def test_first_find(backend):
u = UnionFind(backend=backend)
assert u.find('a') == 'a'
assert u.find('a') == 'a'
assert u.find(1) == 1
assert u.find(1) == 1
assert u.find(12.2) == 12.2
assert u.find(12.2) == 12.2
def find_augmenting_path(g, initial_matching = None):
vertex_state = dict()
if initial_matching is None:
matching = dict()
else:
matching = initial_matching
even_edges = list()
forest = tree.Forest(Vertices = g.vertices())
blossoms = UnionFind(g.vertices())
origin = dict((v,v) for v in g.vertices())
bridge = dict()
for v in g.vertices():
if v not in matching:
vertex_state[v] = EVEN
for e in g.adjacent_edges(v):
even_edges.append((v,other_vertex(e,v),e))
else:
vertex_state[v] = UNREACHED
augmenting_path_edge = None
while even_edges:
u,v,current_edge \
= even_edges.pop(int(random.uniform(0,len(even_edges))))
u_prime = origin[blossoms.find(u)]
v_prime = origin[blossoms.find(v)]
if vertex_state[v_prime] == UNREACHED:
vertex_state[v_prime] = ODD;
v_prime_mate = other_vertex(matching[v_prime], v_prime)
vertex_state[v_prime_mate] = EVEN;
forest.add_edge(parent = u,
child = v_prime,
parent_edge = current_edge
)
forest.add_edge(parent = v_prime,
child = v_prime_mate,
parent_edge = matching[v_prime]
)
for e in g.adjacent_edges(v_prime_mate):
even_edges.append((v_prime_mate,
other_vertex(e,v_prime_mate),e))
elif vertex_state[v_prime] == EVEN and u_prime != v_prime:
try:
nca = forest.nearest_common_ancestor(u_prime, v_prime)
except tree.VertexNotFound:
nca = None
if nca is None:
augmenting_path_edge = current_edge
break
for x in (u_prime, v_prime):
prev_vertex = None
for y in forest.get_tree(x).path_to_root():
if y == nca:
break
curr_vertex = origin[blossoms.find(y.vertex)]
if curr_vertex == prev_vertex:
continue
blossoms.link(curr_vertex, nca.vertex)
bridge[curr_vertex] = (x, current_edge)
prev_vertex = curr_vertex
origin[blossoms.find(nca.vertex)] = nca.vertex
def path(v,w):
if v == w:
return [v]
v_mate = other_vertex(matching[v], v)
if vertex_state[v] == EVEN:
return [v, v_mate] + \
path(forest.get_tree(v_mate).parent().vertex, w)
else: #vertex_state[v] == ODD
x = bridge[v][0]
y = other_vertex(bridge[v][1], bridge[v][0])
return [v] + [i for i in reversed(path(x, v_mate))] + path(y,w)
if augmenting_path_edge:
x = g.source(augmenting_path_edge)
y = g.target(augmenting_path_edge)
x_up = path(x, forest.get_tree(x).get_root().vertex)
y_up = path(y, forest.get_tree(y).get_root().vertex)
print [i for i in reversed(x_up)] + y_up
matching[g.source(augmenting_path_edge)] = augmenting_path_edge
matching[g.target(augmenting_path_edge)] = augmenting_path_edge
for path in (x_up,y_up):
for x,y in izip(islice(path,1,None,2),islice(path,2,None,2)):
matching[x] = matching[y] = forest.get_tree(x).parent_edge
return matching
def test_find(backend):
u = UnionFind(backend=backend)
u.link(0,1)
u.link(2,3)
assert u.find(0) == u.find(1)
assert u.find(2) == u.find(3)
assert u.find(4) == 4
assert u.find(0) != u.find(2)
assert u.find(0) != u.find(4)
assert u.find(2) != u.find(4)
u.link(0,2)
assert u.find(0) == u.find(1)
assert u.find(1) == u.find(2)
assert u.find(2) == u.find(3)
assert u.find(3) != u.find(4)
u.link(3,4)
assert u.find(0) == u.find(1)
assert u.find(1) == u.find(2)
assert u.find(2) == u.find(3)
assert u.find(3) == u.find(4)