




from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass





@dataclass
class  __lowerCamelCase       :




    """simple docstring"""

    snake_case__					=      42
    snake_case__					=      None
    snake_case__					=      None






def 							_A   (						):
     """simple docstring"""

     return TreeNode(3   ,				TreeNode(9			)   ,				TreeNode(20   ,				TreeNode(15			)   ,				TreeNode(7			)			)			)



def 							_A   (						lowerCAmelCase_     :					TreeNode			):
     """simple docstring"""

     def depth_first_search(
         lowerCAmelCase_     :					TreeNode | None   ,				lowerCAmelCase_     :					int   ,				lowerCAmelCase_     :					list[int]			) -> None:
          if not root:
               return

          if depth == len(lowerCAmelCase_			):
               right_view.append(root.val			)

          depth_first_search(root.right   ,				depth + 1   ,				lowerCAmelCase_			)
          depth_first_search(root.left   ,				depth + 1   ,				lowerCAmelCase_			)

     lowerCAmelCase__		= []
     if not root:
          return right_view

     depth_first_search(lowerCAmelCase_   ,				0   ,				lowerCAmelCase_			)
     return right_view



def 							_A   (						lowerCAmelCase_     :					TreeNode			):
     """simple docstring"""

     def depth_first_search(
         lowerCAmelCase_     :					TreeNode | None   ,				lowerCAmelCase_     :					int   ,				lowerCAmelCase_     :					list[int]			) -> None:
          if not root:
               return

          if depth == len(lowerCAmelCase_			):
               left_view.append(root.val			)

          depth_first_search(root.left   ,				depth + 1   ,				lowerCAmelCase_			)
          depth_first_search(root.right   ,				depth + 1   ,				lowerCAmelCase_			)

     lowerCAmelCase__		= []
     if not root:
          return left_view

     depth_first_search(lowerCAmelCase_   ,				0   ,				lowerCAmelCase_			)
     return left_view



def 							_A   (						lowerCAmelCase_     :					TreeNode			):
     """simple docstring"""

     def breadth_first_search(lowerCAmelCase_     :					TreeNode   ,				lowerCAmelCase_     :					list[int]			) -> None:
          lowerCAmelCase__		= [(root, 0)]
          lowerCAmelCase__		= defaultdict(lowerCAmelCase_			)

          while queue:
               lowerCAmelCase__		= queue.pop(0			)
               lowerCAmelCase__	,		lowerCAmelCase__		= first

               lookup[hd].append(node.val			)

               if node.left:
                    queue.append((node.left, hd - 1)			)
               if node.right:
                    queue.append((node.right, hd + 1)			)

          for pair in sorted(lookup.items()   ,				key=lambda lowerCAmelCase_			: each[0]			):
               top_view.append(pair[1][0]			)

     lowerCAmelCase__		= []
     if not root:
          return top_view

     breadth_first_search(lowerCAmelCase_   ,				lowerCAmelCase_			)
     return top_view



def 							_A   (						lowerCAmelCase_     :					TreeNode			):
     """simple docstring"""

     from collections import defaultdict

     def breadth_first_search(lowerCAmelCase_     :					TreeNode   ,				lowerCAmelCase_     :					list[int]			) -> None:
          lowerCAmelCase__		= [(root, 0)]
          lowerCAmelCase__		= defaultdict(lowerCAmelCase_			)

          while queue:
               lowerCAmelCase__		= queue.pop(0			)
               lowerCAmelCase__	,		lowerCAmelCase__		= first
               lookup[hd].append(node.val			)

               if node.left:
                    queue.append((node.left, hd - 1)			)
               if node.right:
                    queue.append((node.right, hd + 1)			)

          for pair in sorted(lookup.items()   ,				key=lambda lowerCAmelCase_			: each[0]			):
               bottom_view.append(pair[1][-1]			)

     lowerCAmelCase__		= []
     if not root:
          return bottom_view

     breadth_first_search(lowerCAmelCase_   ,				lowerCAmelCase_			)
     return bottom_view


if __name__ == "__main__":
     import doctest

     doctest.testmod()


"""simple docstring"""

from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve




def 			lowercase__  (    lowerCAmelCase :    np.ndarray       , lowerCAmelCase :    np.ndarray       , lowerCAmelCase :    np.ndarray       )       ->					np.ndarray:






    """simple docstring"""




    UpperCAmelCase  	=    np.stack((horizontal_flow, vertical_flow)       , 2       )

    # Create a grid of all pixel coordinates and subtract the flow to get the
    # target pixels coordinates
    UpperCAmelCase  	=    np.stack(
        np.meshgrid(np.arange(0       , image.shape[1]       )       , np.arange(0       , image.shape[0]       )       )       , 2       )
    UpperCAmelCase  	=    np.round(grid - flow       ).astype(np.intaa       )

    # Find the locations outside of the original image
    UpperCAmelCase  	=    (grid < 0) | (grid >= np.array([image.shape[1], image.shape[0]]       ))
    UpperCAmelCase  	=    0

    UpperCAmelCase  	=    image[grid[:, :, 1], grid[:, :, 0]]

    # Set pixels at invalid locations to 0
    UpperCAmelCase  	=    0

    return warped




def 			lowercase__  (    lowerCAmelCase :    np.ndarray       , lowerCAmelCase :    np.ndarray       , lowerCAmelCase :    SupportsIndex       , lowerCAmelCase :    float | None = None       , )       ->					tuple[np.ndarray, np.ndarray]:






    """simple docstring"""




    if alpha is None:
        UpperCAmelCase  	=    0.1

    # Initialize flow
    UpperCAmelCase  	=    np.zeros_like(lowerCAmelCase       )
    UpperCAmelCase  	=    np.zeros_like(lowerCAmelCase       )

    # Prepare kernels for the calculation of the derivatives and the average velocity
    UpperCAmelCase  	=    np.array([[-1, 1], [-1, 1]]       ) * 0.25
    UpperCAmelCase  	=    np.array([[-1, -1], [1, 1]]       ) * 0.25
    UpperCAmelCase  	=    np.array([[1, 1], [1, 1]]       ) * 0.25
    UpperCAmelCase  	=    np.array(
        [[1 / 12, 1 / 6, 1 / 12], [1 / 6, 0, 1 / 6], [1 / 12, 1 / 6, 1 / 12]]       )

    # Iteratively refine the flow
    for _ in range(lowerCAmelCase       ):
        UpperCAmelCase  	=    warp(lowerCAmelCase       , lowerCAmelCase       , lowerCAmelCase       )
        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       ) + convolve(lowerCAmelCase       , lowerCAmelCase       )
        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       ) + convolve(lowerCAmelCase       , lowerCAmelCase       )
        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       ) + convolve(lowerCAmelCase       , -kernel_t       )

        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       )
        UpperCAmelCase  	=    convolve(lowerCAmelCase       , lowerCAmelCase       )

        # This updates the flow as proposed in the paper (Step 12)
        UpperCAmelCase  	=    (
            derivative_x * avg_horizontal_velocity
            + derivative_y * avg_vertical_velocity
            + derivative_t
        )
        UpperCAmelCase  	=    update / (alpha**2 + derivative_x**2 + derivative_y**2)

        UpperCAmelCase  	=    avg_horizontal_velocity - derivative_x * update
        UpperCAmelCase  	=    avg_vertical_velocity - derivative_y * update

    return horizontal_flow, vertical_flow


if __name__ == "__main__":
   import doctest

   doctest.testmod()



