
'''simple docstring'''





class 	UpperCamelCase__					:






 def __init__(     self					:Optional[Any]		,			_A					:List[Any]     )			->     str:







       '''simple docstring'''



       __A    		=     val
       # Number of nodes in left subtree
       __A    		=     0
       __A    		=     None
       __A    		=     None
       __A    		=     None






 def 		lowercase_  (     self					:List[str]		,			_A					:List[str]     )			->     Tuple:







       '''simple docstring'''



       assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

       if self.val < other.val:
             __A    		=     self.right
             __A    		=     None
             if self.right:
                   __A    		=     other
             __A    		=     other
             __A    		=     self.left_tree_size * 2 + 1
             return self
       else:
             __A    		=     other.right
             __A    		=     None
             if other.right:
                   __A    		=     self
             __A    		=     self
             __A    		=     other.left_tree_size * 2 + 1
             return other






class 	UpperCamelCase__					:






 def __init__(     self					:int		,			_A					:List[Any]=None		,			_A					:str=None		,			_A					:Any=0     )			->     Optional[int]:







       '''simple docstring'''



       __A    		=     heap_size
       __A    		=     bottom_root
       __A    		=     min_node






 def 		lowercase_  (     self					:Optional[Any]		,			_A					:Optional[int]     )			->     Union[str, Any]:







       '''simple docstring'''



       if other.size == 0:
             return None
       if self.size == 0:
             __A    		=     other.size
             __A    		=     other.bottom_root
             __A    		=     other.min_node
             return None
       # Update size
       __A    		=     self.size + other.size

       # Update min.node
       if self.min_node.val > other.min_node.val:
             __A    		=     other.min_node
       # Merge

       # Order roots by left_subtree_size
       __A    		=     []
       __A		, __A    		=     self.bottom_root, other.bottom_root
       while i or j:
             if i and ((not j) or i.left_tree_size < j.left_tree_size):
                   combined_roots_list.append((i, True)     )
                   __A    		=     i.parent
             else:
                   combined_roots_list.append((j, False)     )
                   __A    		=     j.parent
        # Insert links between them
       for i in range(len(__lowerCAmelCase     ) - 1     ):
             if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                   __A    		=     combined_roots_list[i + 1][0]
                   __A    		=     combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
       __A    		=     combined_roots_list[0][0]
       while i.parent:
             if (
                 (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
             ) or (
                 i.left_tree_size == i.parent.left_tree_size
                 and i.left_tree_size != i.parent.parent.left_tree_size
             ):
                   # Neighbouring Nodes
                   __A    		=     i.left
                   __A    		=     i.parent.parent

                   # Merging trees
                   __A    		=     i.merge_trees(i.parent     )

                   # Updating links
                   __A    		=     previous_node
                   __A    		=     next_node
                   if previous_node:
                         __A    		=     i
                   if next_node:
                         __A    		=     i
             else:
                   __A    		=     i.parent
        # Updating self.bottom_root
       while i.left:
             __A    		=     i.left
       __A    		=     i

       # Update other
       __A    		=     self.size
       __A    		=     self.bottom_root
       __A    		=     self.min_node

       # Return the merged heap
       return self






 def 		lowercase_  (     self					:Dict		,			_A					:Union[str, Any]     )			->     List[Any]:







       '''simple docstring'''



       if self.size == 0:
             __A    		=     Node(__lowerCAmelCase     )
             __A    		=     1
             __A    		=     self.bottom_root
       else:
             # Create new node
             __A    		=     Node(__lowerCAmelCase     )

             # Update size
             self.size += 1

             # update min_node
             if val < self.min_node.val:
                   __A    		=     new_node
             # Put new_node as a bottom_root in heap
             __A    		=     new_node
             __A    		=     self.bottom_root
             __A    		=     new_node

             # Consecutively merge roots with same left_tree_size
             while (
                 self.bottom_root.parent
                 and self.bottom_root.left_tree_size
                 == self.bottom_root.parent.left_tree_size
             ):
                   # Next node
                   __A    		=     self.bottom_root.parent.parent

                   # Merge
                   __A    		=     self.bottom_root.merge_trees(self.bottom_root.parent     )

                   # Update Links
                   __A    		=     next_node
                   __A    		=     None
                   if next_node:
                         __A    		=     self.bottom_root






 def 		lowercase_  (     self					:Any     )			->     List[str]:







       '''simple docstring'''



       return self.min_node.val






 def 		lowercase_  (     self					:Optional[int]     )			->     int:







       '''simple docstring'''



       return self.size == 0






 def 		lowercase_  (     self					:List[Any]     )			->     int:







       '''simple docstring'''



       __A    		=     self.min_node.val

       # Last element in heap corner case
       if self.size == 1:
             # Update size
             __A    		=     0

             # Update bottom root
             __A    		=     None

             # Update min_node
             __A    		=     None

             return min_value
       # No right subtree corner case
       # The structure of the tree implies that this should be the bottom root
       # and there is at least one other root
       if self.min_node.right is None:
             # Update size
             self.size -= 1

             # Update bottom root
             __A    		=     self.bottom_root.parent
             __A    		=     None

             # Update min_node
             __A    		=     self.bottom_root
             __A    		=     self.bottom_root.parent
             while i:
                   if i.val < self.min_node.val:
                         __A    		=     i
                   __A    		=     i.parent
             return min_value
       # General case
       # Find the BinomialHeap of the right subtree of min_node
       __A    		=     self.min_node.right
       __A    		=     None
       __A    		=     bottom_of_new
       __A    		=     1

       # Size, min_node and bottom_root
       while bottom_of_new.left:
             __A    		=     size_of_new * 2 + 1
             __A    		=     bottom_of_new.left
             if bottom_of_new.val < min_of_new.val:
                   __A    		=     bottom_of_new
        # Corner case of single root on top left path
       if (not self.min_node.left) and (not self.min_node.parent):
             __A    		=     size_of_new
             __A    		=     bottom_of_new
             __A    		=     min_of_new
             # print("Single root, multiple nodes case")
             return min_value
       # Remaining cases
       # Construct heap of right subtree
       __A    		=     BinomialHeap(
           bottom_root=__lowerCAmelCase		,			min_node=__lowerCAmelCase		,			heap_size=__lowerCAmelCase     )

       # Update size
       __A    		=     self.size - 1 - size_of_new

       # Neighbour nodes
       __A    		=     self.min_node.left
       __A    		=     self.min_node.parent

       # Initialize new bottom_root and min_node
       __A    		=     previous_node or next_node
       __A    		=     next_node

       # Update links of previous_node and search below for new min_node and
       # bottom_root
       if previous_node:
             __A    		=     next_node

             # Update bottom_root and search for min_node below
             __A    		=     previous_node
             __A    		=     previous_node
             while self.bottom_root.left:
                   __A    		=     self.bottom_root.left
                   if self.bottom_root.val < self.min_node.val:
                         __A    		=     self.bottom_root
       if next_node:
             __A    		=     previous_node

             # Search for new min_node above min_node
             __A    		=     next_node
             while i:
                   if i.val < self.min_node.val:
                         __A    		=     i
                   __A    		=     i.parent
        # Merge heaps
       self.merge_heaps(__lowerCAmelCase     )

       return min_value






 def 		lowercase_  (     self					:Optional[int]     )			->     int:







       '''simple docstring'''



       __A    		=     self.bottom_root
       while top_root.parent:
             __A    		=     top_root.parent
       # preorder
       __A    		=     []
       self.__traversal(__lowerCAmelCase		,			__lowerCAmelCase     )
       return heap_pre_order






 def 		lowercase_  (     self					:Optional[Any]		,			_A					:Union[str, Any]		,			_A					:int		,			_A					:Dict=0     )			->     Optional[Any]:







       '''simple docstring'''



       if curr_node:
             preorder.append((curr_node.val, level)     )
             self.__traversal(curr_node.left		,			__lowerCAmelCase		,			level + 1     )
             self.__traversal(curr_node.right		,			__lowerCAmelCase		,			level + 1     )
       else:
             preorder.append(('#', level)     )






 def __str__(     self					:Union[str, Any]     )			->     str:







       '''simple docstring'''



       if self.is_empty():
             return ""
       __A    		=     self.pre_order()

       return "\n".join(('-' * level + str(__lowerCAmelCase     )) for value, level in preorder_heap     )


# Unit Tests
if __name__ == "__main__":
 import doctest

 doctest.testmod()








'''simple docstring'''





import math
import os

import cva
import numpy as np

a__						:				List[Any]           =    255.0





def     snake_case							(						UpperCAmelCase ,					UpperCAmelCase		)->     float:







      """simple docstring"""
      __A    		=     np.mean((original - contrast) ** 2		)
      if mse == 0:
            return 1_0_0

      return 2_0 * math.logaa(PIXEL_MAX / math.sqrt(UpperCAmelCase		)		)





def     snake_case							(						)->     None:







      """simple docstring"""
      __A    		=     os.path.dirname(os.path.realpath(UpperCAmelCase		)		)
      # Loading images (original image and compressed image)
      __A    		=     cva.imread(os.path.join(UpperCAmelCase ,					'image_data/original_image.png'		)		)
      __A    		=     cva.imread(os.path.join(UpperCAmelCase ,					'image_data/compressed_image.png'		) ,					1		)

      __A    		=     cva.imread(os.path.join(UpperCAmelCase ,					'image_data/PSNR-example-base.png'		)		)
      __A    		=     cva.imread(
          os.path.join(UpperCAmelCase ,					'image_data/PSNR-example-comp-10.jpg'		) ,					1		)

      # Value expected: 29.73dB
      print('-- First Test --'		)
      print(f'PSNR value is {peak_signal_to_noise_ratio(UpperCAmelCase ,					UpperCAmelCase		)} dB'		)

      # # Value expected: 31.53dB (Wikipedia Example)
      print('\n-- Second Test --'		)
      print(f'PSNR value is {peak_signal_to_noise_ratio(UpperCAmelCase ,					UpperCAmelCase		)} dB'		)


if __name__ == "__main__":
 main()






