






def       a__						(  A		,				A		,				A		,				A		,				A		,				A		,				):
   lowercase__						:	Tuple         = list(A					)
   lowercase__						:	Dict         = list(A					)
   lowercase__						:	Dict         = len(A					)
   lowercase__						:	List[Any]         = len(A					)

   lowercase__						:	Optional[Any]         = [
       [0 for _ in range(len_destination_seq + 1					)] for _ in range(len_source_seq + 1					)
   ]
   lowercase__						:	Any         = [
       ["""0""" for _ in range(len_destination_seq + 1					)] for _ in range(len_source_seq + 1					)
   ]

   for i in range(1		,				len_source_seq + 1					):
      lowercase__						:	Optional[Any]         = i * delete_cost
      lowercase__						:	Optional[int]         = F'''D{source_seq[i - 1]:c}'''

   for i in range(1		,				len_destination_seq + 1					):
      lowercase__						:	Optional[Any]         = i * insert_cost
      lowercase__						:	List[Any]         = F'''I{destination_seq[i - 1]:c}'''

   for i in range(1		,				len_source_seq + 1					):
      for j in range(1		,				len_destination_seq + 1					):
         if source_seq[i - 1] == destination_seq[j - 1]:
            lowercase__						:	Optional[int]         = costs[i - 1][j - 1] + copy_cost
            lowercase__						:	Dict         = F'''C{source_seq[i - 1]:c}'''
         else:
            lowercase__						:	Union[str, Any]         = costs[i - 1][j - 1] + replace_cost
            lowercase__						:	Dict         = F'''R{source_seq[i - 1]:c}''' + str(destination_seq[j - 1]					)

         if costs[i - 1][j] + delete_cost < costs[i][j]:
            lowercase__						:	Tuple         = costs[i - 1][j] + delete_cost
            lowercase__						:	Any         = F'''D{source_seq[i - 1]:c}'''

         if costs[i][j - 1] + insert_cost < costs[i][j]:
            lowercase__						:	List[str]         = costs[i][j - 1] + insert_cost
            lowercase__						:	Tuple         = F'''I{destination_seq[j - 1]:c}'''

   return costs, ops
def       a__						(  A		,				A		,				A					):
   if i == 0 and j == 0:
      return []
   else:
      if ops[i][j][0] == "C" or ops[i][j][0] == "R":
         lowercase__						:	str         = assemble_transformation(A		,				i - 1		,				j - 1					)
         seq.append(ops[i][j]					)
         return seq
      elif ops[i][j][0] == "D":
         lowercase__						:	int         = assemble_transformation(A		,				i - 1		,				A					)
         seq.append(ops[i][j]					)
         return seq
      else:
         lowercase__						:	List[str]         = assemble_transformation(A		,				A		,				j - 1					)
         seq.append(ops[i][j]					)
         return seq


if __name__ == "__main__":
 a ,      a     :   Tuple    =       compute_transform_tables('Python', 'Algorithms', -1, 1, 2, 2)

 a     :   Optional[int]    =       len(operations)
 a     :   List[str]    =       len(operations[0])
 a     :   str    =       assemble_transformation(operations, m - 1, n - 1)

 a     :   str    =       list('Python')
 a     :   Any    =       0
 a     :   List[Any]    =       0

 with open('min_cost.txt', 'w') as file:
  for op in sequence:
   print(''.join(string))

   if op[0] == "C":
    file.write('%-16s' % 'Copy %c' % op[1])
    file.write('\t\t\t' + ''.join(string))
    file.write('\r\n')

    cost -= 1
   elif op[0] == "R":
    a     :   str    =       op[2]

    file.write('%-16s' % ('Replace %c' % op[1] + ' with ' + str(op[2])))
    file.write('\t\t' + ''.join(string))
    file.write('\r\n')

    cost += 1
   elif op[0] == "D":
    string.pop(i)

    file.write('%-16s' % 'Delete %c' % op[1])
    file.write('\t\t\t' + ''.join(string))
    file.write('\r\n')

    cost += 2
   else:
    string.insert(i, op[1])

    file.write('%-16s' % 'Insert %c' % op[1])
    file.write('\t\t\t' + ''.join(string))
    file.write('\r\n')

    cost += 2

   i += 1

  print(''.join(string))
  print('Cost: ', cost)

  file.write('\r\nMinimum cost: ' + str(cost))










from typing import SupportsIndex

import numpy as np
from scipy.ndimage import convolve
def       a__						(  A		,				A		,				A					):
   lowercase__						:	Dict         = np.stack((horizontal_flow, vertical_flow)		,				2					)

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

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

   lowercase__						:	Tuple         = image[grid[:, :, 1], grid[:, :, 0]]

   # Set pixels at invalid locations to 0
   lowercase__						:	str         = 0

   return warped
def       a__						(  A		,				A		,				A		,				A = None		,				):
   if alpha is None:
      lowercase__						:	Tuple         = 0.1

   # Initialize flow
   lowercase__						:	Optional[int]         = np.zeros_like(A					)
   lowercase__						:	Tuple         = np.zeros_like(A					)

   # Prepare kernels for the calculation of the derivatives and the average velocity
   lowercase__						:	Tuple         = np.array([[-1, 1], [-1, 1]]					) * 0.2_5
   lowercase__						:	int         = np.array([[-1, -1], [1, 1]]					) * 0.2_5
   lowercase__						:	Optional[int]         = np.array([[1, 1], [1, 1]]					) * 0.2_5
   lowercase__						:	Optional[Any]         = 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(A					):
      lowercase__						:	Optional[int]         = warp(A		,				A		,				A					)
      lowercase__						:	Union[str, Any]         = convolve(A		,				A					) + convolve(A		,				A					)
      lowercase__						:	Union[str, Any]         = convolve(A		,				A					) + convolve(A		,				A					)
      lowercase__						:	str         = convolve(A		,				A					) + convolve(A		,				-kernel_t					)

      lowercase__						:	str         = convolve(A		,				A					)
      lowercase__						:	Tuple         = convolve(A		,				A					)

      # This updates the flow as proposed in the paper (Step 12)
      lowercase__						:	List[Any]         = (
          derivative_x * avg_horizontal_velocity
          + derivative_y * avg_vertical_velocity
          + derivative_t
      )
      lowercase__						:	Union[str, Any]         = update / (alpha**2 + derivative_x**2 + derivative_y**2)

      lowercase__						:	Optional[int]         = avg_horizontal_velocity - derivative_x * update
      lowercase__						:	int         = avg_vertical_velocity - derivative_y * update

   return horizontal_flow, vertical_flow


if __name__ == "__main__":
 import doctest

 doctest.testmod()


