




class     a  :

     '''simple docstring'''





     def __init__(			self     :    int      ,					__snake_case     :    Union[str, Any]       ):
         UpperCAmelCase_											=  val
         # Number of nodes in left subtree
         UpperCAmelCase_											=  0
         UpperCAmelCase_											=  None
         UpperCAmelCase_											=  None
         UpperCAmelCase_											=  None




     def 						lowerCamelCase_     (			self     :    int      ,					__snake_case     :    Union[str, Any]       ):
         assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

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



class     a  :

     '''simple docstring'''





     def __init__(			self     :    Dict      ,					__snake_case     :    str=None      ,					__snake_case     :    Any=None      ,					__snake_case     :    int=0       ):
         UpperCAmelCase_											=  heap_size
         UpperCAmelCase_											=  bottom_root
         UpperCAmelCase_											=  min_node
     def 						lowerCamelCase_     (			self     :    List[Any]      ,					__snake_case     :    str       ):

         # Empty heaps corner cases
         if other.size == 0:
             return None
         if self.size == 0:
             UpperCAmelCase_											=  other.size
             UpperCAmelCase_											=  other.bottom_root
             UpperCAmelCase_											=  other.min_node
             return None
         # Update size
         UpperCAmelCase_											=  self.size + other.size

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

         # Order roots by left_subtree_size
         UpperCAmelCase_											=  []
         UpperCAmelCase_				,							UpperCAmelCase_											=  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)       )
                 UpperCAmelCase_											=  i.parent
             else:
                 combined_roots_list.append((j, False)       )
                 UpperCAmelCase_											=  j.parent
        # Insert links between them
         for i in range(len(__snake_case       ) - 1       ):
             if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                 UpperCAmelCase_											=  combined_roots_list[i + 1][0]
                 UpperCAmelCase_											=  combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
         UpperCAmelCase_											=  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
                 UpperCAmelCase_											=  i.left
                 UpperCAmelCase_											=  i.parent.parent

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

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

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

         # Return the merged heap
         return self
     def 						lowerCamelCase_     (			self     :    Any      ,					__snake_case     :    Optional[int]       ):
         if self.size == 0:
             UpperCAmelCase_											=  Node(__snake_case       )
             UpperCAmelCase_											=  1
             UpperCAmelCase_											=  self.bottom_root
         else:
             # Create new node
             UpperCAmelCase_											=  Node(__snake_case       )

             # Update size
             self.size += 1

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

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

                 # Update Links
                 UpperCAmelCase_											=  next_node
                 UpperCAmelCase_											=  None
                 if next_node:
                     UpperCAmelCase_											=  self.bottom_root
     def 						lowerCamelCase_     (			self     :    Optional[Any]       ):
         return self.min_node.val
     def 						lowerCamelCase_     (			self     :    Optional[Any]       ):
         return self.size == 0
     def 						lowerCamelCase_     (			self     :    List[str]       ):
         UpperCAmelCase_											=  self.min_node.val

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

             # Update bottom root
             UpperCAmelCase_											=  None

             # Update min_node
             UpperCAmelCase_											=  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
             UpperCAmelCase_											=  self.bottom_root.parent
             UpperCAmelCase_											=  None

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

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

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

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

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

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

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

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

         return min_value
     def 						lowerCamelCase_     (			self     :    Tuple       ):
         UpperCAmelCase_											=  self.bottom_root
         while top_root.parent:
             UpperCAmelCase_											=  top_root.parent
         # preorder
         UpperCAmelCase_											=  []
         self.__traversal(__snake_case      ,					__snake_case       )
         return heap_pre_order
     def 						lowerCamelCase_     (			self     :    Tuple      ,					__snake_case     :    str      ,					__snake_case     :    Dict      ,					__snake_case     :    Optional[int]=0       ):
         if curr_node:
             preorder.append((curr_node.val, level)       )
             self.__traversal(curr_node.left      ,					__snake_case      ,					level + 1       )
             self.__traversal(curr_node.right      ,					__snake_case      ,					level + 1       )
         else:
             preorder.append(('''#''', level)       )




     def __str__(			self     :    Optional[int]       ):
         if self.is_empty():
             return ""
         UpperCAmelCase_											=  self.pre_order()

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


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

 doctest.testmod()











import unittest
from pathlib import Path
from tempfile import TemporaryDirectory
from unittest.mock import Mock, patch

import diffusers.utils.hub_utils



class     a  (     unittest.TestCase    ):

     '''simple docstring'''





     @patch('''diffusers.utils.hub_utils.get_full_repo_name'''       )
     def 						lowerCamelCase_     (			self     :    List[Any]      ,					__snake_case     :    Mock       ):
         UpperCAmelCase_											=  '''full_repo_name'''
         with TemporaryDirectory() as tmpdir:
             # Dummy args values
             UpperCAmelCase_											=  Mock()
             UpperCAmelCase_											=  tmpdir
             UpperCAmelCase_											=  0
             UpperCAmelCase_											=  '''hub_token'''
             UpperCAmelCase_											=  '''dataset_name'''
             UpperCAmelCase_											=  0.01
             UpperCAmelCase_											=  10_00_00
             UpperCAmelCase_											=  1_00_00
             UpperCAmelCase_											=  0.01
             UpperCAmelCase_											=  0.02
             UpperCAmelCase_											=  0.03
             UpperCAmelCase_											=  0.0_005
             UpperCAmelCase_											=  0.000_001
             UpperCAmelCase_											=  1
             UpperCAmelCase_											=  10
             UpperCAmelCase_											=  0.001
             UpperCAmelCase_											=  0.1
             UpperCAmelCase_											=  0.2
             UpperCAmelCase_											=  True

             # Model card mush be rendered and saved
             diffusers.utils.hub_utils.create_model_card(__snake_case      ,					model_name='''model_name'''       )
             self.assertTrue((Path(__snake_case       ) / '''README.md''').is_file()       )





