



"""simple docstring"""


from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve

def 					_lowerCAmelCase (  lowercase_						,      lowercase_						,      lowercase_		):
						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 					_lowerCAmelCase (  lowercase_						,      lowercase_						,      lowercase_						,      lowercase_ = None						,      ):
						if alpha is None:
												UpperCAmelCase			 =					0.1

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

						# Prepare kernels for the calculation of the derivatives and the average velocity
						UpperCAmelCase			 =					np.array([[-1, 1], [-1, 1]]		) * 0.2_5
						UpperCAmelCase			 =					np.array([[-1, -1], [1, 1]]		) * 0.2_5
						UpperCAmelCase			 =					np.array([[1, 1], [1, 1]]		) * 0.2_5
						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(lowercase_		):
												UpperCAmelCase			 =					warp(lowercase_						,      lowercase_						,      lowercase_		)
												UpperCAmelCase			 =					convolve(lowercase_						,      lowercase_		) + convolve(lowercase_						,      lowercase_		)
												UpperCAmelCase			 =					convolve(lowercase_						,      lowercase_		) + convolve(lowercase_						,      lowercase_		)
												UpperCAmelCase			 =					convolve(lowercase_						,      lowercase_		) + convolve(lowercase_						,      -kernel_t		)

												UpperCAmelCase			 =					convolve(lowercase_						,      lowercase_		)
												UpperCAmelCase			 =					convolve(lowercase_						,      lowercase_		)

												# 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()










"""simple docstring"""




from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass


@dataclass
class 	a__		:
   _lowerCamelCase       				=					42
   _lowerCamelCase       				=					None
   _lowerCamelCase       				=					None




def 	lowercase__  (      )  ->      TreeNode:






      '''simple docstring'''


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


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      def depth_first_search(
          _UpperCAmelCase						,   _UpperCAmelCase						,   _UpperCAmelCase					) -> None:
            if not root:
                  return

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

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

      lowercase	:   list											= []
      if not root:
            return right_view

      depth_first_search(_UpperCAmelCase						,   0						,   _UpperCAmelCase					)
      return right_view


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      def depth_first_search(
          _UpperCAmelCase						,   _UpperCAmelCase						,   _UpperCAmelCase					) -> None:
            if not root:
                  return

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

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

      lowercase	:   list											= []
      if not root:
            return left_view

      depth_first_search(_UpperCAmelCase						,   0						,   _UpperCAmelCase					)
      return left_view


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      def breadth_first_search(_UpperCAmelCase						,   _UpperCAmelCase					) -> None:
            lowercase	:   List[str]											= [(root, 0)]
            lowercase	:   List[Any]											= defaultdict(_UpperCAmelCase					)

            while queue:
                  lowercase	:   Union[str, Any]											= queue.pop(0					)
                  lowercase						,     lowercase	:   str											= 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 _UpperCAmelCase					: each[0]					):
                  top_view.append(pair[1][0]					)

      lowercase	:   list											= []
      if not root:
            return top_view

      breadth_first_search(_UpperCAmelCase						,   _UpperCAmelCase					)
      return top_view


def 	lowercase__  (      _UpperCAmelCase					)  ->      list[int]:






      '''simple docstring'''


      from collections import defaultdict

      def breadth_first_search(_UpperCAmelCase						,   _UpperCAmelCase					) -> None:
            lowercase	:   Any											= [(root, 0)]
            lowercase	:   Dict											= defaultdict(_UpperCAmelCase					)

            while queue:
                  lowercase	:   str											= queue.pop(0					)
                  lowercase						,     lowercase	:   List[Any]											= 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 _UpperCAmelCase					: each[0]					):
                  bottom_view.append(pair[1][-1]					)

      lowercase	:   list											= []
      if not root:
            return bottom_view

      breadth_first_search(_UpperCAmelCase						,   _UpperCAmelCase					)
      return bottom_view


if __name__ == "__main__":
     import doctest

     doctest.testmod()
