def setUp(self):
self.dg = SimpleGraph()
self.one = Vertex('one')
self.two = Vertex('two')
self.three = Vertex('three')
self.four = Vertex('four')
self.five = Vertex('five')
self.six = Vertex('six')
self.disconnected = Vertex('disconnected')
self.dg.add_vertex(self.one)
self.dg.add_vertex(self.two)
self.dg.add_vertex(self.three)
self.dg.add_vertex(self.four)
self.dg.add_vertex(self.five)
self.dg.add_vertex(self.six)
self.dg.add_vertex(self.disconnected)
self.dg.add_edge(self.one, self.two, 7.0)
self.dg.add_edge(self.two, self.one, 7.0)
self.dg.add_edge(self.one, self.six, 14.0)
self.dg.add_edge(self.six, self.one, 14.0)
self.dg.add_edge(self.one, self.three, 9.0)
self.dg.add_edge(self.three, self.one, 9.0)
self.dg.add_edge(self.two, self.three, 10.0)
self.dg.add_edge(self.three, self.two, 10.0)
self.dg.add_edge(self.two, self.four, 15.0)
self.dg.add_edge(self.four, self.two, 15.0)
self.dg.add_edge(self.three, self.four, 11.0)
self.dg.add_edge(self.four, self.three, 11.0)
self.dg.add_edge(self.three, self.six, 2.0)
self.dg.add_edge(self.six, self.three, 2.0)
self.dg.add_edge(self.four, self.five, 6.0)
self.dg.add_edge(self.five, self.four, 6.0)
self.dg.add_edge(self.five, self.six, 9.0)
self.dg.add_edge(self.six, self.five, 9.0)
def setUp(self):
self.size = 5
self.sg = SimpleGraph(self.size)
self.sg.AddVertex("A")
self.sg.AddVertex("B")
self.sg.AddVertex("C")
self.sg.AddVertex("D")
self.sg.AddVertex("E")
def setUp(self):
self.cc = SimpleGraph()
self.a = Vertex('a')
self.b = Vertex('b')
self.c = Vertex('c')
self.d = Vertex('d')
self.e = Vertex('e')
self.f = Vertex('f')
def fully_connected_graph(nodes):
g = SimpleGraph()
for node in nodes:
g.add_node(node)
for other_node in nodes:
if other_node is not node:
g.add_edge(node, other_node)
return g
def test_del_error():
"""error raised when non-existant value deleted"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
with pytest.raises(KeyError):
g.del_node('p')
def test_edge_error():
"""delete non-existant edge"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
with pytest.raises(KeyError):
g.del_edge('a', 'z')
def test_adjacent_error():
"""error raised when nodes non-existant"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
with pytest.raises(KeyError):
g.adjacent('l', 'm')
def test_del_edge():
"""other edges preserved when one deleted"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
g.del_edge('a', 'c')
assert g.neighbors('a') == {'b': 0}
def test_adjacent():
"""adjacent correctly identify edges, new edge add node"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'd')
g.add_edge('a', 'f')
assert 'f' in g.nodes()
assert g.adjacent('a', 'd')
assert not g.adjacent('a', 'b')
def test_add_nodes():
"""nodes are added"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
assert 'a' in g.nodes()
assert 'b' in g.nodes()
assert 'c' in g.nodes()
def test_sgraph_edges(self):
# Checks for irreflexivity
g = SimpleGraph.rand(5)
self.assertTrue(g.is_irreflexive())
# Checks for loops
with self.assertRaises(IsNotSimpleGraphError):
SimpleGraph(3, [[0, 0], [1, 0], [0, 2]])
# Checks for simetry
with self.assertRaises(IsNotSimpleGraphError):
SimpleGraph(3, [[0, 2], [1, 0], [0, 1]])
def test_depth():
g = SimpleGraph()
g.add_edge('a', 'b')
g.add_edge('a', 'c')
g.add_edge('b', 'd')
g.add_edge('b', 'e')
g.add_edge('e', 'f')
g.add_edge('f', 'g')
assert g.depth_first_traversal('a') == ['a', 'c', 'b', 'e', 'f', 'g', 'd']
def test_has_node():
"""edge added, new node added"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
assert g.has_node('b')
def __init__(self, width, height=None):
height = height or width
assert width > 0 and height > 0
self._width = width
self._height = height
self._graph = SimpleGraph()
self._locationMap = {} # vertex : location
for x, y in product(range(self._width), range(self._height)):
v = self.pushVertex((x, y))
if x > 0:
self._graph.addEdge(v, self.singleVertexAt((x - 1, y)))
if y > 0:
self._graph.addEdge(v, self.singleVertexAt((x, y - 1)))
def test_del_error():
"""error raised when non-existant value deleted"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
with pytest.raises(KeyError):
g.del_node('p')
def test_adjacent_error():
"""error raised when nodes non-existant"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
with pytest.raises(KeyError):
g.adjacent('l', 'm')
def test_edge_error():
"""delete non-existant edge"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
with pytest.raises(KeyError):
g.del_edge('a', 'z')
def test_edges():
"""edges prints correct edges as tuples"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
assert ('a', 'c') in g.edges()
assert ('a', 'b') in g.edges()
def test_add_nodes():
"""nodes are added"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
assert 'a' in g.nodes()
assert 'b' in g.nodes()
assert 'c' in g.nodes()
def test_depth():
g = SimpleGraph()
g.add_edge('a', 'b')
g.add_edge('a', 'c')
g.add_edge('b', 'd')
g.add_edge('b', 'e')
g.add_edge('e', 'f')
g.add_edge('f', 'g')
assert g.depth_first_traversal('a') == ['a', 'c', 'b', 'e', 'f', 'g', 'd']
def test_has_node():
"""edge added, new node added"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
assert g.has_node('b')
def setUp(self):
self.g = SimpleGraph()
self.a = Vertex('a')
self.b = Vertex('b')
self.c = Vertex('c')
self.d = Vertex('d')
self.e = Vertex('e')
self.f = Vertex('f')
self.g.add_vertex(self.a)
self.g.add_vertex(self.b)
self.g.add_vertex(self.c)
self.g.add_vertex(self.d)
self.g.add_vertex(self.e)
self.g.add_edge(self.a, self.b)
self.g.add_edge(self.b, self.c)
self.g.add_edge(self.c, self.b)
self.g.add_edge(self.c, self.d)
def test_edges():
"""edges prints correct edges as tuples"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
assert ('a', 'c') in g.edges()
assert ('a', 'b') in g.edges()
def setUp(self):
self.b = SimpleGraph()
self.l1 = Vertex('l1')
self.l2 = Vertex('l2')
self.l3 = Vertex('l3')
self.l4 = Vertex('l4')
self.r1 = Vertex('r1')
self.r2 = Vertex('r2')
self.r3 = Vertex('r3')
self.b.add_vertex(self.l1)
self.b.add_vertex(self.l2)
self.b.add_vertex(self.l3)
self.b.add_vertex(self.r1)
self.b.add_vertex(self.r2)
self.b.add_edge(self.l1, self.r1)
self.b.add_edge(self.l1, self.r2)
self.b.add_edge(self.l2, self.r1)
self.b.add_edge(self.l2, self.r2)
self.b.add_edge(self.l3, self.r1)
self.b.add_edge(self.l3, self.r2)
def fully_connected_graph(nodes):
g = SimpleGraph()
for node in nodes:
g.add_node(node)
for other_node in nodes:
if other_node is not node:
g.add_edge(node, other_node)
return g
def blockForest(self):
bf = SimpleGraph()
vertexmap = {} # vertex: vertex in block forest
articulations = set() # separators mapped to block forest
for sv in self._separators:
av = bf.pushVertex()
articulations.add(av)
vertexmap[sv] = av
for bc_k, bc in self._biconComponents.items():
seps = self._separatorMap[bc_k]
if len(bc) == 2 and len(seps) == 2:
it = iter(bc)
bf.addEdge(vertexmap[next(it)], vertexmap[next(it)])
else:
bcv = bf.pushVertex()
for v in bc - seps:
vertexmap[v] = bcv
for sv in seps:
bf.addEdge(bcv, vertexmap[sv])
return bf, vertexmap, articulations
class DijkstrasAlgorithmTests(unittest.TestCase):
def setUp(self):
self.dg = SimpleGraph()
self.one = Vertex('one')
self.two = Vertex('two')
self.three = Vertex('three')
self.four = Vertex('four')
self.five = Vertex('five')
self.six = Vertex('six')
self.disconnected = Vertex('disconnected')
self.dg.add_vertex(self.one)
self.dg.add_vertex(self.two)
self.dg.add_vertex(self.three)
self.dg.add_vertex(self.four)
self.dg.add_vertex(self.five)
self.dg.add_vertex(self.six)
self.dg.add_vertex(self.disconnected)
self.dg.add_edge(self.one, self.two, 7.0)
self.dg.add_edge(self.two, self.one, 7.0)
self.dg.add_edge(self.one, self.six, 14.0)
self.dg.add_edge(self.six, self.one, 14.0)
self.dg.add_edge(self.one, self.three, 9.0)
self.dg.add_edge(self.three, self.one, 9.0)
self.dg.add_edge(self.two, self.three, 10.0)
self.dg.add_edge(self.three, self.two, 10.0)
self.dg.add_edge(self.two, self.four, 15.0)
self.dg.add_edge(self.four, self.two, 15.0)
self.dg.add_edge(self.three, self.four, 11.0)
self.dg.add_edge(self.four, self.three, 11.0)
self.dg.add_edge(self.three, self.six, 2.0)
self.dg.add_edge(self.six, self.three, 2.0)
self.dg.add_edge(self.four, self.five, 6.0)
self.dg.add_edge(self.five, self.four, 6.0)
self.dg.add_edge(self.five, self.six, 9.0)
self.dg.add_edge(self.six, self.five, 9.0)
def test_dijkstras_algo(self):
self.assertTrue(
self.dg.dijkstras_algorithm(self.one, self.five)
== (20.0, [self.one, self.three, self.six, self.five]))
def test_dijkstras_unconnected(self):
self.assertTrue(
self.dg.dijkstras_algorithm(self.one, self.disconnected)
== (math.inf, []))
def _build4by4():
# makes a grid structure like:
# 0 - 1 - 2 - 3
# ! ! ! !
# 4 - 5 - 6 - 7
# ! ! ! !
# 8 - 9 - 10- 11
# ! ! ! !
# 12- 13- 14- 15
g = SimpleGraph()
g.addVertices(range(16))
for k in range(0, 16, 4):
for i in range(k, k + 3):
g.addEdge(i, i + 1)
for k in range(4):
for i in range(k, 12, 4):
g.addEdge(i, i + 4)
for i in [0, 3, 12, 15]:
assert g.degree(i) == 2
for i in [1, 2, 7, 11, 14, 13, 8, 4]:
assert g.degree(i) == 3
for i in [5, 6, 9, 10]:
assert g.degree(i) == 4
return g
class GraphOntoRectangularGrid(object):
"""
Locations in the grid are tuples (x, y), 0-based.
Each vertex maps to one grid location.
It is possible for a grid location to map to multiple vertices.
"""
def __init__(self, width, height=None):
height = height or width
assert width > 0 and height > 0
self._width = width
self._height = height
self._graph = SimpleGraph()
self._locationMap = {} # vertex : location
for x, y in product(range(self._width), range(self._height)):
v = self.pushVertex((x, y))
if x > 0:
self._graph.addEdge(v, self.singleVertexAt((x - 1, y)))
if y > 0:
self._graph.addEdge(v, self.singleVertexAt((x, y - 1)))
@property
def width(self):
return self._width
@property
def height(self):
return self._height
@property
def graph(self):
return self._graph.asReadOnly()
def getLocationMap(self):
return dict((v, tuple(c)) for v, c in self._locationMap.items())
def pushVertex(self, xy):
x, y = xy
assert 0 <= x < self._width
assert 0 <= y < self._height
v = self._graph.pushVertex()
self._locationMap[v] = xy
return v
def removeVertex(self, v):
self._graph.removeVertex(v)
del self._locationMap[v]
def removeVertexAt(self, xy):
self.removeVertex(self.singleVertexAt(xy))
def addEdge(self, v1, v2):
self._graph.addEdge(v1, v2)
def removeUniqueEdge(self, xy1, xy2):
v1, v2 = map(self.singleVertexAt, (xy1, xy2))
self._graph.removeEdge(v1, v2)
def verticesAt(self, xy):
"""Get the set of any/all vertices mapped to location."""
return set(k for k, v in self._locationMap.items() if v == xy)
def singleVertexAt(self, xy):
"""Get the single vertex mapped to location. Error if not 1-to-1."""
v = self.verticesAt(xy)
assert len(v) == 1
return v.pop()
def adjacenciesAt(self, xy):
return self._graph.adjacencies(self.singleVertexAt(xy))
def orthogonalAdjacencies(self, xy):
x, y = xy
a = self.adjacenciesAt(xy)
xa = a & (self.verticesAt((x - 1, y)) | self.verticesAt((x + 1, y)))
ya = a & (self.verticesAt((x, y - 1)) | self.verticesAt((x, y + 1)))
return xa, ya
class TestUM(unittest.TestCase):
def setUp(self):
self.size = 5
self.sg = SimpleGraph(self.size)
self.sg.AddVertex("A")
self.sg.AddVertex("B")
self.sg.AddVertex("C")
self.sg.AddVertex("D")
self.sg.AddVertex("E")
def test_init(self):
sg = SimpleGraph(3)
self.assertEqual(sg.max_vertex, 3)
self.assertEqual(sg.m_adjacency, [[0, 0, 0], [0, 0, 0], [0, 0, 0]])
self.assertEqual(sg.vertex, [None, None, None])
def test_add_vertex_without_adjacency(self):
self.sg.AddVertex("F")
self.assertEqual(len(self.sg.vertex), self.size)
self.assertEqual([x.Value for x in self.sg.vertex],
["A", "B", "C", "D", "E"])
self.assertEqual(self.sg.m_adjacency,
[[0] * self.size for _ in range(self.size)])
self.assertEqual(
self.sg.m_adjacency,
[
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
],
)
def test_add_edge(self):
self.assertEqual(self.sg.m_adjacency,
[[0] * self.size for _ in range(self.size)])
self.sg.AddEdge(0, 2) # A + C
self.assertEqual(self.sg.m_adjacency[0][2], 1)
self.assertEqual(self.sg.m_adjacency[2][0], 1)
self.assertEqual(self.sg.IsEdge(0, 2), True)
self.sg.AddEdge(0, 1) # A + B
self.assertEqual(self.sg.m_adjacency[0][1], 1)
self.assertEqual(self.sg.m_adjacency[1][0], 1)
self.assertEqual(self.sg.IsEdge(0, 1), True)
self.sg.AddEdge(0, 3) # A + D
self.assertEqual(self.sg.m_adjacency[0][3], 1)
self.assertEqual(self.sg.m_adjacency[3][0], 1)
self.assertEqual(self.sg.IsEdge(0, 3), True)
self.sg.AddEdge(3, 3) # D + D
self.assertEqual(self.sg.m_adjacency[3][3], 1)
self.assertEqual(self.sg.m_adjacency[3][3], 1)
self.assertEqual(self.sg.IsEdge(3, 3), True)
self.sg.AddEdge(1, 4) # B + E
self.assertEqual(self.sg.m_adjacency[1][4], 1)
self.assertEqual(self.sg.m_adjacency[4][1], 1)
self.assertEqual(self.sg.IsEdge(1, 4), True)
self.sg.AddEdge(3, 4) # D + E
self.assertEqual(self.sg.m_adjacency[3][4], 1)
self.assertEqual(self.sg.m_adjacency[3][4], 1)
self.assertEqual(self.sg.IsEdge(3, 4), True)
self.sg.AddEdge(1, 3) # B + D
self.assertEqual(self.sg.m_adjacency[1][3], 1)
self.assertEqual(self.sg.m_adjacency[3][1], 1)
self.assertEqual(self.sg.IsEdge(1, 3), True)
self.sg.AddEdge(2, 3) # C + D
self.assertEqual(self.sg.m_adjacency[2][3], 1)
self.assertEqual(self.sg.m_adjacency[3][2], 1)
self.assertEqual(self.sg.IsEdge(2, 3), True)
self.assertEqual(
self.sg.m_adjacency,
[
[0, 1, 1, 1, 0],
[1, 0, 0, 1, 1],
[1, 0, 0, 1, 0],
[1, 1, 1, 1, 1],
[0, 1, 0, 1, 0],
],
)
def test_delete_vertex(self):
self.assertEqual(self.sg.m_adjacency,
[[0] * self.size for _ in range(self.size)])
self.sg.AddEdge(0, 2) # A + C
self.assertEqual(self.sg.m_adjacency[0][2], 1)
self.assertEqual(self.sg.m_adjacency[2][0], 1)
self.assertEqual(self.sg.IsEdge(0, 2), True)
self.assertEqual(
self.sg.m_adjacency,
[
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0],
[1, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
],
)
self.sg.RemoveVertex(2)
self.assertEqual(self.sg.vertex[2], None)
self.assertEqual(self.sg.m_adjacency[0][2], 0)
self.assertEqual(self.sg.m_adjacency[2][0], 0)
self.assertEqual(self.sg.IsEdge(0, 2), False)
self.assertEqual(
self.sg.m_adjacency,
[
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
],
)
def test_delete_edge(self):
self.assertEqual(self.sg.m_adjacency,
[[0] * self.size for _ in range(self.size)])
self.sg.AddEdge(0, 2) # A + C
self.assertEqual(self.sg.m_adjacency[0][2], 1)
self.assertEqual(self.sg.m_adjacency[2][0], 1)
self.assertEqual(self.sg.IsEdge(0, 2), True)
self.assertEqual(
self.sg.m_adjacency,
[
[0, 0, 1, 0, 0],
[0, 0, 0, 0, 0],
[1, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
],
)
self.sg.RemoveEdge(0, 2)
self.assertEqual(self.sg.m_adjacency[0][2], 0)
self.assertEqual(self.sg.m_adjacency[2][0], 0)
self.assertEqual(self.sg.IsEdge(0, 2), False)
self.assertEqual(
self.sg.m_adjacency,
[
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
[0, 0, 0, 0, 0],
],
)
def _testGraph():
g = SimpleGraph()
assert isinstance(g, QueryableSimpleGraph)
assert not isinstance(g.asReadOnly(), SimpleGraph)
assert isinstance(g.asReadOnly(), QueryableSimpleGraph)
g.assertSimple()
verts = []
for i in range(10):
verts.append(g.pushVertex())
try:
g.addVertex(verts[0])
raise AssertionError
except ValueError:
pass
assert len(set(verts)) == len(verts)
for v in verts:
assert not g.adjacencies(v)
assert g.connectedComponent(v) == {v}
assert not g.isSeparator(v)
assert g.isConnectedSet([v])
parts = g.disjointPartitions()
assert len(parts) == len(verts)
s = set()
for p in parts:
assert len(p) == 1
s.add(p.pop())
assert s == set(verts)
edgeCount = 0
assert g.edgeCount() == edgeCount
assert g.edgeCount(without=set()) == g.edgeCount()
for i in range(len(verts) - 1):
edgeCount += 1
g.addEdge(verts[i], verts[i + 1])
for v in verts[i + 2:]:
assert not g.connected(verts[i + 1], v)
assert not g.connected(v, verts[i + 1])
for j in range(i + 1):
if j > 0:
assert g.connected(verts[0], verts[j])
assert g.connected(verts[j], verts[0])
assert g.connectedComponent(verts[j]) == set(verts[:i + 2])
assert g.edgeCount() == edgeCount
assert g.edgeCount(without=set()) == g.edgeCount()
assert g.edgeCount(mask=verts) == g.edgeCount()
for v in verts:
assert g.edgeCount(mask={v}) == 0
assert g.connectedComponent(v) == set(verts)
assert g.isConnectedSet(verts)
assert g.isConnectedSet([verts[2], verts[4]], verts[2:5])
assert not g.isConnectedSet([verts[2], verts[4]], [verts[2], verts[4]])
assert g.isConnectedSet(verts[:4] + verts[5:])
assert not g.isConnectedSet(verts[:4] + verts[5:], verts[:4] + verts[5:])
assert not g.isSeparator(verts[0])
assert not g.isSeparator(verts[-1])
assert all(g.isSeparator(v) for v in verts[1:-1])
assert g.shortestPath(verts[0], verts[-1]) == verts
assert g.shortestPath(verts[-1], verts[0]) == list(reversed(verts))
assert g.shortestPath(verts[3], verts[3]) == [verts[3]]
shortcut = g.pushVertex()
edgeCount += 2
g.addEdge(verts[0], shortcut)
g.addEdge(verts[-1], shortcut)
assert g.shortestPath(verts[0], verts[-1]) == \
[verts[0], shortcut, verts[-1]]
assert verts[0] == 0
edgeCount -= 1
g.removeEdge(verts[-1], shortcut)
assert g.shortestPath(shortcut, verts[1]) == [shortcut, verts[0], verts[1]]
edgeCount -= len(g.adjacencies(shortcut))
assert g.edgeCount(without={shortcut}) == edgeCount
g.removeVertex(shortcut)
assert g.edgeCount() == edgeCount
# noinspection PyUnusedLocal
edgeCount = None
g.addEdge(verts[0], verts[-1])
assert g.shortestPath(verts[0], verts[-1]) == [verts[0], verts[-1]]
assert not any(g.isSeparator(v) for v in verts)
g.removeEdge(verts[0], verts[-1])
g.asReadOnly()
mask = verts[:2] + verts[3:]
parts = g.disjointPartitions(mask)
assert len(parts) == 2
assert not parts[0].intersection(parts[1])
assert g.isConnectedSet(parts[0])
assert g.isConnectedSet(parts[1])
for v1 in parts[0]:
for v2 in parts[1]:
assert g.shortestPath(v1, v2, mask) == []
assert not g.isConnectedSet(mask, mask)
assert verts[2] not in parts[0].union(parts[1])
assert parts[0].union(parts[1]) == set(verts) - set(verts[2:3])
drops = [verts[i] for i in [2, 5, 8]]
for v in drops:
g.removeVertex(v)
verts.remove(v)
assert not g.adjacencies(verts[-1])
for v in verts[:-1]:
assert len(g.adjacencies(v)) == 1
assert not g.isSeparator(v)
g.assertSimple()
assert len(g.disjointPartitions()) == 4
assert len(g.disjointPartitions(verts[1:])) == 4
assert len(g.disjointPartitions(verts[2:])) == 3
assert g.connectedComponent(verts[-1]) == set(verts[-1:])
assert g.connectedComponent(verts[1], verts[1:]) == set(verts[1:2])
backbone = [list(p)[0] for p in g.disjointPartitions()]
for i in range(len(backbone) - 1):
g.addEdge(backbone[i], backbone[i + 1])
g.addEdge(backbone[0], backbone[-1])
assert len(g.disjointPartitions()) == 1
assert g.connectedComponent(verts[0]) == set(verts)
assert g.connected(verts[0], verts[-1])
assert g.isConnectedSet(set(verts[:1] + verts[-1:]))
assert g.edgeCount(without={3, 6}) == g.edgeCount() - 5
assert g.edgeCount(without={0, 9}) == g.edgeCount() - 4
def main():
""" Função main.
"""
mais = 's'
while mais != 'n':
print("""\n ===== Gerador de Grafos =====
[S] Simple
[U] Não orientado
[M] Multigrafo
[O] Ordenado
[R] Randômico
""")
tipo = input('Selecione o tipo de grafo (R padrão): ').lower()
arestas = []
if tipo in ['r', '']:
tipo = random.choice(['m', 's', 'u', 'o'])
v_qty = random.randint(2, 7)
else:
pattern = re.compile(r'\d{1,}')
v_qty = int(input('\nQuantidade de vértices: '))
print('Vértices: {}'.format(list(range(v_qty))))
a_qty = int(input('\nQuantidade de arestas: '))
print('Ingrese as arestas no formato "a,b":\n')
for i in range(a_qty):
padding = (len(str(a_qty)) - len(str(i + 1))) * ' '
aresta = input('{}[{}] '.format(padding, i + 1))
match = re.findall(pattern, aresta)
if match and len(match) == 2:
match[0] = int(match[0])
match[1] = int(match[1])
arestas.append(match)
if tipo == 'm':
graph = Graph(v_qty, arestas) if arestas else Graph.rand(v_qty)
elif tipo == 'u':
graph = UndirectedGraph(
v_qty, arestas) if arestas else UndirectedGraph.rand(v_qty)
elif tipo == 's':
graph = SimpleGraph(
v_qty, arestas) if arestas else SimpleGraph.rand(v_qty)
elif tipo == 'o':
if arestas:
opt = ''
while opt not in ['m', 'M']:
opt = input('\nInforme minofidade ou maioridade (m/M): ')
minority = opt == 'm'
graph = OrderedGraph(v_qty, arestas, minority) \
if arestas else OrderedGraph.rand(v_qty)
else:
return
order = ""
if isinstance(graph, OrderedGraph) and graph.is_order():
order = """\n
Máximo: {}
Mínimo: {}
Maximais: {}
Minimais: {}
""".format(graph.max(), graph.min(), graph.maximal(), graph.minimal())
print("""
Tipo: {}
Vértices: {}
Arestas: {}
Reflexiva: {}
Irreflexiva: {}
Simétrica: {}
Antisimétrica: {}
Transitiva: {}
Relação de ordem: {}{}
Matriz de adjacência:
{}
Matriz de incidência:
{}
""".format(graph.__class__, graph.vertices, graph.edges, graph.is_reflexive(),
graph.is_irreflexive(), graph.is_symmetric(),
graph.is_antisymmetric(), graph.is_transitive(), graph.is_order(),
order, graph.to_adjacency(), graph.to_incidence()))
mais = input('\nMais um (S/n)? ').lower()
class IsBipartiteTests(unittest.TestCase):
def setUp(self):
self.b = SimpleGraph()
self.l1 = Vertex('l1')
self.l2 = Vertex('l2')
self.l3 = Vertex('l3')
self.l4 = Vertex('l4')
self.r1 = Vertex('r1')
self.r2 = Vertex('r2')
self.r3 = Vertex('r3')
self.b.add_vertex(self.l1)
self.b.add_vertex(self.l2)
self.b.add_vertex(self.l3)
self.b.add_vertex(self.r1)
self.b.add_vertex(self.r2)
self.b.add_edge(self.l1, self.r1)
self.b.add_edge(self.l1, self.r2)
self.b.add_edge(self.l2, self.r1)
self.b.add_edge(self.l2, self.r2)
self.b.add_edge(self.l3, self.r1)
self.b.add_edge(self.l3, self.r2)
def test_is_bipartite(self):
self.assertTrue(self.b.is_bipartite())
self.bl1 = Vertex('bl1')
self.bl2 = Vertex('bl2')
self.br1 = Vertex('br1')
self.b.add_vertex(self.bl1)
self.b.add_vertex(self.bl2)
self.b.add_vertex(self.br1)
self.b.add_edge(self.bl1, self.br1)
self.b.add_edge(self.bl2, self.br1)
self.assertTrue(self.b.is_bipartite())
def test_is_not_bipartite(self):
self.c1 = Vertex('c1')
self.b.add_vertex(self.c1)
self.b.add_edge(self.l1, self.c1)
self.b.add_edge(self.r1, self.c1)
self.assertFalse(self.b.is_bipartite())
def test_weighted_edges_with_node_delete():
g = SimpleGraph()
g.add_edge('a', 'b', 5)
g.add_edge('a', 'c', 2)
g.del_node('c')
assert g.dict_graph['a'] == {'b': 5}
def _testMatching():
g = SimpleGraph()
verts = list(range(7))
g.addVertices(verts)
assert g.isMatching()
g.addEdge(0, 1)
assert g.isMatching()
g.addEdge(1, 2)
assert not g.isMatching()
g.addEdge(2, 3)
g.addEdge(4, 5)
assert not g.isMatching()
g.removeEdge(1, 2)
assert g.isMatching()
assert not g.isPerfectMatching()
g.addEdge(6, g.pushVertex())
assert g.isPerfectMatching()
g = _build4by4()
assert not g.isMatching()
assert g.maximumMatching().isPerfectMatching()
v_a = g.pushVertex()
g.addEdge(0, v_a)
m = g.maximumMatching()
assert m.isMatching()
assert not m.isPerfectMatching()
v_b = g.pushVertex()
g.addEdge(v_a, v_b)
assert g.maximumMatching().isPerfectMatching()
g.addEdge(v_b, 4)
assert g.maximumMatching().isPerfectMatching()
g = SimpleGraph()
A = _makeChain(g, 9)
assert not g.isCycle(A)
assert g.maximumMatching().edgeCount() == 4
g.addEdge(A[0], A[-1])
assert g.isCycle(A)
assert g.maximumMatching().edgeCount() == 4
hub = g.pushVertex()
for Av in A:
g.addEdge(hub, Av)
assert g.maximumMatching().isPerfectMatching()
for Av in A:
g.addEdge(Av, _makeLoop(g, 5)[0])
assert not g.maximumMatching().isPerfectMatching()
g.removeVertex(hub)
assert g.maximumMatching().isPerfectMatching()
g = _build4by4()
g.removeVertices([4, 8, 3, 15])
assert g.maximumMatching().isPerfectMatching()
class LargestConnectedComponentTests(unittest.TestCase):
def setUp(self):
self.cc = SimpleGraph()
self.a = Vertex('a')
self.b = Vertex('b')
self.c = Vertex('c')
self.d = Vertex('d')
self.e = Vertex('e')
self.f = Vertex('f')
def test_no_connected_components(self):
self.assertTrue(self.cc.largest_connected_component() == 0)
def test_single_vertex_cc(self):
self.cc.add_vertex(self.a)
self.cc.add_vertex(self.b)
self.cc.add_vertex(self.c)
self.assertTrue(self.cc.largest_connected_component() == 1)
def test_cc_of_size_3(self):
self.cc.add_vertex(self.a)
self.cc.add_vertex(self.b)
self.cc.add_vertex(self.c)
self.cc.add_vertex(self.d)
self.cc.add_vertex(self.e)
self.cc.add_vertex(self.f)
self.cc.add_edge(self.a, self.b)
self.cc.add_edge(self.a, self.c)
self.cc.add_edge(self.d, self.e)
self.assertTrue(self.cc.largest_connected_component() == 3)
def test_one_depth():
g = SimpleGraph()
g.add_node('a')
assert g.depth_first_traversal('a') == ['a']
def test_add_edge():
"""edge added, new node added"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
g.add_edge('q', 'a')
assert g.has_node('q')
assert g.neighbors('q') == {'a': 0}
def test_one_loop_depth():
g = SimpleGraph()
g.add_edge('a', 'a')
assert g.depth_first_traversal('a') == ['a']
class SimpleGraphTests(unittest.TestCase):
def setUp(self):
self.g = SimpleGraph()
self.a = Vertex('a')
self.b = Vertex('b')
self.c = Vertex('c')
self.d = Vertex('d')
self.e = Vertex('e')
self.f = Vertex('f')
self.g.add_vertex(self.a)
self.g.add_vertex(self.b)
self.g.add_vertex(self.c)
self.g.add_vertex(self.d)
self.g.add_vertex(self.e)
self.g.add_edge(self.a, self.b)
self.g.add_edge(self.b, self.c)
self.g.add_edge(self.c, self.b)
self.g.add_edge(self.c, self.d)
def test_is_empty(self):
self.assertFalse(self.g.is_empty())
self.g.remove_edge(self.a, self.b)
self.g.remove_edge(self.b, self.c)
self.g.remove_edge(self.c, self.b)
self.g.remove_edge(self.c, self.d)
self.g.remove_vertex(self.a)
self.g.remove_vertex(self.b)
self.g.remove_vertex(self.c)
self.g.remove_vertex(self.d)
self.g.remove_vertex(self.e)
self.assertTrue(self.g.is_empty())
def test_contains_vertex(self):
self.assertTrue(self.g.contains_vertex(self.a))
self.assertFalse(self.g.contains_vertex(self.f))
def test_size(self):
self.assertTrue(self.g.size() == (5, 4))
self.g.add_edge(self.a, self.e)
self.assertTrue(self.g.size() == (5, 5))
self.g.remove_edge(self.a, self.e)
self.assertTrue(self.g.size() == (5, 4))
self.g.add_edge(self.a, self.b)
self.assertTrue(self.g.size() == (5, 4))
def test_get_neighbors(self):
b_neighbors = self.g.get_neighbors(self.b)
self.assertTrue(len(b_neighbors) == 2)
self.assertTrue(self.a in b_neighbors)
self.assertTrue(self.c in b_neighbors)
self.assertTrue(self.g.is_neighbor(self.a, self.b))
self.assertFalse(self.g.is_neighbor(self.a, self.d))
self.assertTrue(all([not self.g.is_neighbor(self.e, v) for v in self.g.verts]))
self.g.add_vertex(self.f)
self.assertTrue(len(self.g.get_neighbors(self.f)) == 0)
def test_is_reachable(self):
self.assertTrue(self.g.is_reachable(self.a, self.d))
self.assertTrue(self.g.is_reachable(self.a, self.d))
self.assertFalse(self.g.is_reachable(self.d, self.a))
self.assertFalse(self.g.is_reachable(self.a, self.e))
self.g.remove_vertex(self.b)
self.assertTrue(self.g.size() == (4, 1))
self.assertFalse(self.g.is_reachable(self.a, self.d))
def test_adjacent():
"""adjacent correctly identify edges, new edge add node"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'd')
g.add_edge('a', 'f')
assert 'f' in g.nodes()
assert g.adjacent('a', 'd')
assert not g.adjacent('a', 'b')
def test_init(self):
sg = SimpleGraph(3)
self.assertEqual(sg.max_vertex, 3)
self.assertEqual(sg.m_adjacency, [[0, 0, 0], [0, 0, 0], [0, 0, 0]])
self.assertEqual(sg.vertex, [None, None, None])
def _testGraphBiconnected():
random.seed('consistent seed')
edgesets = 3 * [{
0: set(),
2: {3, 13},
3: {2, 4, 14},
4: {3, 15},
13: {2, 14},
14: {25, 3, 13, 15},
15: {4, 14},
17: {18, 28},
18: {17, 29},
22: {23},
23: {34, 22},
25: {36, 14},
28: {17, 29, 39},
29: {18, 28},
34: {35, 45, 23},
35: {34, 36},
36: {25, 35, 37, 47},
37: {36, 38},
38: {37, 39},
39: {28, 38},
42: {119},
44: {45},
45: {34, 44},
47: {58, 36},
52: {120, 63},
54: {120, 65},
57: {58, 68},
58: {57, 59, 47},
59: {58, 70},
63: {52, 118},
65: {118, 54},
66: {77},
68: {57, 79},
70: {81, 59},
72: set(),
75: {117},
77: {66},
79: {80, 68},
80: {81, 91, 79},
81: {80, 70},
84: {95},
91: {80, 102},
94: {105, 95},
95: {96, 106, 84, 94},
96: {95},
99: {100},
100: {99, 111},
102: {91},
104: {105, 115},
105: {104, 106, 116, 94},
106: {105, 95},
111: {100},
115: {104, 116},
116: {105, 115},
117: {75, 119},
118: {65, 63},
119: {42, 117},
120: {52, 54}
}, {
2: {3},
3: {2, 4, 10},
4: {3},
10: {17, 3},
14: {21},
16: {17, 23},
17: {16, 24, 10, 18},
18: {17, 25},
20: {27},
21: {28, 22, 14},
22: {21, 23},
23: {16, 24, 30, 22},
24: {17, 31, 25, 23},
25: {24, 32, 18, 26},
26: {25, 27},
27: {26, 20, 34},
28: {21},
30: {31, 23},
31: {24, 32, 38, 30},
32: {25, 31},
34: {27},
38: {45, 31},
44: {45},
45: {44, 46, 38},
46: {45}
}, {
20: {31},
24: {35},
31: {42, 20},
34: {35, 45},
35: {24, 34, 46},
39: {40},
40: {41, 51, 39},
41: {40, 42, 52},
42: {41, 53, 31},
44: {45, 55},
45: {56, 34, 44, 46},
46: {57, 35, 45},
51: {40, 52, 62},
52: {41, 51, 53, 63},
53: {64, 42, 52},
55: {56, 66, 44},
56: {57, 67, 45, 55},
57: {56, 68, 46},
62: {73, 51, 63},
63: {64, 74, 52, 62},
64: {53, 63},
66: {67, 55},
67: {56, 66, 68, 78},
68: {57, 67, 69, 79},
69: {80, 68},
72: {73, 83},
73: {72, 74, 62},
74: {73, 63},
78: {67, 79},
79: {80, 90, 68, 78},
80: {81, 91, 69, 79},
81: {80, 82, 92},
82: {81, 83},
83: {72, 82},
90: {91, 79},
91: {80, 90, 92},
92: {81, 91}
}]
for es in edgesets:
es = deepcopy(es)
g = SimpleGraph(es)
g2 = SimpleGraph(g)
assert set(g.vertices) == set(g2.vertices)
g2.removeVertex(list(g2.vertices)[0])
assert set(g.vertices) != set(g2.vertices)
verts = set(g.vertices)
vertlist = list(verts)
random.shuffle(vertlist)
rgstack = [OnlineReducedGraph(QueryableSimpleGraph(deepcopy(es)))]
for v in vertlist:
rgstack.append(rgstack[-1].copy())
rgstack[-1].maskVertex(v)
while vertlist:
assert set(es) == verts
bcs, seps = g.biconnectedComponents()
for bc1, bc2 in combinations(bcs, 2):
assert len(bc1 & bc2) < 2
assert not bc1.issubset(bc2)
assert not bc2.issubset(bc1)
rg = rgstack.pop(0)
# noinspection PyProtectedMember
rg._assertValidState()
rg_bcs, rg_seps = rg.biconnectedComponents()
assert _equalSetSets(bcs, rg_bcs)
assert seps == rg_seps
assert reduce(set.union, bcs) == verts
innerbcs = [bc - seps for bc in bcs]
assert sum(map(len, innerbcs)) + len(seps) == len(verts)
memberbcs = dict((v, set()) for v in verts)
for i, bc in enumerate(bcs):
for v in bc:
memberbcs[v].add(i)
parts = g.disjointPartitions()
assert _equalSetSets(parts, rg.disjointPartitions())
for part in parts:
for v in part:
assert rg.connectedComponent(v) == part
for v in verts:
novparts = g.disjointPartitions(verts - {v})
if g.isSeparator(v):
assert rg.isSeparator(v)
assert v in seps
assert len(memberbcs[v]) > 1
assert len(novparts) == len(parts) + len(memberbcs[v]) - 1
else:
assert not rg.isSeparator(v)
assert v not in seps
assert len(memberbcs[v]) == 1
if len(g.connectedComponent(v)) == 1:
assert len(novparts) == len(parts) - 1
else:
assert len(novparts) == len(parts)
for bc in bcs:
bcs_, seps_ = g.biconnectedComponents(bc)
assert len(bcs_) == 1
assert bcs_[0] == bc
assert not seps_
for v in bc:
assert bc.issubset(g.connectedComponent(v))
assert bc == g.connectedComponent(v, bc)
v = vertlist.pop(0)
verts.remove(v)
g.removeVertex(v)
def test_dijkstra():
graph = SimpleGraph([('a', 'b', 6), ('b', 'a', 5),
('a', 'g', 1), ('g', 'b', 1)])
assert graph.dijkstra('a') == {'a': 0, 'b': 2, 'g': 1}
def test_weighted_edges():
g = SimpleGraph()
g.add_edge('a', 'b', 5)
g.add_edge('a', 'c', 2)
g.add_edge('b', 'c', 1)
assert g.dict_graph['a'] == {'b': 5, 'c': 2}
if __name__ == '__main__':
from graph import SimpleGraph
parser = argparse.ArgumentParser(
description='Given site map, build a graph and find its diameter')
parser.add_argument('input',
metavar='FILE',
type=str,
default='sitemap.json',
help='input file name')
args = parser.parse_args()
logging.basicConfig(
level=logging.DEBUG,
datefmt='%Y-%m-%d %H:%M:%S',
format='%(asctime)s - %(levelname)-8s - %(message)s',
)
try:
g = SimpleGraph.from_json(args.input)
path = find_diameter(g)
if path:
d = (len(path) - 1)
print('Length: %d' % d)
print('\n-->'.join(path))
else:
print('Empty!')
except KeyboardInterrupt:
logging.warn('Interrupted.')
except Exception as ex:
logging.error(ex, exc_info=True)
def test_del_nodes():
"""nodes are deleted"""
g = SimpleGraph()
g.add_node('a')
g.add_node('b')
g.add_node('c')
g.add_edge('a', 'c')
g.add_edge('a', 'b')
g.del_node('a')
assert 'a' not in g.nodes()
assert g.has_node('a') is False