


"""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))




"""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()
