





'''simple docstring'''





import heapq




def    __UpperCAmelCase(      lowercase_      ):
       _lowerCamelCase							:     list[list]	=		[]

       # for each node and his adjacency list add them and the rank of the node to queue
       # using heapq module the queue will be filled like a Priority Queue
       # heapq works with a min priority queue, so I used -1*len(v) to build it
       for key, value in graph.items():
              # O(log(n))
              heapq.heappush(lowercase_ ,    [-1 * len(lowercase_      ), (key, value)]      )

       # chosen_vertices = set of chosen vertices
       _lowerCamelCase							:     int	=		set()

       # while queue isn't empty and there are still edges
       #   (queue[0][0] is the rank of the node with max rank)
       while queue and queue[0][0] != 0:
              # extract vertex with max rank from queue and add it to chosen_vertices
              _lowerCamelCase							:     Union[str, Any]	=		heapq.heappop(lowercase_      )[1][0]
              chosen_vertices.add(lowercase_      )

              # Remove all arcs adjacent to argmax
              for elem in queue:
                     # if v haven't adjacent node, skip
                     if elem[0] == 0:
                            continue
                     # if argmax is reachable from elem
                     # remove argmax from elem's adjacent list and update his rank
                     if argmax in elem[1][1]:
                            _lowerCamelCase							:     int	=		elem[1][1].index(lowercase_      )
                            del elem[1][1][index]
                            elem[0] += 1
        # re-order the queue
              heapq.heapify(lowercase_      )
       return chosen_vertices


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       _lowerCamelCase			       =      {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
       print(F'''Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}''')








import qiskit




def    __UpperCAmelCase(      lowercase_ = 2      ):
       _lowerCamelCase							:     Optional[Any]	=		qubits

       # Using Aer's simulator
       _lowerCamelCase							:     Optional[int]	=		qiskit.Aer.get_backend('''aer_simulator'''      )

       # Creating a Quantum Circuit acting on the q register
       _lowerCamelCase							:     List[str]	=		qiskit.QuantumCircuit(lowercase_ ,    lowercase_      )

       # Adding a H gate on qubit 0 (now q0 in superposition)
       circuit.h(0      )

       for i in range(1 ,    lowercase_      ):
              # Adding CX (CNOT) gate
              circuit.cx(i - 1 ,    lowercase_      )

       # Mapping the quantum measurement to the classical bits
       circuit.measure(list(range(lowercase_      )      ) ,    list(range(lowercase_      )      )      )

       # Now measuring any one qubit would affect other qubits to collapse
       # their super position and have same state as the measured one.

       # Executing the circuit on the simulator
       _lowerCamelCase							:     str	=		qiskit.execute(lowercase_ ,    lowercase_ ,    shots=10_00      )

       return job.result().get_counts(lowercase_      )


if __name__ == "__main__":
       print(F'''Total count for various states are: {quantum_entanglement(3)}''')

