class LazyPrimMST(object):
'''
given a connected, undirected, weighted graph, finds an MST and its weight
key = edge; priority = weight of edge
delete-min to determine next edge to add to to Tree
disregard if both endpoints v, w are in T
if w is vertex not in T:
1. add w to T
2. add edge to T
3. add to PQ any edge incident to w (if other endpoint not in T)
PQ has 1 entry per edge
'''
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continue # edge is obsolete; both vertices are on Tree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 _visit(self, EG, v):
"add v to Tree; add each edge e incident on v to PQ if e.other() is not in Tree"
self._marked[v] = True
for e in EG.adj(v):
w = e.other(v)
if (not self._marked[w]):
self._pq.insert(e)
def mst(self):
"returns edges in MST"
return self._mst
def weight(self):
"returns weight of MST"
return self._weight
def __repr__(self):
"Everything about MST"
return "edges=%r wt=%r" % (self.mst(), self.weight())
class LazyPrimMST(object): ''' given a connected, undirected, weighted graph, finds an MST and its weight key = edge; priority = weight of edge delete-min to determine next edge to add to to Tree disregard if both endpoints v, w are in T if w is vertex not in T: 1. add w to T 2. add edge to T 3. add to PQ any edge incident to w (if other endpoint not in T) PQ has 1 entry per edge ''' 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- 1): e = self._pq.delMin() v = e.either(); w = e.other(v) if (self._marked[v] and self._marked[w]): continue # edge is obsolete; both vertices are on Tree # add edge to MST list self._mst.append(e) self._weight += e.weight() # visit non-Tree vertex if (not self._marked[v]):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 _visit(self, EG, v): "add v to Tree; add each edge e incident on v to PQ if e.other() is not in Tree" self._marked[v] = True for e in EG.adj(v): w = e.other(v) if (not self._marked[w]): self._pq.insert(e) def mst(self): "returns edges in MST" return self._mst def weight(self): "returns weight of MST" return self._weight def __repr__(self): "Everything about MST" return "edges=%r wt=%r" % (self.mst(), self.weight())
class KruskalMST(object): "Kruskal's algorithm" 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() def mst(self): "returns edges in MST" return self._mst def weight(self): "returns sum of weights of MST" return self._weight def __repr__(self): "Everything about MST" return "edges=%r wt=%r" % ([e for e in self.mst()], self.weight())
class KruskalMST(object):
"Kruskal's algorithm"
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()
def mst(self):
"returns edges in MST"
return self._mst
def weight(self):
"returns sum of weights of MST"
return self._weight
def __repr__(self):
"Everything about MST"
return "edges=%r wt=%r" % ([e for e in self.mst()], self.weight())