def prim(G, s):
""" Implementation of Prims to find MST """
for v in G.V:
v.rank = sys.maxsize
v.p = None
s.rank = 0
Q = MinHeap(G.V)
while Q.size() > 0:
u = Q.extract_min()
for v, weigth in G.adj(u):
if v in Q and weigth < v.rank:
# updates the predecessor and rank such that we are getting spanning tree with lowest total edge weight
v.p = u
v.rank = weigth
# update heap since ranks have changed
Q.build_min_heap()
# find all the edges that spans the tree
result = []
total_weight = 0
for u in G.V:
for v, weigth in G.adj(u):
if v.p == u and (u, v, weigth) not in result:
result.append((u, v, weigth))
total_weight += weigth
print(result, "Minimal weight:", total_weight)
def heapsort(a):
a = list(a)
heap = MinHeap()
heap.heapify(a)
a_sorted = []
while heap.peek():
a_sorted.append(heap.extract_min())
return a_sorted
