def __init__(self, g):
self.mst = Queue()
self.pq = MinPQ()
self.uf = UF(g.v)
for e in g.edges:
self.pq.insert(e)
while not self.pq.is_empty() and self.mst.size() < g.v - 1:
e = self.pq.del_min()
v = e.either()
w = e.other(v)
if self.uf.connected(v, w):
continue
self.mst.enqueue(e)
self.uf.union(v, w)
def __init__(self, g):
self.pq = MinPQ()
self.marked = []
self.mst = Queue()
for i in range(g.v):
self.marked.append(False)
self.visit(g, 0)
while not self.pq.is_empty():
e = self.pq.del_min()
v = e.either()
w = e.other(v)
if self.marked[v] and self.marked[w]:
continue
self.mst.enqueue(e)
if not self.marked[v]:
self.visit(g, v)
if not self.marked[w]:
self.visit(g, w)
def __init__(self, EG):
self._marked = [False for _ in range(EG.V())] # MST vertices
self._mst = [] # list of MST edges
self._weight = 0
self._pq = MinPQ() # MinPQ of edges
self._visit(EG, 0)
while (not self._pq.isEmpty() and len(self._mst) < EG.V() - 1):
e = self._pq.delMin()
v = e.either()
w = e.other(v)
if (self._marked[v] and self._marked[w]):
continue # edge is obsolete; both vertices are on Tree
# add edge to MST list
self._mst.append(e)
self._weight += e.weight()
# visit non-Tree vertex
if (not self._marked[v]): self._visit(EG, v)
if (not self._marked[w]): self._visit(EG, w)
def __init__(self, EG):
"given a connected, undirected, weighted graph, finds an MST and its weight"
# list of edges in mst
self._mst = []
self._weight = 0
# build priority queue of edges
self._pq = MinPQ()
for e in EG.edges():
self._pq.insert(e)
# build union-find data structure
uf = UF(EG.V())
while (not self._pq.isEmpty() and len(self._mst) < EG.V() - 1):
# get next edge from PQ
e = self._pq.delMin() # greedily add edges to MST
v = e.either()
w = e.other(v)
if (not uf.isConnected(v, w)): # edge v-w does not create a cycle
uf.union(v, w) # merge components
self._mst.append(e) # add edge to MST
self._weight += e.weight()
