




from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch





@dataclass
class 			lowerCamelCase_				:


 '''simple docstring'''







 lowercase_							       =       42  # [batch_size x 3]
 lowercase_							       =       42  # [batch_size x 3]
 lowercase_							       =       42  # [batch_size x 3]
 lowercase_							       =       42  # [batch_size x 3]
 lowercase_							       =       42
 lowercase_							       =       42
 lowercase_							       =       42
 lowercase_							       =       42
 lowercase_							       =       42



 def  lowerCAmelCase_    (				self    :						Dict		):
       assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
       assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
       assert len(self.x.shape		) == len(self.y.shape		) == len(self.z.shape		) == len(self.origin.shape		) == 2



 def  lowerCAmelCase_    (				self    :						Optional[Any]		):
       return torch.from_numpy(np.array([self.width, self.height]							,							dtype=np.floataa		)		)



 def  lowerCAmelCase_    (				self    :						str		):
       return torch.from_numpy(np.array([self.x_fov, self.y_fov]							,							dtype=np.floataa		)		)



 def  lowerCAmelCase_    (				self    :						Any		):
       SCREAMING_SNAKE_CASE_      		=     torch.arange(self.height * self.width		)
       SCREAMING_SNAKE_CASE_      		=     torch.stack(
           [
               pixel_indices % self.width,
               torch.div(_lowerCAmelCase							,							self.width							,							rounding_mode='trunc'		),
           ]							,							axis=1							,							)
       return coords



 @property
 def  lowerCAmelCase_    (				self    :						str		):
       SCREAMING_SNAKE_CASE_		,					*SCREAMING_SNAKE_CASE_      		=     self.shape
       SCREAMING_SNAKE_CASE_      		=     int(np.prod(_lowerCAmelCase		)		)

       SCREAMING_SNAKE_CASE_      		=     self.get_image_coords()
       SCREAMING_SNAKE_CASE_      		=     torch.broadcast_to(coords.unsqueeze(0		)							,							[batch_size * inner_batch_size, *coords.shape]		)
       SCREAMING_SNAKE_CASE_      		=     self.get_camera_rays(_lowerCAmelCase		)

       SCREAMING_SNAKE_CASE_      		=     rays.view(_lowerCAmelCase							,							inner_batch_size * self.height * self.width							,							2							,							3		)

       return rays



 def  lowerCAmelCase_    (				self    :						str							,							_lowerCAmelCase    :						torch.Tensor		):
       SCREAMING_SNAKE_CASE_		,					*SCREAMING_SNAKE_CASE_		,					SCREAMING_SNAKE_CASE_      		=     coords.shape
       assert n_coords == 2
       assert batch_size == self.origin.shape[0]

       SCREAMING_SNAKE_CASE_      		=     coords.view(_lowerCAmelCase							,							-1							,							2		)

       SCREAMING_SNAKE_CASE_      		=     self.resolution()
       SCREAMING_SNAKE_CASE_      		=     self.fov()

       SCREAMING_SNAKE_CASE_      		=     (flat.float() / (res - 1)) * 2 - 1
       SCREAMING_SNAKE_CASE_      		=     fracs * torch.tan(fov / 2		)

       SCREAMING_SNAKE_CASE_      		=     fracs.view(_lowerCAmelCase							,							-1							,							2		)
       SCREAMING_SNAKE_CASE_      		=     (
           self.z.view(_lowerCAmelCase							,							1							,							3		)
           + self.x.view(_lowerCAmelCase							,							1							,							3		) * fracs[:, :, :1]
           + self.y.view(_lowerCAmelCase							,							1							,							3		) * fracs[:, :, 1:]
       )
       SCREAMING_SNAKE_CASE_      		=     directions / directions.norm(dim=-1							,							keepdim=_lowerCAmelCase		)
       SCREAMING_SNAKE_CASE_      		=     torch.stack(
           [
               torch.broadcast_to(self.origin.view(_lowerCAmelCase							,							1							,							3		)							,							[batch_size, directions.shape[1], 3]		),
               directions,
           ]							,							dim=2							,							)
       return rays.view(_lowerCAmelCase							,							*_lowerCAmelCase							,							2							,							3		)




 def  lowerCAmelCase_    (				self    :						Optional[Any]							,							_lowerCAmelCase    :						int							,							_lowerCAmelCase    :						int		):
       assert width * self.height == height * self.width, "The aspect ratio should not change."
       return DifferentiableProjectiveCamera(
           origin=self.origin							,							x=self.x							,							y=self.y							,							z=self.z							,							width=_lowerCAmelCase							,							height=_lowerCAmelCase							,							x_fov=self.x_fov							,							y_fov=self.y_fov							,							)


def    UpperCAmelCase_				( __UpperCAmelCase		:      int				)   ->					DifferentiableProjectiveCamera:
      SCREAMING_SNAKE_CASE_      		=     []
      SCREAMING_SNAKE_CASE_      		=     []
      SCREAMING_SNAKE_CASE_      		=     []
      SCREAMING_SNAKE_CASE_      		=     []
      for theta in np.linspace(0     ,     2 * np.pi     ,     num=20				):
            SCREAMING_SNAKE_CASE_      		=     np.array([np.sin(__UpperCAmelCase				), np.cos(__UpperCAmelCase				), -0.5]				)
            z /= np.sqrt(np.sum(z**2				)				)
            SCREAMING_SNAKE_CASE_      		=     -z * 4
            SCREAMING_SNAKE_CASE_      		=     np.array([np.cos(__UpperCAmelCase				), -np.sin(__UpperCAmelCase				), 0.0]				)
            SCREAMING_SNAKE_CASE_      		=     np.cross(__UpperCAmelCase     ,     __UpperCAmelCase				)
            origins.append(__UpperCAmelCase				)
            xs.append(__UpperCAmelCase				)
            ys.append(__UpperCAmelCase				)
            zs.append(__UpperCAmelCase				)
      return DifferentiableProjectiveCamera(
          origin=torch.from_numpy(np.stack(__UpperCAmelCase     ,     axis=0				)				).float()     ,     x=torch.from_numpy(np.stack(__UpperCAmelCase     ,     axis=0				)				).float()     ,     y=torch.from_numpy(np.stack(__UpperCAmelCase     ,     axis=0				)				).float()     ,     z=torch.from_numpy(np.stack(__UpperCAmelCase     ,     axis=0				)				).float()     ,     width=__UpperCAmelCase     ,     height=__UpperCAmelCase     ,     x_fov=0.7     ,     y_fov=0.7     ,     shape=(1, len(__UpperCAmelCase				))     ,     )

"""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())

