class LazyPrimMST:
# Compute a minimum spanning tree (or forest) of an edge-weighted graph.
#the edge-weighted graph
def __init__(self, G):
self._mst = []
self._pq = MinPQ(G.V())
self._marked = [False] * G.V()
self._weight = 0
for v in range(0, G.V()):
if not self._marked[v]:
self._prim(G, v)
# run Prim's algorithm
def _prim(self, G, s):
self._scan(G, s)
while not self._pq.isEmpty():
e = self._pq.del_min()
v = e.either()
w = e.other(v)
assert (self._marked[v] or self._marked[w])
if (self._marked[v] and self._marked[w]):
continue
self._mst.append(e)
self._weight += e.weight()
if not self._marked[v]:
self._scan(G, v)
if not self._marked[w]:
self._scan(G, w)
# add all edges e incident to v onto pq if the other endpoint has not yet been scanned
def _scan(self, G, v):
assert not self._marked[v]
self._marked[v] = True
for e in G.adj(v):
if not self._marked[e.other(v)]:
self._pq.insert(e)
def weight(self):
return self._weight
def edges(self):
return self._mst
class LazyPrimMST(MST):
"""最小生成树的Prim算法的延时实现"""
def __init__(self, G):
self.pq = MinPQ() # 横切边（包括失效的边）
self.marked = [False] * G.V() # 最小生成树的顶点
self.mst = [] # 最小生成树的边
self.visit(G, 0) # 假设G是联通的
while not self.pq.isEmpty():
# 遍历横切边
e = self.pq.delMin() # 取最小的边
v = e.either()
w = e.other(v)
if self.marked[v] and self.marked[w]:
# 如果边的两个顶点都已经在树里就跳过这个边
continue
self.mst.append(e) # 将边加入最小生成树
if not self.marked[v]:
self.visit(G, v)
if not self.marked[w]:
self.visit(G, w)
def visit(self, G, v):
"""
将顶点加入最小生成树
"""
self.marked[v] = True
for e in G.adj(v):
# 将另一个顶点不在最小生成树中的邻接边加入横切边中
if not self.marked[e.other(v)]:
self.pq.insert(e)
def edges(self):
return self.mst
def weight(self):
weights = 0
for e in self.mst:
weights += e.weight()
return weights
class LazyPrimMST(MST):
"""最小生成树的Prim算法的延时实现"""
def __init__(self, G):
self.pq = MinPQ() # 横切边（包括失效的边）
self.marked = [False] * G.V() # 最小生成树的顶点
self.mst = [] # 最小生成树的边
self.visit(G, 0) # 假设G是联通的
while not self.pq.isEmpty():
# 遍历横切边
e = self.pq.delMin() # 取最小的边
v = e.either()
w = e.other(v)
if self.marked[v] and self.marked[w]:
# 如果边的两个顶点都已经在树里就跳过这个边
continue
self.mst.append(e) # 将边加入最小生成树
if not self.marked[v]:
self.visit(G, v)
if not self.marked[w]:
self.visit(G, w)
def visit(self, G, v):
"""
将顶点加入最小生成树
"""
self.marked[v] = True
for e in G.adj(v):
# 将另一个顶点不在最小生成树中的邻接边加入横切边中
if not self.marked[e.other(v)]:
self.pq.insert(e)
def edges(self):
return self.mst
def weight(self):
weights = 0
for e in self.mst:
weights += e.weight()
return weights
