def gabow(graph, k=None):
def find_exchange(father, included, excluded):
X = NamedUnionFind(vertices)
find = X.find
union = X.union
(min_weight, e, f) = (inf, None, None)
for (x, y) in included:
# Make it so that y = father[x]
if y != father[x]:
x, y = y, x
y = find(y)
union(x, y, y)
for edge in excluded:
mark(edge)
for (x, y) in edges:
if (x, y) in marked or (y, x) in marked:
unmark((x, y))
unmark((y, x))
elif father[x] != y and father[y] != x:
a = find(x)
ancestors = set()
while a not in ancestors:
ancestors.add(a)
a = find(father[a])
a = find(y)
while a not in ancestors:
a = find(father[a])
for u in [x, y]:
v = find(u)
while v != a:
fv = father[v]
exchange_weight = weight[x, y] - weight[v, fv]
if exchange_weight < min_weight:
min_weight = exchange_weight
e = (v, fv)
f = (x, y)
w = find(fv)
union(v, w, w)
v = w
return (min_weight, e, f)
inf = float('inf')
if k is None:
k = inf
weight = {(u, v): graph[u][v] for u in graph for v in graph[u]}
marked = set()
mark = marked.add
unmark = marked.discard
edges = sorted(graph.edge_set(), key=lambda (u, v): weight[(u, v)])
vertices = graph.vertices()
# arbitrary root vertex
root = vertices[0]
tree_weight, father = prim(graph, root, edge_list=False)
father[root] = root
(exchange_weight, e, f) = find_exchange(father, [], [])
heap = [(tree_weight + exchange_weight, e, f, father, [], [])]
tree_edges = sorted([(min(x, y), max(x, y)) for (x, y) in father.items()
if x != y])
yield tree_weight, tree_edges
j = 1
while j < k:
(tree_weight, e, f, father, included, excluded) = heappop(heap)
if tree_weight == inf:
return
new_graph = Graph()
new_graph.add_edges(father.items())
new_graph.delete_edge(e)
new_graph.add_edge(f)
new_father = breadth_first_search_tree(new_graph, root)
new_father[root] = root
tree_edges = sorted([(min(x, y), max(x, y))
for (x, y) in new_father.items() if x != y])
yield tree_weight, tree_edges
new_tree_weight = tree_weight - weight[f] + weight[e]
included_i = included + [e]
excluded_j = excluded + [e]
(exchange_weight, e, f) = find_exchange(father, included_i, excluded)
heappush(heap, (new_tree_weight + exchange_weight, e, f, father,
included_i, excluded))
(exchange_weight, e, f) = find_exchange(new_father, included,
excluded_j)
heappush(heap, (tree_weight + exchange_weight, e, f, new_father,
included, excluded_j))
j += 1
def test_breadth_first_search_tree(self):
pred = breadth_first_search_tree(self.graph, 's')
ans = {'a': 's', 'b': 'a', 'c': 's', 'd': 's', 'e': 's', 's': None}
self.assertEqual(pred, ans)
def gabow(graph, k=None):
def find_exchange(father, included, excluded):
X = NamedUnionFind(vertices)
find = X.find
union = X.union
(min_weight, e, f) = (inf, None, None)
for (x, y) in included:
# Make it so that y = father[x]
if y != father[x]:
x, y = y, x
y = find(y)
union(x, y, y)
for edge in excluded:
mark(edge)
for (x, y) in edges:
if (x, y) in marked or (y, x) in marked:
unmark((x, y))
unmark((y, x))
elif father[x] != y and father[y] != x:
a = find(x)
ancestors = set()
while a not in ancestors:
ancestors.add(a)
a = find(father[a])
a = find(y)
while a not in ancestors:
a = find(father[a])
for u in [x, y]:
v = find(u)
while v != a:
fv = father[v]
exchange_weight = weight[x, y] - weight[v, fv]
if exchange_weight < min_weight:
min_weight = exchange_weight
e = (v, fv)
f = (x, y)
w = find(fv)
union(v, w, w)
v = w
return (min_weight, e, f)
inf = float('inf')
if k is None:
k = inf
weight = {(u, v): graph[u][v] for u in graph for v in graph[u]}
marked = set()
mark = marked.add
unmark = marked.discard
edges = sorted(graph.edge_set(), key=lambda (u, v): weight[(u, v)])
vertices = graph.vertices()
# arbitrary root vertex
root = vertices[0]
tree_weight, father = prim(graph, root, edge_list=False)
father[root] = root
(exchange_weight, e, f) = find_exchange(father, [], [])
heap = [(tree_weight + exchange_weight, e, f, father, [], [])]
tree_edges = sorted([(min(x, y), max(x, y)) for (x, y) in father.items() if x != y])
yield tree_weight, tree_edges
j = 1
while j < k:
(tree_weight, e, f, father, included, excluded) = heappop(heap)
if tree_weight == inf:
return
new_graph = Graph()
new_graph.add_edges(father.items())
new_graph.delete_edge(e)
new_graph.add_edge(f)
new_father = breadth_first_search_tree(new_graph, root)
new_father[root] = root
tree_edges = sorted([(min(x, y), max(x, y)) for (x, y) in new_father.items() if x != y])
yield tree_weight, tree_edges
new_tree_weight = tree_weight - weight[f] + weight[e]
included_i = included + [e]
excluded_j = excluded + [e]
(exchange_weight, e, f) = find_exchange(father, included_i, excluded)
heappush(heap, (new_tree_weight + exchange_weight, e, f, father, included_i, excluded))
(exchange_weight, e, f) = find_exchange(new_father, included, excluded_j)
heappush(heap, (tree_weight + exchange_weight, e, f, new_father, included, excluded_j))
j += 1
def test_breadth_first_search_tree(self):
pred = breadth_first_search_tree(self.graph, 's')
ans = {'a': 's', 'b': 'a', 'c': 's', 'd': 's', 'e': 's', 's': None}
self.assertEqual(pred, ans)