def tie_well_graph(G):
"""
efficiency: O(V+E)
"""
tie_well = sccg(G)
G_scc = Graph()
for v_group, i in zip(tie_well, range(len(tie_well))):
v = Vertex(name=str(v_group), data={'group': v_group})
for v1 in v_group:
v1.data['group'] = v
for v in G.V:
for u in v.Adj:
if v.data['group'] != u.data['group']:
G_scc.connect(from_=v.data['group'],
to=u.data['group'],
weight=v.Adj[u].weight)
return G_scc
def init_G_r(G):
"""
init the Residual graph
@params:
@G: graph
efficiency: O(|E|+|V|)
"""
G_r = Graph()
V = [Vertex(name=v.name) for v in G.V]
dic = {}
for v1, v2 in zip(G.V, V):
dic[v1] = v2
for e in G.E:
G_r.connect(from_=dic[e.from_], to=dic[e.to], weight=e.weight)
return G_r, dic
def max_pairs(V1, V2, func=dfs):
"""
ford fulkerson algorithm For maximum pairing:
@params:
@G: graph
@V1,V2: groups of vertex for finding mach
@func: function to use for find adding way by default is dfs, can be bfs
return: list of vertexes pairs for max pairing (=Original vertices)
efficiency: O(|E|*n) where n is max pairing, in worst case n=|V1|
"""
G_pairs = Graph()
dic1, dic2 = {v: Vertex(name=v.name)
for v in V1}, {v: Vertex(name=v.name)
for v in V2}
dic, s, t = {**dic1, **dic2}, Vertex(name='s'), Vertex(name='t')
dic = {dic[k]: k for k in dic}
for v in dic1:
G_pairs.connect(from_=s, to=dic1[v], weight=1)
for v in dic2:
G_pairs.connect(from_=dic2[v], to=t, weight=1)
for v in dic1:
for u in v.Adj:
if u in dic2:
G_pairs.connect(from_=dic1[v], to=dic2[u], weight=1)
max_flow_ = ford_fulkerson(G_pairs, s, t, func=func)
pairs = []
for e in max_flow_:
if max_flow_[e] and e.from_ != s and e.to != t:
# pairs.append(dic[e.from_].Adj[dic[e.to]])
pairs.append((dic[e.from_], dic[e.to]))
return pairs
v1.data['group'] = v
for v in G.V:
for u in v.Adj:
if v.data['group'] != u.data['group']:
G_scc.connect(from_=v.data['group'],
to=u.data['group'],
weight=v.Adj[u].weight)
return G_scc
if __name__ == '__main__':
V = [Vertex(name=str(i)) for i in range(5)]
# r = Edge(from_=V[0], to=V[1], weight=3)
G = Graph(V={v: None for v in V})
G.connect(from_=V[1], to=V[2], weight=1)
G.connect(from_=V[2], to=V[1], weight=1)
# G.connect(e=r)
G.connect(from_=V[3], to=V[2])
G.connect(from_=V[4], to=V[0])
G.connect(from_=V[3], to=V[0])
G.connect(from_=V[1], to=V[4])
dfs(G, list(G.V.keys())[0])
search_circle(G)
forest(G, list(G.V.keys())[0])
# print(G.V.keys()[0])
topology(G)
print(topology(G))
print(sccg(G))
print(leaves(G))
print(tie_well_graph(G))
pairs = []
for e in max_flow_:
if max_flow_[e] and e.from_ != s and e.to != t:
# pairs.append(dic[e.from_].Adj[dic[e.to]])
pairs.append((dic[e.from_], dic[e.to]))
return pairs
if __name__ == '__main__':
V = [Vertex(name=str(i)) for i in range(8)]
V[0].name, V[1].name, V[2].name, V[3].name, V[4].name, V[5].name, V[6].name, V[7].name = \
's', '1', '2', '3', '4', '5', '6', 't'
G = Graph()
for i in range(8):
G.V[V[i]] = None
G.connect(from_=V[0], to=V[1], weight=3)
G.connect(from_=V[0], to=V[2], weight=3)
G.connect(from_=V[1], to=V[2], weight=1)
G.connect(from_=V[1], to=V[3], weight=3)
G.connect(from_=V[2], to=V[3], weight=1)
G.connect(from_=V[2], to=V[4], weight=3)
G.connect(from_=V[3], to=V[4], weight=2)
G.connect(from_=V[3], to=V[5], weight=3)
G.connect(from_=V[4], to=V[5], weight=2)
G.connect(from_=V[4], to=V[6], weight=3)
G.connect(from_=V[5], to=V[6], weight=3)
G.connect(from_=V[5], to=V[7], weight=3)
G.connect(from_=V[6], to=V[7], weight=3)
print(ford_fulkerson(G, V[0], V[7], func=dfs))
print(ford_fulkerson(G, V[0], V[7], func=bfs))
print('-------------------- scalling ------------------------')