"""simple docstring"""






from __future__ import annotations

from collections import deque
from queue import Queue
from timeit import timeit

lowerCAmelCase__  :  Tuple											=     {
    'A': ['B', 'C'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F'],
    'D': ['B'],
    'E': ['B', 'F'],
    'F': ['C', 'E'],
}



def   a_						( lowerCamelCase ,      lowerCamelCase	):
    UpperCAmelCase__					=							{start}
    UpperCAmelCase__					=							[start]
    UpperCAmelCase__					=							Queue()
    queue.put(lowerCamelCase	)
    while not queue.empty():
        UpperCAmelCase__					=							queue.get()
        for w in graph[v]:
            if w not in explored:
                explored.add(lowerCamelCase	)
                result.append(lowerCamelCase	)
                queue.put(lowerCamelCase	)
    return result



def   a_						( lowerCamelCase ,      lowerCamelCase	):
    UpperCAmelCase__					=							{start}
    UpperCAmelCase__					=							[start]
    UpperCAmelCase__					=							deque([start]	)
    while queue:
        UpperCAmelCase__					=							queue.popleft()
        for child in graph[v]:
            if child not in visited:
                visited.add(lowerCamelCase	)
                result.append(lowerCamelCase	)
                queue.append(lowerCamelCase	)
    return result



def   a_						( lowerCamelCase	):
    UpperCAmelCase__					=							f'''from __main__ import G, {name}'''
    UpperCAmelCase__					=							1_0_0_0_0
    UpperCAmelCase__					=							timeit(f'''{name}(G, \'A\')''' ,      setup=lowerCamelCase ,      number=lowerCamelCase	)
    print(f'''{name:<35} finished {number} runs in {res:.5f} seconds'''	)


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      benchmark_function('breadth_first_search')
      benchmark_function('breadth_first_search_with_deque')
      # breadth_first_search                finished 10000 runs in 0.20999 seconds
      # breadth_first_search_with_deque     finished 10000 runs in 0.01421 seconds




"""simple docstring"""






from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve



def   a_						( lowerCamelCase ,      lowerCamelCase ,      lowerCamelCase	):
				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   a_						( lowerCamelCase ,      lowerCamelCase ,      lowerCamelCase ,      lowerCamelCase = None ,      ):
				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 / 1_2, 1 / 6, 1 / 1_2], [1 / 6, 0, 1 / 6], [1 / 1_2, 1 / 6, 1 / 1_2]]	)

				# 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()



