

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
a_         =      {
    '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 	lowerCamelCase__	(   _a):
 SCREAMING_SNAKE_CASE				: Tuple			       =    {node: {node} for node in graph}

 SCREAMING_SNAKE_CASE				: Optional[Any]			       =    {node: graph[node][:] for node in graph}

 while len(SCREAMING_SNAKE_CASE_) > 2:
  # Choose a random edge.
  SCREAMING_SNAKE_CASE				: Any			       =    random.choice(list(graph_copy.keys()))
  SCREAMING_SNAKE_CASE				: List[Any]			       =    random.choice(graph_copy[u])

  # Contract edge (u, v) to new node uv
  SCREAMING_SNAKE_CASE				: Union[str, Any]			       =    u + v
  SCREAMING_SNAKE_CASE				: Tuple			       =    list(set(graph_copy[u] + graph_copy[v]))
  uv_neighbors.remove(SCREAMING_SNAKE_CASE_)
  uv_neighbors.remove(SCREAMING_SNAKE_CASE_)
  SCREAMING_SNAKE_CASE				: Any			       =    uv_neighbors
  for neighbor in uv_neighbors:
   graph_copy[neighbor].append(SCREAMING_SNAKE_CASE_)

  SCREAMING_SNAKE_CASE				: Union[str, Any]			       =    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(SCREAMING_SNAKE_CASE_)
   if v in graph_copy[neighbor]:
    graph_copy[neighbor].remove(SCREAMING_SNAKE_CASE_)

  # Find cutset.
 SCREAMING_SNAKE_CASE				: str			       =    [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))


from __future__ import annotations

def 	lowerCamelCase__	(   _a							,     _a							,     _a):
	if len(_a) == 0:
		raise ValueError("find_min() arg is an empty sequence")
	if (
	    left >= len(_a)
	    or left < -len(_a)
	    or right >= len(_a)
	    or right < -len(_a)
	):
		raise IndexError("list index out of range")
	if left == right:
		return nums[left]
	SCREAMING_SNAKE_CASE				: List[str]			       =    (left + right) >> 1  # the middle
	SCREAMING_SNAKE_CASE				: Tuple			       =    find_min(_a							,     _a							,     _a)  # find min in range[left, mid]
	SCREAMING_SNAKE_CASE				: Optional[Any]			       =    find_min(_a							,     mid + 1							,     _a)  # find min in range[mid + 1, right]

	return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
			import doctest

			doctest.testmod(verbose=True)