import sys

import numpy as np

__a         =   tuple[int, int]
class 					lowercase__:



	"""simple docstring"""




	def __init__(			self    :     Union[str, Any]			)			->	Any:
					lowercase_	    =   []
					lowercase_	    =   set()
	def 		_lowercase    (			self    :     Dict			)			->	Tuple:
					if not self.empty():
									return self.elements[0][0]
					else:
									return float('''inf'''			)
	def 		_lowercase    (			self    :     int			)			->	Any:
					return len(self.elements			) == 0
	def 		_lowercase    (			self    :     List[Any]			,				SCREAMING_SNAKE_CASE_    :     Dict			,				SCREAMING_SNAKE_CASE_    :     str			)			->	str:
					if item not in self.set:
									heapq.heappush(self.elements			,				(priority, item)			)
									self.set.add(SCREAMING_SNAKE_CASE_			)
					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 		_lowercase    (			self    :     Any			,				SCREAMING_SNAKE_CASE_    :     List[Any]			)			->	Optional[Any]:
					if item in self.set:
									self.set.remove(SCREAMING_SNAKE_CASE_			)
									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 		_lowercase    (			self    :     Any			)			->	Optional[int]:
					return self.elements[0][1]




	def 		_lowercase    (			self    :     Tuple			)			->	str:
					((lowercase_)    ,      (lowercase_))	    =   heapq.heappop(self.elements			)
					self.set.remove(SCREAMING_SNAKE_CASE_			)
					return (priority, item)




def 							a		(				snake_case__:   TPos		,  snake_case__:   TPos   ):


				'''simple docstring'''
				# euclidean distance
				lowercase_	    =   np.array(snake_case__   )
				lowercase_	    =   np.array(snake_case__   )
				return np.linalg.norm(a - b   )




def 							a		(				snake_case__:   TPos		,  snake_case__:   TPos   ):


				'''simple docstring'''
				# integer division by time variable
				return consistent_heuristic(snake_case__		,  snake_case__   ) // t




def 							a		(				snake_case__:   TPos		,  snake_case__:   TPos   ):


				'''simple docstring'''
				# manhattan distance
				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]   ):


				'''simple docstring'''
				lowercase_	    =   g_function[start] + Wa * heuristics[i](snake_case__		,  snake_case__   )
				return ans




def 							a		(				snake_case__:   List[Any]		,  snake_case__:   Dict		,  snake_case__:   List[str]   ):


				'''simple docstring'''
				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 							a		(				snake_case__:   TPos   ):


				'''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__:   Optional[Any]		,  snake_case__:   List[str]		,  snake_case__:   Dict		,  snake_case__:   str		,  snake_case__:   Dict		,  snake_case__:   Optional[Any]		,  snake_case__:   List[Any]		,  snake_case__:   Optional[int]		,  ):


				'''simple docstring'''
				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 							a		(				):


				'''simple docstring'''
				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


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

__a         =   [
    (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),
]
__a         =   make_common_ground()


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

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

__a         =   1




def 							a		(				snake_case__:   TPos		,  snake_case__:   TPos		,  snake_case__:   int   ):


				'''simple docstring'''
				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)






"""simple docstring"""



from __future__ import annotations

import queue





class 				a			:



      def __init__(   self     ,	UpperCamelCase_      ):
          UpperCAmelCase__	:      int     							=					data
          UpperCAmelCase__	:      Dict     							=					None
          UpperCAmelCase__	:      Optional[int]     							=					None




def 					lowerCamelCase   (     ):
    print('\n********Press N to stop entering at any point of time********\n' )
    UpperCAmelCase__	:      int     							=					input('Enter the value of the root node: ' ).strip().lower()
    UpperCAmelCase__	:      queue.Queue     							=					queue.Queue()
    UpperCAmelCase__	:      Dict     							=					TreeNode(int(_snake_case ) )
    q.put(_snake_case )
    while not q.empty():
        UpperCAmelCase__	:      Tuple     							=					q.get()
        UpperCAmelCase__	:      List[Any]     							=					F'''Enter the left node of {node_found.data}: '''
        UpperCAmelCase__	:      Dict     							=					input(_snake_case ).strip().lower() or 'n'
        if check == "n":
            return tree_node
        UpperCAmelCase__	:      Optional[int]     							=					TreeNode(int(_snake_case ) )
        UpperCAmelCase__	:      Tuple     							=					left_node
        q.put(_snake_case )
        UpperCAmelCase__	:      int     							=					F'''Enter the right node of {node_found.data}: '''
        UpperCAmelCase__	:      int     							=					input(_snake_case ).strip().lower() or 'n'
        if check == "n":
            return tree_node
        UpperCAmelCase__	:      int     							=					TreeNode(int(_snake_case ) )
        UpperCAmelCase__	:      Any     							=					right_node
        q.put(_snake_case )
    raise
def 					lowerCamelCase   (     _snake_case ):
    if not isinstance(_snake_case    ,_snake_case ) or not node:
        return
    print(node.data    ,end=',' )
    pre_order(node.left )
    pre_order(node.right )
def 					lowerCamelCase   (     _snake_case ):
    if not isinstance(_snake_case    ,_snake_case ) or not node:
        return
    in_order(node.left )
    print(node.data    ,end=',' )
    in_order(node.right )
def 					lowerCamelCase   (     _snake_case ):
    if not isinstance(_snake_case    ,_snake_case ) or not node:
        return
    post_order(node.left )
    post_order(node.right )
    print(node.data    ,end=',' )
def 					lowerCamelCase   (     _snake_case ):
    if not isinstance(_snake_case    ,_snake_case ) or not node:
        return
    UpperCAmelCase__	:      queue.Queue     							=					queue.Queue()
    q.put(_snake_case )
    while not q.empty():
        UpperCAmelCase__	:      int     							=					q.get()
        print(node_dequeued.data    ,end=',' )
        if node_dequeued.left:
            q.put(node_dequeued.left )
        if node_dequeued.right:
            q.put(node_dequeued.right )
def 					lowerCamelCase   (     _snake_case ):
    if not isinstance(_snake_case    ,_snake_case ) or not node:
        return
    UpperCAmelCase__	:      queue.Queue     							=					queue.Queue()
    q.put(_snake_case )
    while not q.empty():
        UpperCAmelCase__	:      Optional[Any]     							=					[]
        while not q.empty():
            UpperCAmelCase__	:      Union[str, Any]     							=					q.get()
            print(node_dequeued.data    ,end=',' )
            if node_dequeued.left:
                list_.append(node_dequeued.left )
            if node_dequeued.right:
                list_.append(node_dequeued.right )
        print()
        for node in list_:
            q.put(_snake_case )
def 					lowerCamelCase   (     _snake_case ):
    if not isinstance(_snake_case    ,_snake_case ) or not node:
        return
    UpperCAmelCase__	:      list[TreeNode]     							=					[]
    UpperCAmelCase__	:      Optional[int]     							=					node
    while n or stack:
        while n:  # start from root node, find its left child
            print(n.data    ,end=',' )
            stack.append(_snake_case )
            UpperCAmelCase__	:      Optional[int]     							=					n.left
        # end of while means current node doesn't have left child
        UpperCAmelCase__	:      Union[str, Any]     							=					stack.pop()
        # start to traverse its right child
        UpperCAmelCase__	:      Dict     							=					n.right
def 					lowerCamelCase   (     _snake_case ):
    if not isinstance(_snake_case    ,_snake_case ) or not node:
        return
    UpperCAmelCase__	:      list[TreeNode]     							=					[]
    UpperCAmelCase__	:      Optional[Any]     							=					node
    while n or stack:
        while n:
            stack.append(_snake_case )
            UpperCAmelCase__	:      int     							=					n.left
        UpperCAmelCase__	:      Tuple     							=					stack.pop()
        print(n.data    ,end=',' )
        UpperCAmelCase__	:      Tuple     							=					n.right
def 					lowerCamelCase   (     _snake_case ):
    if not isinstance(_snake_case    ,_snake_case ) or not node:
        return
    UpperCAmelCase__							,							UpperCAmelCase__	:      str     							=					[], []
    UpperCAmelCase__	:      Union[str, Any]     							=					node
    stacka.append(_snake_case )
    while stacka:  # to find the reversed order of post order, store it in stack2
        UpperCAmelCase__	:      Tuple     							=					stacka.pop()
        if n.left:
            stacka.append(n.left )
        if n.right:
            stacka.append(n.right )
        stacka.append(_snake_case )
    while stacka:  # pop up from stack2 will be the post order
        print(stacka.pop().data    ,end=',' )
def 					lowerCamelCase   (     _snake_case = ""    ,_snake_case=50    ,_snake_case="*" ):
    if not s:
        return "\n" + width * char
    UpperCAmelCase__							,							UpperCAmelCase__	:      str     							=					divmod(width - len(_snake_case ) - 2    ,2 )
    return F'''{left * char} {s} {(left + extra) * char}'''


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    print(prompt('Binary Tree Traversals'))

    UpperCamelCase__          =	build_tree()
    print(prompt('Pre Order Traversal'))
    pre_order(node)
    print(prompt() + '\n')

    print(prompt('In Order Traversal'))
    in_order(node)
    print(prompt() + '\n')

    print(prompt('Post Order Traversal'))
    post_order(node)
    print(prompt() + '\n')

    print(prompt('Level Order Traversal'))
    level_order(node)
    print(prompt() + '\n')

    print(prompt('Actual Level Order Traversal'))
    level_order_actual(node)
    print('*' * 50 + '\n')

    print(prompt('Pre Order Traversal - Iteration Version'))
    pre_order_iter(node)
    print(prompt() + '\n')

    print(prompt('In Order Traversal - Iteration Version'))
    in_order_iter(node)
    print(prompt() + '\n')

    print(prompt('Post Order Traversal - Iteration Version'))
    post_order_iter(node)
    print(prompt())

