
'''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
A__ :		Optional[Any]					={
    '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_  (    __SCREAMING_SNAKE_CASE    :	dict[str, list[str]]			)					->							set[tuple[str, str]]:





  """simple docstring"""

  __A		:  Optional[int]       				=		{node: {node} for node in graph}

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

  while len(__SCREAMING_SNAKE_CASE			) > 2:
    # Choose a random edge.
    __A		:  Optional[Any]       				=		random.choice(list(graph_copy.keys()			)			)
    __A		:  Optional[int]       				=		random.choice(graph_copy[u]			)

    # Contract edge (u, v) to new node uv
    __A		:  Optional[int]       				=		u + v
    __A		:  Tuple       				=		list(set(graph_copy[u] + graph_copy[v]			)			)
    uv_neighbors.remove(__SCREAMING_SNAKE_CASE			)
    uv_neighbors.remove(__SCREAMING_SNAKE_CASE			)
    __A		:  Tuple       				=		uv_neighbors
    for neighbor in uv_neighbors:
      graph_copy[neighbor].append(__SCREAMING_SNAKE_CASE			)

    __A		:  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.
  __A		:  int       				=		[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'''
A__ :		dict[str, float]					={
    "kilogram": 1,
    "gram": pow(10, 3),
    "milligram": pow(10, 6),
    "metric-ton": pow(10, -3),
    "long-ton": 0.0_0_0_9_8_4_2_0_7_3,
    "short-ton": 0.0_0_1_1_0_2_3_1_2_2,
    "pound": 2.2_0_4_6_2_4_4_2_0_2,
    "stone": 0.1_5_7_4_7_3_1_7_2_8,
    "ounce": 3_5.2_7_3_9_9_0_7_2_3,
    "carrat": 5_000,
    "atomic-mass-unit": 6.0_2_2_1_3_6_6_5_2E2_6,
}

A__ :		dict[str, float]					={
    "kilogram": 1,
    "gram": pow(10, -3),
    "milligram": pow(10, -6),
    "metric-ton": pow(10, 3),
    "long-ton": 1_0_1_6.0_4_6_0_8,
    "short-ton": 9_0_7.1_8_4,
    "pound": 0.4_5_3_5_9_2,
    "stone": 6.3_5_0_2_9,
    "ounce": 0.0_2_8_3_4_9_5,
    "carrat": 0.0_0_0_2,
    "atomic-mass-unit": 1.6_6_0_5_4_0_1_9_9E-2_7,
}







def 							A_  (    __SCREAMING_SNAKE_CASE    :	str      ,  __SCREAMING_SNAKE_CASE    :	str      ,  __SCREAMING_SNAKE_CASE    :	float			)					->							float:





  """simple docstring"""

  if to_type not in KILOGRAM_CHART or from_type not in WEIGHT_TYPE_CHART:
    __A		:  Tuple       				=		(
        F"Invalid 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"
        F"Supported values are: {', '.join(__SCREAMING_SNAKE_CASE			)}"
    )
    raise ValueError(__SCREAMING_SNAKE_CASE			)
  return value * KILOGRAM_CHART[to_type] * WEIGHT_TYPE_CHART[from_type]


if __name__ == "__main__":
     import doctest

     doctest.testmod()



