def prim(first, graph):
pQueue = PriorityQueue()
graph[first]['dist'] = 0
for i in graph:
pQueue.enqueue((graph[i]['dist'], i))
mst = []
# dictionary to record for each vertex in the queue its nearest vertex in the tree
nearestInTreeTo = {}
print('Removing front item', first, 'from priority queue')
while not pQueue.isEmpty():
u = pQueue.dequeue()
print('Inspecting neighbours of vertex', u)
for w in graph[u]['edgeTo']:
edgeLen = graph[u]['edgeTo'][w]
print(u, 'to', w,':', edgeLen)
currentDist = graph[w]['dist']
if w in pQueue and edgeLen < currentDist:
graph[w]['dist'] = edgeLen
pQueue.changePriority(w, edgeLen)
nearestInTreeTo[w] = u
if not pQueue.isEmpty():
print('PriorityQueue is now :', pQueue.getEntries())
print()
nextVertex = pQueue.peek()
print('Next vertex is:', nextVertex)
weight = graph[nextVertex]['dist']
newEdge = [[(nearestInTreeTo[nextVertex], nextVertex), weight]]
print('Nearest in tree to', nextVertex,'is', nearestInTreeTo[nextVertex])
print('Adding', newEdge, 'to the tree')
mst = mst + [[(nearestInTreeTo[nextVertex], nextVertex), weight]]
print('Tree is now :', mst)
print()
print('Removing front item', nextVertex, 'from priority queue')
print('MST completed')
return mst
