def brute_perf_matchings(g: Graph) -> int:
"""Computes the number of perfect matchings in g using brute force."""
n = g.vertex_count()
if n % 2 != 0: return 0
return len([
c for c in combinations(g.edges(), n // 2)
if gh.is_perf_matching(g, c)
])
def make_random(n: int, p: float) -> Graph:
"""Constructs a random graph where each edge is sampled with probability p"""
assert (n >= 0 and 0 <= p <= 1)
g = Graph(n)
for (u, v) in combinations(range(n), 2):
if random() < p:
g.add_edge(u, v)
return g
def make_clique(n: int) -> Graph:
"""Constructs a clique with n vertices"""
assert (n >= 0)
g = Graph(n)
if n < 2: return g
for (u, v) in combinations(range(n), 2):
g.add_edge(u, v)
return g
def tsp_dp(start, g):
vts = frozenset(g.vertices())
table = {frozenset(sub): {v: inf for v in vts} for sub in subsets(vts)}
table[frozenset([start])][start] = 0
for k in range(1, g.vertex_count() + 1):
for subset in map(frozenset, combinations(vts, k)):
for v in subset:
reduced = subset - frozenset([v])
for u in filter(lambda u: g.edge_exists(u, v), vts):
table[subset][v] = min(
table[subset][v],
table[reduced][u] + g.edge_weight(u, v))
cycle = [start]
while len(vts) > 0:
u = cycle[-1]
v = min(g.adjacent(u),
key=lambda v: table[vts][v] + g.edge_weight(v, u))
cycle.append(v)
vts -= {v}
return cycle
def at_most_one(cnf, vars):
for x, y in combinations(vars, 2):
cnf.add_clause([-x, -y])