





"""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__    :   List[str]    						= {
    """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__	(     _UpperCAmelCase		)			->     set[tuple[str, str]]:

 '''simple docstring'''






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

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

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

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

  snake_case__										= 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(__UpperCamelCase		)
   if v in graph_copy[neighbor]:
    graph_copy[neighbor].remove(__UpperCamelCase		)

    # Find cutset.
 snake_case__										= [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))







import math

import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute




def 					SCREAMING_SNAKE_CASE	(       __UpperCamelCase			:						int = 1       ,     __UpperCamelCase			:						int = 1      )  ->							qiskit.result.counts.Counts:
    if isinstance(__UpperCamelCase       ,     __UpperCamelCase      ) or isinstance(__UpperCamelCase       ,     __UpperCamelCase      ):
        raise TypeError('''inputs must be integers.'''      )
    if (bit_a < 0) or (bit_a < 0):
        raise ValueError('''inputs must be positive.'''      )
    if (math.floor(__UpperCamelCase      ) != bit_a) or (math.floor(__UpperCamelCase      ) != bit_a):
        raise ValueError('''inputs must be exact integers.'''      )
    if (bit_a > 1) or (bit_a > 1):
        raise ValueError('''inputs must be less or equal to 1.'''      )

    # build registers
    UpperCAmelCase_							 =     QuantumRegister(2       ,     '''qr'''      )
    UpperCAmelCase_							 =     ClassicalRegister(2       ,     '''cr'''      )

    UpperCAmelCase_							 =     QuantumCircuit(__UpperCamelCase       ,     __UpperCamelCase      )

    # entanglement the qubits
    quantum_circuit.h(1      )
    quantum_circuit.cx(1       ,     0      )

    # send the information
    UpperCAmelCase_							 =     str(__UpperCamelCase      ) + str(__UpperCamelCase      )

    if c_information == "11":
        quantum_circuit.x(1      )
        quantum_circuit.z(1      )
    elif c_information == "10":
        quantum_circuit.z(1      )
    elif c_information == "01":
        quantum_circuit.x(1      )
    else:
        quantum_circuit.i(1      )

    # unentangled the circuit
    quantum_circuit.cx(1       ,     0      )
    quantum_circuit.h(1      )

    # measure the circuit
    quantum_circuit.measure(__UpperCamelCase       ,     __UpperCamelCase      )

    UpperCAmelCase_							 =     Aer.get_backend('''aer_simulator'''      )
    UpperCAmelCase_							 =     execute(__UpperCamelCase       ,     __UpperCamelCase       ,     shots=1000      )

    return job.result().get_counts(__UpperCamelCase      )


if __name__ == "__main__":
 print(F"Counts for classical state send: {superdense_coding(1,1)}")





