def is_forest(g):
"""
A forest is an acyclic, undirected graph.
:param g: undirected graph
:return: True if graph is a forest, otherwise False
"""
if not isinstance(g, Graph):
return False
djset = DisjointSet()
for v in g.vertices:
djset.make_set(v)
eset = set()
for v1, v2 in g.edges:
if (v2, v1) not in eset:
eset.add((v1, v2))
for v1, v2 in eset:
if djset.find_set(v1) != djset.find_set(v2):
djset.union(v1, v2)
else:
return False
return True
def connected_components(self):
"Returns a list of sets of connected components"
ds = DisjointSet()
for v in self.vertices():
ds.make_set(v)
for u,v in self.edges():
if ds.find_set(u) != ds.find_set(v):
ds.union(u,v)
return ds.collection
def connected_components_dj(g):
djset = DisjointSet()
for v in g.vertices:
djset.make_set(v)
for v1, v2 in g.edges:
if djset.find_set(v1) != djset.find_set(v2):
djset.union(v1, v2)
return djset.get_set()
def mst_kruskal(g):
djset = DisjointSet()
mst = Graph()
for u in g.vertices:
djset.make_set(u)
for u, v in sorted(g.edges, key=lambda e: g.weight(e[0], e[1])):
if djset.find_set(u) != djset.find_set(v):
djset.union(u, v)
mst.add_edge(u, v, g.weight(u, v))
return mst
