
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
UpperCAmelCase_											=  {
    "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_      :			Optional[int]	)     ->     List[str]:






   """simple docstring"""







   _UpperCAmelCase											=      {node: {node} for node in graph}

   _UpperCAmelCase											=      {node: graph[node][:] for node in graph}

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

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

      _UpperCAmelCase											=      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.
   _UpperCAmelCase											=      [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))






def     A__					(						SCREAMING_SNAKE_CASE_      :			Optional[int]							,  SCREAMING_SNAKE_CASE_      :			str	)     ->     List[str]:






   """simple docstring"""







   print('''\nVertex Distance'''	)
   for i in range(SCREAMING_SNAKE_CASE_	):
      if dist[i] != float('''inf'''	):
         print(SCREAMING_SNAKE_CASE_							,  '''\t'''							,  int(dist[i]	)							,  end='''\t'''	)
      else:
         print(SCREAMING_SNAKE_CASE_							,  '''\t'''							,  '''INF'''							,  end='''\t'''	)
      print()
def     A__					(						SCREAMING_SNAKE_CASE_      :			Any							,  SCREAMING_SNAKE_CASE_      :			Optional[Any]							,  SCREAMING_SNAKE_CASE_      :			str	)     ->     Any:






   """simple docstring"""







   _UpperCAmelCase											=      float('''inf'''	)
   _UpperCAmelCase											=      -1
   for i in range(SCREAMING_SNAKE_CASE_	):
      if (not vset[i]) and mdist[i] < min_val:
         _UpperCAmelCase											=      i
         _UpperCAmelCase											=      mdist[i]
   return min_ind
def     A__					(						SCREAMING_SNAKE_CASE_      :			str							,  SCREAMING_SNAKE_CASE_      :			Dict							,  SCREAMING_SNAKE_CASE_      :			int	)     ->     Any:






   """simple docstring"""







   _UpperCAmelCase											=      [float('''inf'''	) for _ in range(SCREAMING_SNAKE_CASE_	)]
   _UpperCAmelCase											=      [False for _ in range(SCREAMING_SNAKE_CASE_	)]
   _UpperCAmelCase											=      0.0

   for _ in range(v - 1	):
      _UpperCAmelCase											=      min_dist(SCREAMING_SNAKE_CASE_							,  SCREAMING_SNAKE_CASE_							,  SCREAMING_SNAKE_CASE_	)
      _UpperCAmelCase											=      True

      for i in range(SCREAMING_SNAKE_CASE_	):
         if (
             (not vset[i])
             and graph[u][i] != float('''inf'''	)
             and mdist[u] + graph[u][i] < mdist[i]
         ):
            _UpperCAmelCase											=      mdist[u] + graph[u][i]

   print_dist(SCREAMING_SNAKE_CASE_							,  SCREAMING_SNAKE_CASE_	)


if __name__ == "__main__":
   UpperCAmelCase_											=  int(input("Enter number of vertices: ").strip())
   UpperCAmelCase_											=  int(input("Enter number of edges: ").strip())

   UpperCAmelCase_											=  [[float("inf") for i in range(V)] for j in range(V)]

   for i in range(V):
      UpperCAmelCase_											=  0.0

   for i in range(E):
      print("\nEdge ", i + 1)
      UpperCAmelCase_											=  int(input("Enter source:").strip())
      UpperCAmelCase_											=  int(input("Enter destination:").strip())
      UpperCAmelCase_											=  float(input("Enter weight:").strip())
      UpperCAmelCase_											=  weight

   UpperCAmelCase_											=  int(input("\nEnter shortest path source:").strip())
   dijkstra(graph, V, gsrc)