def __init__(self, G):
if not isinstance(G, EdgeWeightedGraph):
raise ValueError(
'Graph must be edge weighted and undirected to run MST')
vertex_count = G.vertex_count()
self.pq = IndexMinPQ(vertex_count)
self.path = Bag()
self.marked = [False] * vertex_count
self.visit(G, 0)
while not self.pq.is_empty() and self.path.size() < vertex_count - 1:
e = self.pq.min_key()
w = self.pq.del_min()
self.path.add(e)
if not self.marked[w]:
self.visit(G, w)
def __init__(self, G):
if not isinstance(G, EdgeWeightedGraph):
raise ValueError(
'Graph must be edge weighted and undirected to run MST')
minpq = MinPQ.create()
self.tree = Bag()
for e in G.edges():
minpq.enqueue(e)
uf = UnionFind.create(G.vertex_count())
while not minpq.is_empty() and self.tree.size() < G.vertex_count() - 1:
e = minpq.del_min()
v = e.either()
w = e.other(v)
if not uf.connected(v, w):
uf.union(v, w)
self.tree.add(e)
def test_bag(self):
bag = Bag.create()
bag.add(100)
bag.add(200)
bag.add(300)
bag.add(400)
print([i for i in bag.iterate()])
self.assertEqual(4, bag.size())
self.assertFalse(bag.is_empty())
def __init__(self, G):
if not isinstance(G, EdgeWeightedGraph):
raise ValueError(
'Graph must be edge weighted and undirected to run MST')
self.minpq = MinPQ.create()
self.tree = Bag()
vertex_count = G.vertex_count()
self.marked = [False] * vertex_count
self.visit(G, 0)
while not self.minpq.is_empty(
) and self.tree.size() < vertex_count - 1:
edge = self.minpq.del_min()
v = edge.either()
w = edge.other(v)
if self.marked[v] and self.marked[w]:
continue
self.tree.add(edge)
if not self.marked[v]:
self.visit(G, v)
if not self.marked[w]:
self.visit(G, w)
class EagerPrimMST(MST):
path = None
pq = None
marked = None
def __init__(self, G):
if not isinstance(G, EdgeWeightedGraph):
raise ValueError(
'Graph must be edge weighted and undirected to run MST')
vertex_count = G.vertex_count()
self.pq = IndexMinPQ(vertex_count)
self.path = Bag()
self.marked = [False] * vertex_count
self.visit(G, 0)
while not self.pq.is_empty() and self.path.size() < vertex_count - 1:
e = self.pq.min_key()
w = self.pq.del_min()
self.path.add(e)
if not self.marked[w]:
self.visit(G, w)
def visit(self, G, v):
self.marked[v] = True
for e in G.adj(v):
w = e.other(v)
if not self.marked[w]:
if self.pq.contains_index(w):
old_e = self.pq.get(w)
if less(e, old_e):
self.pq.decrease_key(w, e)
else:
self.pq.insert(w, e)
def spanning_tree(self):
return self.path.iterate()
class LazyPrimMST(MST):
tree = None
marked = None
minpq = None
def __init__(self, G):
if not isinstance(G, EdgeWeightedGraph):
raise ValueError(
'Graph must be edge weighted and undirected to run MST')
self.minpq = MinPQ.create()
self.tree = Bag()
vertex_count = G.vertex_count()
self.marked = [False] * vertex_count
self.visit(G, 0)
while not self.minpq.is_empty(
) and self.tree.size() < vertex_count - 1:
edge = self.minpq.del_min()
v = edge.either()
w = edge.other(v)
if self.marked[v] and self.marked[w]:
continue
self.tree.add(edge)
if not self.marked[v]:
self.visit(G, v)
if not self.marked[w]:
self.visit(G, w)
def visit(self, G, v):
self.marked[v] = True
for e in G.adj(v):
w = e.other(v)
if not self.marked[w]:
self.minpq.enqueue(e)
def spanning_tree(self):
return self.tree.iterate()
def __init__(self, V):
self.V = V
self.adjList = [None] * V
for v in range(V):
self.adjList[v] = Bag()
def __init__(self, vertex_count):
self.V = vertex_count
self.adjList = [None] * vertex_count
for v in range(vertex_count):
self.adjList[v] = Bag()