
"""simple docstring"""

class    _UpperCAmelCase							:




      def __init__(							self      ,				lowercase_							)  ->    int:
          UpperCAmelCase  	=    val
          # Number of nodes in left subtree
          UpperCAmelCase  	=    0
          UpperCAmelCase  	=    None
          UpperCAmelCase  	=    None
          UpperCAmelCase  	=    None




      def 			a_					(							self      ,				lowercase_							)  ->    Dict:
          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    _UpperCAmelCase							:




      def __init__(							self      ,				lowercase_=None      ,				lowercase_=None      ,				lowercase_=0							)  ->    Any:
          UpperCAmelCase  	=    heap_size
          UpperCAmelCase  	=    bottom_root
          UpperCAmelCase  	=    min_node




      def 			a_					(							self      ,				lowercase_							)  ->    Optional[Any]:

          # 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(lowercase_							) - 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 			a_					(							self      ,				lowercase_							)  ->    Dict:
          if self.size == 0:
              UpperCAmelCase  	=    Node(lowercase_							)
              UpperCAmelCase  	=    1
              UpperCAmelCase  	=    self.bottom_root
          else:
              # Create new node
              UpperCAmelCase  	=    Node(lowercase_							)

              # 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 			a_					(							self							)  ->    Optional[int]:
          return self.min_node.val




      def 			a_					(							self							)  ->    Dict:
          return self.size == 0




      def 			a_					(							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=lowercase_      ,				min_node=lowercase_      ,				heap_size=lowercase_							)

          # 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(lowercase_							)

          return min_value




      def 			a_					(							self							)  ->    List[str]:
          UpperCAmelCase  	=    self.bottom_root
          while top_root.parent:
              UpperCAmelCase  	=    top_root.parent
          # preorder
          UpperCAmelCase  	=    []
          self.__traversal(lowercase_      ,				lowercase_							)
          return heap_pre_order




      def 			a_					(							self      ,				lowercase_      ,				lowercase_      ,				lowercase_=0							)  ->    int:
          if curr_node:
              preorder.append((curr_node.val, level)							)
              self.__traversal(curr_node.left      ,				lowercase_      ,				level + 1							)
              self.__traversal(curr_node.right      ,				lowercase_      ,				level + 1							)
          else:
              preorder.append(('#', level)							)




      def __str__(							self							)  ->    Dict:
          if self.is_empty():
              return ""
          UpperCAmelCase  	=    self.pre_order()

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


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

   doctest.testmod()





"""simple docstring"""

import doctest

import projectq
from projectq.ops import H, Measure




def 			lowercase__  (    lowerCAmelCase :    projectq.cengines._main.MainEngine       )       ->					int:






    """simple docstring"""




    UpperCAmelCase  	=    quantum_engine.allocate_qubit()
    H | qubit
    Measure | qubit
    return int(lowerCAmelCase       )


if __name__ == "__main__":
   doctest.testmod()

   # initialises a new quantum backend
   SCREAMING_SNAKE_CASE_			    =  projectq.MainEngine()

   # Generate a list of 10 random numbers
   SCREAMING_SNAKE_CASE_			    =  [get_random_number(quantum_engine) for _ in range(10)]

   # Flushes the quantum engine from memory
   quantum_engine.flush()

   print('''Random numbers''', random_numbers_list)



