



"""simple docstring"""






class    __snake_case:




    def __init__(   self    ,							A_			):





      '''simple docstring'''



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




    def   A   (   self    ,							A_			):





      '''simple docstring'''



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

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




class    __snake_case:




    def __init__(   self    ,							A_=None    ,							A_=None    ,							A_=0			):





      '''simple docstring'''



      _SCREAMING_SNAKE_CASE        =			heap_size
      _SCREAMING_SNAKE_CASE        =			bottom_root
      _SCREAMING_SNAKE_CASE        =			min_node




    def   A   (   self    ,							A_			):





      '''simple docstring'''



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

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

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

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

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

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

      # Return the merged heap
      return self




    def   A   (   self    ,							A_			):





      '''simple docstring'''



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

        # Update size
        self.size += 1

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

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

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




    def   A   (   self			):





      '''simple docstring'''



      return self.min_node.val




    def   A   (   self			):





      '''simple docstring'''



      return self.size == 0




    def   A   (   self			):





      '''simple docstring'''



      _SCREAMING_SNAKE_CASE        =			self.min_node.val

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

        # Update bottom root
        _SCREAMING_SNAKE_CASE        =			None

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

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

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

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

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

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

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

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

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

      return min_value




    def   A   (   self			):





      '''simple docstring'''



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




    def   A   (   self    ,							A_    ,							A_    ,							A_=0			):





      '''simple docstring'''



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




    def __str__(   self			):





      '''simple docstring'''



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

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


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

    doctest.testmod()





"""simple docstring"""






from transformers import ProcessorMixin




class    __snake_case(					__A       ):
    _A       = '''AutoFeatureExtractor'''
    _A       = '''AutoTokenizer'''
