code: 
  
  
  """simple docstring"""
  
  
  
  
  from __future__ import annotations
  
  import random
  
  # Adjacency list representation of this graph:
  # https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
  __SCREAMING_SNAKE_CASE					=						{
      """1""": ["""2""", """3""", """4""", """5"""],
      """2""": ["""1""", """3""", """4""", """5"""],
      """3""": ["""1""", """2""", """4""", """5""", """10"""],
      """4""": ["""1""", """2""", """3""", """5""", """6"""],
      """5""": ["""1""", """2""", """3""", """4""", """7"""],
      """6""": ["""7""", """8""", """9""", """10""", """4"""],
      """7""": ["""6""", """8""", """9""", """10""", """5"""],
      """8""": ["""6""", """7""", """9""", """10"""],
      """9""": ["""6""", """7""", """8""", """10"""],
      """10""": ["""6""", """7""", """8""", """9""", """3"""],
  }
  
  
  
  def 						__a      (  a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         _a          =				{node: {node} for node in graph}
  
         _a          =				{node: graph[node][:] for node in graph}
  
         while len(a					) > 2:
                # Choose a random edge.
                _a          =				random.choice(list(graph_copy.keys()					)					)
                _a          =				random.choice(graph_copy[u]					)
  
                # Contract edge (u, v) to new node uv
                _a          =				u + v
                _a          =				list(set(graph_copy[u] + graph_copy[v]					)					)
                uv_neighbors.remove(a					)
                uv_neighbors.remove(a					)
                _a          =				uv_neighbors
                for neighbor in uv_neighbors:
                       graph_copy[neighbor].append(a					)
  
                _a          =				set(contracted_nodes[u].union(contracted_nodes[v]					)					)
  
                # Remove nodes u and v.
                del graph_copy[u]
                del graph_copy[v]
                for neighbor in uv_neighbors:
                       if u in graph_copy[neighbor]:
                              graph_copy[neighbor].remove(a					)
                       if v in graph_copy[neighbor]:
                              graph_copy[neighbor].remove(a					)
  
      # Find cutset.
         _a          =				[contracted_nodes[node] for node in graph_copy]
         return {
             (node, neighbor)
             for node in groups[0]
             for neighbor in graph[node]
             if neighbor in groups[1]
         }
  
  
  if __name__ == "__main__":
     print(partition_graph(TEST_GRAPH))
  
style_context: 
  
  
  """simple docstring"""
  
  
  
  
  from __future__ import annotations
  
  __SCREAMING_SNAKE_CASE					=						[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]
  
  
  
  
  
  class __snake_case		:
  
  
  
  
  
  
  
     """simple docstring"""
  
  
  
  
     def __init__(		self							:Optional[Any]				,  UpperCamelCase__							:int       ):
            _a          =				-1
            _a          =				-1
            _a          =				[-1] * length
            _a          =				None
            _a          =				None
  
  
  
  
     def __repr__(		self							:Optional[Any]       ):
            return f'Node(min_value={self.minn} max_value={self.maxx})'
  
  
  
  
  
  
  def 						__a      (  a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         _a          =				Node(len(a					)					)
         _a   , _a          =				min(a					), max(a					)
         # Leaf node case where the node contains only one unique value
         if root.minn == root.maxx:
                return root
         _a          =				(root.minn + root.maxx) // 2
  
         _a          =				[]
         _a          =				[]
  
         for index, num in enumerate(a					):
                if num <= pivot:
                       left_arr.append(a					)
                else:
                       right_arr.append(a					)
                _a          =				len(a					)
         _a          =				build_tree(a					)
         _a          =				build_tree(a					)
         return root
  
  
  
  def 						__a      (  a,		a,		a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         if index < 0 or node is None:
                return 0
         # Leaf node cases
         if node.minn == node.maxx:
                return index + 1 if node.minn == num else 0
         _a          =				(node.minn + node.maxx) // 2
         if num <= pivot:
                # go the left subtree and map index to the left subtree
                return rank_till_index(node.left,		a,		node.map_left[index] - 1					)
         else:
                # go to the right subtree and map index to the right subtree
                return rank_till_index(node.right,		a,		index - node.map_left[index]					)
  
  
  
  def 						__a      (  a,		a,		a,		a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         if start > end:
                return 0
         _a          =				rank_till_index(a,		a,		a					)
         _a          =				rank_till_index(a,		a,		start - 1					)
         return rank_till_end - rank_before_start
  
  
  
  def 						__a      (  a,		a,		a,		a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         if index > (end - start) or start > end or node is None:
                return -1
         # Leaf node case
         if node.minn == node.maxx:
                return node.minn
         # Number of elements in the left subtree in interval [start, end]
         _a          =				node.map_left[end] - (
             node.map_left[start - 1] if start else 0
         )
         if num_elements_in_left_tree > index:
                return quantile(
                    node.left,		a,		(node.map_left[start - 1] if start else 0),		node.map_left[end] - 1,		)
         else:
                return quantile(
                    node.right,		index - num_elements_in_left_tree,		start - (node.map_left[start - 1] if start else 0),		end - node.map_left[end],		)
  
  
  
  def 						__a      (  a,		a,		a,		a,		a					):
  
  
  
  
  
         """simple docstring"""
  
  
  
  
  
  
  
         if (
             start > end
             or node is None
             or start_num > end_num
             or node.minn > end_num
             or node.maxx < start_num
         ):
                return 0
         if start_num <= node.minn and node.maxx <= end_num:
                return end - start + 1
         _a          =				range_counting(
             node.left,		(node.map_left[start - 1] if start else 0),		node.map_left[end] - 1,		a,		a,		)
         _a          =				range_counting(
             node.right,		start - (node.map_left[start - 1] if start else 0),		end - node.map_left[end],		a,		a,		)
         return left + right
  
  
  if __name__ == "__main__":
     import doctest
  
     doctest.testmod()
  