def enumerate(self):
GraphSet.set_universe(self.bond_universe)
# 全域グラフのみ列挙
self.paths = GraphSet.graphs(
vertex_groups=[self.atm_no_list],
degree_constraints=self.degree_constraints,
no_loop=True)
self.paths_num = len(self.paths)
def connected_edges(start_node, target_node, num_edges):
"""
start_nodeをパスのスタートノードとし、かつtarget_nodeを含まない
長さがnum_edgesのパスを含むグラフセットを返す
パスが仮想ノードを２個以上通るときnum_edgesよりも短いパスもグラフセットに含まれてしまう
arguments:
* start_node(node label)
* target_node(node label)
* num_edges(int)
パスの長さ
returns:
* di_path(GraphSet)
有向性を考慮したパスだけを含むグラフセット
"""
all_nodes = set(original_nodes()) | set(virtual_nodes())
v_nodes = virtual_nodes()
degree_constraints = {}
for node in all_nodes:
if node in v_nodes:
degree_constraints[node] = [0, 2]
elif node == start_node:
degree_constraints[node] = 1
elif node == target_node:
degree_constraints[node] = 0
else:
degree_constraints[node] = [0, 1, 2]
elms = invalid_direction_elms(start_node, target_node)
v_edges = virtual_node_edges()
n_range = GraphSet.graphs(vertex_groups=[[start_node]],
no_loop=True,
num_edges=num_edges,
degree_constraints=degree_constraints)
n_inc_range = GraphSet.graphs(vertex_groups=[[start_node]],
no_loop=True,
num_edges=num_edges + 1,
degree_constraints=degree_constraints)
n_range = n_range.excluding(GraphSet(elms))\
.excluding(GraphSet(v_edges))
n_inc_range = n_inc_range.excluding(GraphSet(elms))\
.including(GraphSet(v_edges))
return n_range | n_inc_range
def _enumerate_forests(self, suspicious_cut):
vg = [[r] for r in self.graph.roots]
dc = {}
l = len(self.graph.graph.nodes())
for v in self.graph.graph.nodes():
if v in suspicious_cut: dc[v] = 0
elif v in self.graph.roots: dc[v] = xrange(l)
else: dc[v] = xrange(1, l)
return GraphSet.graphs(vertex_groups=vg, degree_constraints=dc,
no_loop=True)
def test_linear_constraints(self):
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
gs = GraphSet.graphs(linear_constraints=[([(2, 3)], (2, 1))])
self.assertEqual(gs, GraphSet())
gs = GraphSet.graphs(linear_constraints=[([], (1, 2))])
self.assertEqual(gs, GraphSet())
gs = GraphSet.graphs(linear_constraints=[([(5, 6, -1.5)], (-1.5, 0))])
self.assertEqual(gs, GraphSet.graphs())
gs = GraphSet.graphs(linear_constraints=[([(1, 2, 3.14)], (0, float("inf")))])
self.assertEqual(gs, GraphSet.graphs())
gs = GraphSet.graphs(linear_constraints=[(GraphSet.universe(), (0, float("inf")))])
self.assertEqual(gs, GraphSet.graphs())
gs = GraphSet.graphs(linear_constraints=[(GraphSet.universe(), (7, 7))])
self.assertEqual(gs, GraphSet([GraphSet.universe()]))
gs = GraphSet.graphs(linear_constraints=[(GraphSet.universe(), (1, 7))])
self.assertEqual(gs, GraphSet.graphs() - GraphSet([[]]))
gs = GraphSet.graphs(linear_constraints=[([(2, 3, -1), (2, 5, 10), (4, 1),
(3, 6), (4, 5, -1), (5, 6)],
(10, 100))])
self.assertEqual(len(gs), 52)
gs = GraphSet.graphs(linear_constraints=[([(2, 3), (2, 5, -10), (4, 1, -1),
(3, 6, -1), (4, 5), (5, 6, -1)],
(-100, -10))])
self.assertEqual(len(gs), 52)
gs = GraphSet.graphs(linear_constraints=[([(1, 2)], (1, 1)),
([(1, 4)], (1, 2)),
([(2, 3)], (1, 3)),
([(2, 5)], (1, 4)),
([(4, 5)], (1, 6)),
([(5, 6)], (1, 7))])
self.assertEqual(len(gs), 2)
def test_graphs(self):
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
# any subgraph
gs = GraphSet.graphs()
self.assertTrue(isinstance(gs, GraphSet))
self.assertEqual(len(gs), 2**7)
self.assertTrue([(1, 2)] in gs)
# subgraphs separating [1, 5] and [2]
gs = GraphSet.graphs(vertex_groups=[[1, 5], [2]])
self.assertEqual(len(gs), 6)
self.assertTrue([(1, 4), (4, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (4, 5)] not in gs)
# matching
dc = {}
for v in range(1, 7):
dc[v] = range(0, 2)
gs = GraphSet.graphs(degree_constraints=dc)
self.assertEqual(len(gs), 22)
self.assertTrue([(1, 2), (3, 6)] in gs)
self.assertTrue([(1, 2), (2, 3), (3, 6)] not in gs)
for g in gs:
self.assertTrue(len(g) < 4)
# subgraphs with 1 or 2 edges
gs = GraphSet.graphs(num_edges=range(1, 3))
self.assertEqual(len(gs), 28)
for g in gs:
self.assertTrue(1 <= len(g) and len(g) < 3)
# single connected component and vertex islands
gs = GraphSet.graphs(vertex_groups=[[]])
self.assertEqual(len(gs), 80)
self.assertTrue([(1, 2), (2, 3)] in gs)
self.assertTrue([(1, 2), (2, 3), (4, 5)] not in gs)
# any forest
gs = GraphSet.graphs(no_loop=True)
self.assertEqual(len(gs), 112)
self.assertTrue([(1, 2), (1, 4), (2, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
for g in gs:
self.assertTrue(len(g) < 6)
# constrained by GraphSet
gs = GraphSet.graphs(no_loop=True)
gs = gs.graphs(vertex_groups=[[]])
self.assertEqual(len(gs), 66)
self.assertTrue([(1, 2), (1, 4), (2, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
# single connected components across 1, 3, and 5
gs = GraphSet.connected_components([1, 3, 5])
self.assertEqual(len(gs), 35)
self.assertTrue([(1, 2), (2, 3), (2, 5)] in gs)
self.assertTrue([(1, 2), (2, 3), (5, 6)] not in gs)
GraphSet.set_universe([(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4),
(2, 5), (3, 4), (3, 5), (4, 5)])
# cliques with 4 vertices
gs = GraphSet.cliques(4)
self.assertEqual(len(gs), 5)
self.assertTrue([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)] in gs)
self.assertTrue([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 5)] not in gs)
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
# trees rooted at 1
gs = GraphSet.trees(1)
self.assertEqual(len(gs), 45)
self.assertTrue([] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
# spanning trees
gs = GraphSet.trees(is_spanning=True)
self.assertEqual(len(gs), 15)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5), (4, 5)] not in gs)
for g in gs:
self.assertEqual(len(g), 5)
# forests rooted at 1 and 3
gs = GraphSet.forests([1, 3])
self.assertEqual(len(gs), 54)
self.assertTrue([] in gs)
self.assertTrue([(1, 2), (2, 3)] not in gs)
# spanning forests rooted at 1 and 3
gs = GraphSet.forests([1, 3], is_spanning=True)
self.assertEqual(len(gs), 20)
self.assertTrue([(1, 2), (1, 4), (2, 5), (3, 6)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5)] not in gs)
for g in gs:
self.assertEqual(len(g), 4)
# cycles
gs = GraphSet.cycles()
self.assertEqual(len(gs), 3)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] in gs)
self.assertTrue([] not in gs)
# hamilton cycles
gs = GraphSet.cycles(is_hamilton=True)
self.assertEqual(len(gs), 1)
self.assertTrue([(1, 2), (1, 4), (2, 3), (3, 6), (4, 5), (5, 6)] in gs)
# paths between 1 and 6
gs = GraphSet.paths(1, 6)
self.assertEqual(len(gs), 4)
self.assertTrue([(1, 2), (2, 3), (3, 6)] in gs)
self.assertTrue([(1, 2), (2, 3), (5, 6)] not in gs)
# hamilton paths between 1 and 6
gs = GraphSet.paths(1, 6, is_hamilton=True)
self.assertEqual(len(gs), 1)
self.assertTrue([(1, 4), (2, 3), (2, 5), (3, 6), (4, 5)] in gs)
# called as instance methods
gs = GraphSet.graphs(no_loop=True)
_ = gs.connected_components([1, 3, 5])
_ = gs.cliques(4)
_ = gs.trees(1)
_ = gs.forests([1, 3])
_ = gs.cycles()
_ = gs.paths(1, 6)
# exceptions
self.assertRaises(KeyError, GraphSet.graphs, vertex_groups=[[7]])
self.assertRaises(KeyError, GraphSet.graphs, degree_constraints={7: 1})
def test_linear_constraints(self):
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
gs = GraphSet.graphs(linear_constraints=[([(2, 3)], (2, 1))])
self.assertEqual(gs, GraphSet())
gs = GraphSet.graphs(linear_constraints=[([], (1, 2))])
self.assertEqual(gs, GraphSet())
gs = GraphSet.graphs(linear_constraints=[([(5, 6, -1.5)], (-1.5, 0))])
self.assertEqual(gs, GraphSet.graphs())
gs = GraphSet.graphs(linear_constraints=[([(1, 2, 3.14)],
(0, float("inf")))])
self.assertEqual(gs, GraphSet.graphs())
gs = GraphSet.graphs(linear_constraints=[(GraphSet.universe(),
(0, float("inf")))])
self.assertEqual(gs, GraphSet.graphs())
gs = GraphSet.graphs(linear_constraints=[(GraphSet.universe(), (7,
7))])
self.assertEqual(gs, GraphSet([GraphSet.universe()]))
gs = GraphSet.graphs(linear_constraints=[(GraphSet.universe(), (1,
7))])
self.assertEqual(gs, GraphSet.graphs() - GraphSet([[]]))
gs = GraphSet.graphs(
linear_constraints=[([(2, 3, -1), (2, 5,
10), (4, 1), (3, 6), (4, 5,
-1), (5,
6)],
(10, 100))])
self.assertEqual(len(gs), 52)
gs = GraphSet.graphs(
linear_constraints=[([(2, 3), (2, 5,
-10), (4, 1,
-1), (3, 6,
-1), (4, 5), (5, 6,
-1)],
(-100, -10))])
self.assertEqual(len(gs), 52)
gs = GraphSet.graphs(linear_constraints=[([(1, 2)], (
1, 1)), ([(1, 4)],
(1, 2)), ([(2, 3)],
(1, 3)), ([(2, 5)],
(1, 4)), ([(4, 5)],
(1, 6)), ([(5, 6)], (1,
7))])
self.assertEqual(len(gs), 2)
def test_graphs(self):
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
# any subgraph
gs = GraphSet.graphs()
self.assertTrue(isinstance(gs, GraphSet))
self.assertEqual(len(gs), 2**7)
self.assertTrue([(1, 2)] in gs)
# subgraphs separating [1, 5] and [2]
gs = GraphSet.graphs(vertex_groups=[[1, 5], [2]])
self.assertEqual(len(gs), 6)
self.assertTrue([(1, 4), (4, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (4, 5)] not in gs)
# matching
dc = {}
for v in range(1, 7):
dc[v] = range(0, 2)
gs = GraphSet.graphs(degree_constraints=dc)
self.assertEqual(len(gs), 22)
self.assertTrue([(1, 2), (3, 6)] in gs)
self.assertTrue([(1, 2), (2, 3), (3, 6)] not in gs)
for g in gs:
self.assertTrue(len(g) < 4)
# subgraphs with 1 or 2 edges
gs = GraphSet.graphs(num_edges=range(1, 3))
self.assertEqual(len(gs), 28)
for g in gs:
self.assertTrue(1 <= len(g) and len(g) < 3)
# single connected component and vertex islands
gs = GraphSet.graphs(vertex_groups=[[]])
self.assertEqual(len(gs), 80)
self.assertTrue([(1, 2), (2, 3)] in gs)
self.assertTrue([(1, 2), (2, 3), (4, 5)] not in gs)
# any forest
gs = GraphSet.graphs(no_loop=True)
self.assertEqual(len(gs), 112)
self.assertTrue([(1, 2), (1, 4), (2, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
for g in gs:
self.assertTrue(len(g) < 6)
# constrained by GraphSet
gs = GraphSet.graphs(no_loop=True)
gs = gs.graphs(vertex_groups=[[]])
self.assertEqual(len(gs), 66)
self.assertTrue([(1, 2), (1, 4), (2, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
# single connected components across 1, 3, and 5
gs = GraphSet.connected_components([1, 3, 5])
self.assertEqual(len(gs), 35)
self.assertTrue([(1, 2), (2, 3), (2, 5)] in gs)
self.assertTrue([(1, 2), (2, 3), (5, 6)] not in gs)
GraphSet.set_universe([(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4),
(2, 5), (3, 4), (3, 5), (4, 5)])
# cliques with 4 vertices
gs = GraphSet.cliques(4)
self.assertEqual(len(gs), 5)
self.assertTrue([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)] in gs)
self.assertTrue([(1, 2), (1, 3), (1, 4), (2, 3), (2,
4), (3,
5)] not in gs)
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
# trees rooted at 1
gs = GraphSet.trees(1)
self.assertEqual(len(gs), 45)
self.assertTrue([] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
# spanning trees
gs = GraphSet.trees(is_spanning=True)
self.assertEqual(len(gs), 15)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5), (4, 5)] not in gs)
for g in gs:
self.assertEqual(len(g), 5)
# forests rooted at 1 and 3
gs = GraphSet.forests([1, 3])
self.assertEqual(len(gs), 54)
self.assertTrue([] in gs)
self.assertTrue([(1, 2), (2, 3)] not in gs)
# spanning forests rooted at 1 and 3
gs = GraphSet.forests([1, 3], is_spanning=True)
self.assertEqual(len(gs), 20)
self.assertTrue([(1, 2), (1, 4), (2, 5), (3, 6)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5)] not in gs)
for g in gs:
self.assertEqual(len(g), 4)
# cycles
gs = GraphSet.cycles()
self.assertEqual(len(gs), 3)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] in gs)
self.assertTrue([] not in gs)
# hamilton cycles
gs = GraphSet.cycles(is_hamilton=True)
self.assertEqual(len(gs), 1)
self.assertTrue([(1, 2), (1, 4), (2, 3), (3, 6), (4, 5), (5, 6)] in gs)
# paths between 1 and 6
gs = GraphSet.paths(1, 6)
self.assertEqual(len(gs), 4)
self.assertTrue([(1, 2), (2, 3), (3, 6)] in gs)
self.assertTrue([(1, 2), (2, 3), (5, 6)] not in gs)
# hamilton paths between 1 and 6
gs = GraphSet.paths(1, 6, is_hamilton=True)
self.assertEqual(len(gs), 1)
self.assertTrue([(1, 4), (2, 3), (2, 5), (3, 6), (4, 5)] in gs)
# called as instance methods
gs = GraphSet.graphs(no_loop=True)
_ = gs.connected_components([1, 3, 5])
_ = gs.cliques(4)
_ = gs.trees(1)
_ = gs.forests([1, 3])
_ = gs.cycles()
_ = gs.paths(1, 6)
# exceptions
self.assertRaises(KeyError, GraphSet.graphs, vertex_groups=[[7]])
self.assertRaises(KeyError, GraphSet.graphs, degree_constraints={7: 1})
if a[i][j] != 0:
degs[cellId[i][j]] = 1
if a[i][j] in clue:
clue[a[i][j]].append(cellId[i][j])
else:
clue[a[i][j]] = [cellId[i][j]]
else:
degs[cellId[i][j]] = 2
grps = []
for _, p in clue.items():
grps.append(p)
GraphSet.set_universe(edges)
sols = GraphSet.graphs(vertex_groups=grps,
degree_constraints=degs,
no_loop=True)
print('# of Solutions: %d' % sols.len())
def choose(gs):
for g in gs.rand_iter():
return g
sol = choose(sols)
def output(sol):
sh, sw = h * 2 + 1, w * 4 + 1
if a[i][j] != 0:
degs[cellId[i][j]] = 1
if a[i][j] in clue:
clue[a[i][j]].append(cellId[i][j])
else:
clue[a[i][j]] = [cellId[i][j]]
else:
degs[cellId[i][j]] = 2
grps = []
for _,p in clue.items():
grps.append(p)
GraphSet.set_universe(edges)
sols = GraphSet.graphs(vertex_groups=grps,
degree_constraints=degs,
no_loop=True)
print('# of Solutions: %d' % sols.len())
def choose(gs):
for g in gs.rand_iter():
return g
sol = choose(sols)
def output(sol):
sh,sw = h*2+1,w*4+1
s = [[' ' for j in range(sw)] for i in range(sh)]
for i in range(sh):
s[i][0] = s[i][-1] = '|'
