"""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()




"""simple docstring"""






from __future__ import annotations
class     snake_case	:




					"""simple docstring"""

					def __init__(    self       :     Tuple   ,lowerCamelCase__       :     int      ):
									UpperCAmelCase__					=							vertices
									UpperCAmelCase__					=							[[0] * vertices for _ in range(lowerCamelCase__      )]







					def 		__lowerCAmelCase						(    self       :     Dict   ,lowerCamelCase__       :     list[int]      ):
									print('Vertex \t Distance from Source'      )
									for vertex in range(self.vertices      ):
													print(lowerCamelCase__   ,'\t\t'   ,distances_from_source[vertex]      )







					def 		__lowerCAmelCase						(    self       :     List[Any]   ,lowerCamelCase__       :     list[int]   ,lowerCamelCase__       :     list[bool]      ):
									UpperCAmelCase__					=							1e7
									UpperCAmelCase__					=							0

									# Search not nearest vertex not in the shortest path tree
									for vertex in range(self.vertices      ):
													if distances_from_source[vertex] < minimum and visited[vertex] is False:
																	UpperCAmelCase__					=							distances_from_source[vertex]
																	UpperCAmelCase__					=							vertex
									return min_index







					def 		__lowerCAmelCase						(    self       :     List[Any]   ,lowerCamelCase__       :     int      ):
									UpperCAmelCase__					=							[int(1e7      )] * self.vertices  # distances from the source
									UpperCAmelCase__					=							0
									UpperCAmelCase__					=							[False] * self.vertices

									for _ in range(self.vertices      ):
													UpperCAmelCase__					=							self.minimum_distance(lowerCamelCase__   ,lowerCamelCase__      )
													UpperCAmelCase__					=							True

													# Update dist value of the adjacent vertices
													# of the picked vertex only if the current
													# distance is greater than new distance and
													# the vertex in not in the shortest path tree
													for v in range(self.vertices      ):
																	if (
																	    self.graph[u][v] > 0
																	    and visited[v] is False
																	    and distances[v] > distances[u] + self.graph[u][v]
																	):
																					UpperCAmelCase__					=							distances[u] + self.graph[u][v]

									self.print_solution(lowerCamelCase__      )


if __name__ == "__main__":
						lowerCAmelCase__  :  List[str]											=     Graph(9)
						lowerCAmelCase__  :  Tuple											=     [
						    [0, 4, 0, 0, 0, 0, 0, 8, 0],
						    [4, 0, 8, 0, 0, 0, 0, 11, 0],
						    [0, 8, 0, 7, 0, 4, 0, 0, 2],
						    [0, 0, 7, 0, 9, 14, 0, 0, 0],
						    [0, 0, 0, 9, 0, 10, 0, 0, 0],
						    [0, 0, 4, 14, 10, 0, 2, 0, 0],
						    [0, 0, 0, 0, 0, 2, 0, 1, 6],
						    [8, 11, 0, 0, 0, 0, 1, 0, 7],
						    [0, 0, 2, 0, 0, 0, 6, 7, 0],
						]
						graph.dijkstra(0)



