





'''simple docstring'''






import sys


def 					_a   (__SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

  _UpperCamelCase       			=len(__SCREAMING_SNAKE_CASE   )
  _UpperCamelCase       			=[[0 for x in range(__SCREAMING_SNAKE_CASE   )] for x in range(__SCREAMING_SNAKE_CASE   )]
  _UpperCamelCase       			=[[0 for x in range(__SCREAMING_SNAKE_CASE   )] for x in range(__SCREAMING_SNAKE_CASE   )]

  for chain_length in range(2  ,      __SCREAMING_SNAKE_CASE   ):
    for a in range(1  ,      n - chain_length + 1   ):
      _UpperCamelCase       			=a + chain_length - 1

      _UpperCamelCase       			=sys.maxsize
      for c in range(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):
        _UpperCamelCase       			=(
            matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
        )
        if cost < matrix[a][b]:
          _UpperCamelCase       			=cost
          _UpperCamelCase       			=c
  return matrix, sol


def 					_a   (__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

  if i == j:
    print('''A''' + str(__SCREAMING_SNAKE_CASE   )  ,      end=''' '''   )
  else:
    print('''('''  ,      end=''' '''   )
    print_optiomal_solution(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      optimal_solution[i][j]   )
    print_optiomal_solution(__SCREAMING_SNAKE_CASE  ,      optimal_solution[i][j] + 1  ,      __SCREAMING_SNAKE_CASE   )
    print(''')'''  ,      end=''' '''   )


def 					_a   ():


  """simple docstring"""

  _UpperCamelCase       			=[30, 35, 15, 5, 10, 20, 25]
  _UpperCamelCase       			=len(__SCREAMING_SNAKE_CASE   )
  # Size of matrix created from above array will be
  # 30*35 35*15 15*5 5*10 10*20 20*25
  _UpperCamelCase			,     _UpperCamelCase       			=matrix_chain_order(__SCREAMING_SNAKE_CASE   )

  print('''No. of Operation required: ''' + str(matrix[1][n - 1]   )   )
  print_optiomal_solution(__SCREAMING_SNAKE_CASE  ,      1  ,      n - 1   )


if __name__ == "__main__":
      main()













'''simple docstring'''






from pathlib import Path

import cva
import numpy as np
from matplotlib import pyplot as plt


def 					_a   (__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   ):


  """simple docstring"""

  _UpperCamelCase       			=cva.getAffineTransform(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE   )
  return cva.warpAffine(__SCREAMING_SNAKE_CASE  ,      __SCREAMING_SNAKE_CASE  ,      (rows, cols)   )


if __name__ == "__main__":
      # read original image
      __lowerCamelCase						: List[Any]		=   cva.imread(
          str(Path(__file__).resolve().parent.parent / 'image_data' / 'lena.jpg')
      )
      # turn image in gray scale value
      __lowerCamelCase						: List[Any]		=   cva.cvtColor(image, cva.COLOR_BGR2GRAY)
      # get image shape
      __lowerCamelCase		, __lowerCamelCase						: Any		=   gray_img.shape

      # set different points to rotate image
      __lowerCamelCase						: Optional[Any]		=   np.array([[50, 50], [200, 50], [50, 200]], np.floataa)
      __lowerCamelCase						: Any		=   np.array([[10, 100], [200, 50], [100, 250]], np.floataa)
      __lowerCamelCase						: int		=   np.array([[50, 50], [150, 50], [120, 200]], np.floataa)
      __lowerCamelCase						: List[Any]		=   np.array([[10, 100], [80, 50], [180, 250]], np.floataa)

      # add all rotated images in a list
      __lowerCamelCase						: int		=   [
          gray_img,
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
      ]

      # plot different image rotations
      __lowerCamelCase						: Optional[Any]		=   plt.figure(1)
      __lowerCamelCase						: Tuple		=   ['Original', 'Rotation 1', 'Rotation 2', 'Rotation 3']
      for i, image in enumerate(images):
            plt.subplot(2, 2, i + 1), plt.imshow(image, 'gray')
            plt.title(titles[i])
            plt.axis('off')
            plt.subplots_adjust(left=0.0, bottom=0.0_5, right=1.0, top=0.9_5)
      plt.show()






