

from pathlib import Path

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







def       lowercase					(	__A :					List[str] ,    __A :					Optional[Any] ,    __A :					Dict ,    __A :					str ,    __A :					Any		)				->			Dict:





    '''simple docstring'''




    snake_case							:		Optional[Any]        =		cva.getAffineTransform(__lowercase ,    __lowercase		)
    return cva.warpAffine(__lowercase ,    __lowercase ,    (rows, cols)		)


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

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

     # add all rotated images in a list
     __lowercase     : Optional[Any]       =						[
         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
     __lowercase     : Optional[int]       =						plt.figure(1)
     __lowercase     : int       =						["""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=0.05, right=1.0, top=0.95)
     plt.show()











from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

snake_case__   :						List[str]													=   TypeVar("""T""")






def      _snake_case     (__lowercase):
   return (position - 1) // 2






def      _snake_case     (__lowercase):
   return (2 * position) + 1






def      _snake_case     (__lowercase):
   return (2 * position) + 2


class     _a							(	Generic[T]     ):






  """simple docstring"""





  def __init__(  self			)      ->			None:
     UpperCamelCase_						=  []
     UpperCamelCase_						=  {}
     UpperCamelCase_						=  0




  def __len__(  self			)      ->			int:
     return self.elements




  def __repr__(  self			)      ->			str:
     return str(self.heap			)




  def  _UpperCAmelCase  (  self			)      ->			bool:
     # Check if the priority queue is empty
     return self.elements == 0




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase			)      ->			None:
     # Add an element with given priority to the queue
     self.heap.append((elem, weight)			)
     UpperCamelCase_						=  self.elements
     self.elements += 1
     self._bubble_up(_UpperCAmelCase			)




  def  _UpperCAmelCase  (  self			)      ->			T:
     # Remove and return the element with lowest weight (highest priority)
     if self.elements > 1:
        self._swap_nodes(0		,		self.elements - 1			)
     UpperCamelCase_		,   UpperCamelCase_						=  self.heap.pop()
     del self.position_map[elem]
     self.elements -= 1
     if self.elements > 0:
        UpperCamelCase_		,   UpperCamelCase_						=  self.heap[0]
        self._bubble_down(_UpperCAmelCase			)
     return elem




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase			)      ->			None:
     # Update the weight of the given key
     UpperCamelCase_						=  self.position_map[elem]
     UpperCamelCase_						=  (elem, weight)
     if position > 0:
        UpperCamelCase_						=  get_parent_position(_UpperCAmelCase			)
        UpperCamelCase_		,   UpperCamelCase_						=  self.heap[parent_position]
        if parent_weight > weight:
           self._bubble_up(_UpperCAmelCase			)
        else:
           self._bubble_down(_UpperCAmelCase			)
     else:
        self._bubble_down(_UpperCAmelCase			)




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase			)      ->			None:
     # Place a node at the proper position (upward movement) [to be used internally
     # only]
     UpperCamelCase_						=  self.position_map[elem]
     if curr_pos == 0:
        return None
     UpperCamelCase_						=  get_parent_position(_UpperCAmelCase			)
     UpperCamelCase_		,   UpperCamelCase_						=  self.heap[curr_pos]
     UpperCamelCase_		,   UpperCamelCase_						=  self.heap[parent_position]
     if parent_weight > weight:
        self._swap_nodes(_UpperCAmelCase		,		_UpperCAmelCase			)
        return self._bubble_up(_UpperCAmelCase			)
     return None




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase			)      ->			None:
     # Place a node at the proper position (downward movement) [to be used
     # internally only]
     UpperCamelCase_						=  self.position_map[elem]
     UpperCamelCase_		,   UpperCamelCase_						=  self.heap[curr_pos]
     UpperCamelCase_						=  get_child_left_position(_UpperCAmelCase			)
     UpperCamelCase_						=  get_child_right_position(_UpperCAmelCase			)
     if child_left_position < self.elements and child_right_position < self.elements:
        UpperCamelCase_		,   UpperCamelCase_						=  self.heap[child_left_position]
        UpperCamelCase_		,   UpperCamelCase_						=  self.heap[child_right_position]
        if child_right_weight < child_left_weight and child_right_weight < weight:
           self._swap_nodes(_UpperCAmelCase		,		_UpperCAmelCase			)
           return self._bubble_down(_UpperCAmelCase			)
     if child_left_position < self.elements:
        UpperCamelCase_		,   UpperCamelCase_						=  self.heap[child_left_position]
        if child_left_weight < weight:
           self._swap_nodes(_UpperCAmelCase		,		_UpperCAmelCase			)
           return self._bubble_down(_UpperCAmelCase			)
     else:
        return None
     if child_right_position < self.elements:
        UpperCamelCase_		,   UpperCamelCase_						=  self.heap[child_right_position]
        if child_right_weight < weight:
           self._swap_nodes(_UpperCAmelCase		,		_UpperCAmelCase			)
           return self._bubble_down(_UpperCAmelCase			)
     return None




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase			)      ->			None:
     # Swap the nodes at the given positions
     UpperCamelCase_						=  self.heap[nodea_pos][0]
     UpperCamelCase_						=  self.heap[nodea_pos][0]
     UpperCamelCase_		,   UpperCamelCase_						=  (
         self.heap[nodea_pos],
         self.heap[nodea_pos],
     )
     UpperCamelCase_						=  nodea_pos
     UpperCamelCase_						=  nodea_pos




class     _a							(	Generic[T]     ):






  """simple docstring"""





  def __init__(  self			)      ->			None:
     UpperCamelCase_						=  {}
     UpperCamelCase_						=  0




  def __repr__(  self			)      ->			str:
     return str(self.connections			)




  def __len__(  self			)      ->			int:
     return self.nodes




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase			)      ->			None:
     # Add a node in the graph if it is not in the graph
     if node not in self.connections:
        UpperCamelCase_						=  {}
        self.nodes += 1




  def  _UpperCAmelCase  (  self		,		_UpperCAmelCase		,		_UpperCAmelCase		,		_UpperCAmelCase			)      ->			None:
     # Add an edge between 2 nodes in the graph
     self.add_node(_UpperCAmelCase			)
     self.add_node(_UpperCAmelCase			)
     UpperCamelCase_						=  weight
     UpperCamelCase_						=  weight






def      _snake_case     (__lowercase     ,   ):
   UpperCamelCase_						=  {node: maxsize for node in graph.connections}
   UpperCamelCase_						=  {node: None for node in graph.connections}

   UpperCamelCase_						=  MinPriorityQueue()
   for node, weight in dist.items():
      priority_queue.push(__lowercase     ,   __lowercase)

   if priority_queue.is_empty():
      return dist, parent

   # initialization
   UpperCamelCase_						=  priority_queue.extract_min()
   UpperCamelCase_						=  0
   for neighbour in graph.connections[node]:
      if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
         UpperCamelCase_						=  dist[node] + graph.connections[node][neighbour]
         priority_queue.update_key(__lowercase     ,   dist[neighbour])
         UpperCamelCase_						=  node

    # running prim's algorithm
   while not priority_queue.is_empty():
      UpperCamelCase_						=  priority_queue.extract_min()
      for neighbour in graph.connections[node]:
         if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
            UpperCamelCase_						=  dist[node] + graph.connections[node][neighbour]
            priority_queue.update_key(__lowercase     ,   dist[neighbour])
            UpperCamelCase_						=  node
   return dist, parent





