def dijkstra(aGraph, start):
    pq = PriorityQueue()
    start.setDistance(0)
    pq.buildHeap([(v.getDistance(), v) for v in aGraph])
    while not pq.isEmpty():
        currentVert = pq.delMin()
        for nextVert in currentVert.getConnections():
            newDist = currentVert.getDistance() \
                      + currentVert.getWeight(nextVert)
            if newDist < nextVert.getDistance():
                nextVert.setDistance(newDist)
                nextVert.setPred(currentVert)
                pq.decreaseKey(nextVert, newDist)
def prim(G, start):
    pq = PriorityQueue()
    for v in G:
        v.setDistance(sys.maxsize)
        v.setPred(None)
    start.setDistance(0)
    pq.buildHeap([(v.getDistance(), v) for v in G])
    while not pq.isEmpty():
        currentVert = pq.delMin()
        for nextVert in currentVert.getConnections():
            newCost = currentVert.getWeight(nextVert) \
                      + currentVert.getDistance()
            if v in pq and newCost < nextVert.getDistance():
                nextVert.setPred(currentVert)
                nextVert.setDistance(newCost)
                pq.decreaseKey(nextVert, newCost)