






import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
  # Create universe of discourse in Python using linspace ()
  SCREAMING_SNAKE_CASE 							=						np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)

  # Create two fuzzy sets by defining any membership function
  # (trapmf(), gbellmf(), gaussmf(), etc).
  SCREAMING_SNAKE_CASE 							=						[0, 25, 50]
  SCREAMING_SNAKE_CASE 							=						[25, 50, 75]
  SCREAMING_SNAKE_CASE 							=						fuzz.membership.trimf(X, abca)
  SCREAMING_SNAKE_CASE 							=						fuzz.membership.trimf(X, abca)

  # Compute the different operations using inbuilt functions.
  SCREAMING_SNAKE_CASE 							=						np.ones(75)
  SCREAMING_SNAKE_CASE 							=						np.zeros((75,))
  # 1. Union = max(µA(x), µB(x))
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_or(X, young, X, middle_aged)[1]
  # 2. Intersection = min(µA(x), µB(x))
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_and(X, young, X, middle_aged)[1]
  # 3. Complement (A) = (1- min(µA(x))
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_not(young)
  # 4. Difference (A/B) = min(µA(x),(1- µB(x)))
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
  # 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
  SCREAMING_SNAKE_CASE 							=						young + middle_aged - (young * middle_aged)
  # 6. Algebraic Product = (µA(x) * µB(x))
  SCREAMING_SNAKE_CASE 							=						young * middle_aged
  # 7. Bounded Sum = min[1,(µA(x), µB(x))]
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
  # 8. Bounded difference = min[0,(µA(x), µB(x))]
  SCREAMING_SNAKE_CASE 							=						fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

  # max-min composition
  # max-product composition

  # Plot each set A, set B and each operation result using plot() and subplot().
  from matplotlib import pyplot as plt

  plt.figure()

  plt.subplot(4, 3, 1)
  plt.plot(X, young)
  plt.title('Young')
  plt.grid(True)

  plt.subplot(4, 3, 2)
  plt.plot(X, middle_aged)
  plt.title('Middle aged')
  plt.grid(True)

  plt.subplot(4, 3, 3)
  plt.plot(X, union)
  plt.title('union')
  plt.grid(True)

  plt.subplot(4, 3, 4)
  plt.plot(X, intersection)
  plt.title('intersection')
  plt.grid(True)

  plt.subplot(4, 3, 5)
  plt.plot(X, complement_a)
  plt.title('complement_a')
  plt.grid(True)

  plt.subplot(4, 3, 6)
  plt.plot(X, difference)
  plt.title('difference a/b')
  plt.grid(True)

  plt.subplot(4, 3, 7)
  plt.plot(X, alg_sum)
  plt.title('alg_sum')
  plt.grid(True)

  plt.subplot(4, 3, 8)
  plt.plot(X, alg_product)
  plt.title('alg_product')
  plt.grid(True)

  plt.subplot(4, 3, 9)
  plt.plot(X, bdd_sum)
  plt.title('bdd_sum')
  plt.grid(True)

  plt.subplot(4, 3, 10)
  plt.plot(X, bdd_difference)
  plt.title('bdd_difference')
  plt.grid(True)

  plt.subplots_adjust(hspace=0.5)
  plt.show()












import heapq

def      _lowerCamelCase	(						__A    :							dict )      ->					set[int]:
    _UpperCAmelCase				:      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(__A		,		[-1 * len(__A ), (key, value)] )

    # chosen_vertices = set of chosen vertices
    _UpperCAmelCase				:      Union[str, Any]			  =				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
        _UpperCAmelCase				:      Tuple			  =				heapq.heappop(__A )[1][0]
        chosen_vertices.add(__A )

        # 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]:
                _UpperCAmelCase				:      Dict			  =				elem[1][1].index(__A )
                del elem[1][1][index]
                elem[0] += 1
        # re-order the queue
        heapq.heapify(__A )
    return chosen_vertices


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  SCREAMING_SNAKE_CASE 							=						{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)}')




