def test_component_list(self):
g = SimpleGraph()
g.from_graph_sequence([4, 3, 3, 2, 2, 1, 1])
comps = g.component_list()
assert [1, 2, 3, 4, 5] in comps.values()
assert [6, 7] in comps.values()
def find_shortest_path_dijkstra(
g: SimpleGraph,
source: Node) -> Tuple[Dict[int, float], Dict[int, int]]:
""" Przyjmuje graf i zrodlo (wierzcholek).
Zwraca:
- slownik odleglosci od zrodla
- slownik poprzednikow
"""
predecessors = {}
distance = {}
# kolejka priorytetowa dla wierzchołkow grafu (klucz: aktualnie wyliczona odleglosc)
Q = []
for node in g.nodes:
distance[node] = float("inf")
predecessors[node] = None
Q.append(node)
distance[source] = 0
while Q:
Q.sort(key=lambda n: distance[n])
u = Q.pop(0)
for v in g.node_neighbours(u):
if v in Q:
new_distance = distance[u] + g.edge_to_node(u, v).weight
old_distance = distance[v]
if new_distance < old_distance:
distance[v] = new_distance
predecessors[v] = u
d = {node: distance[node] for node in g.nodes}
p = {node: predecessors[node] for node in g.nodes}
return d, p
def test_components(self):
g = SimpleGraph()
g.from_graph_sequence([4, 3, 3, 2, 2, 1, 1])
comps = g.components()
assert comps[1] == comps[2] == comps[3] == comps[4] == comps[5]
assert comps[6] == comps[7]
assert comps[1] != comps[6]
def example05():
g = SimpleGraph().from_coordinates("input.dat")
P = None
for MAX_IT in range(10, 150, 5):
P = simulated_annealing(g, MAX_IT, save=True, P=P)
length = circuit_length(g.to_adjacency_matrix(), P)
with open("P_5.tmp", "a") as f:
f.write(f"{length:.3f}, {P}\n")
def example01():
"""Ciąg graficzny"""
print(is_valid_graph_sequence([4, 3, 3, 2, 2, 1, 1]))
print(is_valid_graph_sequence([4, 3, 3, 2, 2, 1]))
print(is_valid_graph_sequence([4, 4, 3, 1, 2]))
g = SimpleGraph().from_graph_sequence([4, 3, 3, 2, 2, 1, 1])
g.save(filename="graph1", file_format="png")
def example07():
g = SimpleGraph().from_coordinates("input.dat")
P = None
for _ in range(100):
P = simulated_annealing(g, MAX_IT=100, save=True, P=P)
length = circuit_length(g.to_adjacency_matrix(), P)
print(length)
with open("P.dat", "a") as f:
f.write(f"{length:.3f}, {P}\n")
def test_save_to_file_and_load(self):
g = SimpleGraph(8)
g.add_random_edges(15)
before = g.to_adjacency_list()
g.save("test", "al")
g.load("test.al")
after = g.to_adjacency_list()
assert before == after
def test_incidence_matrix_file(self):
g = SimpleGraph(8)
g.add_random_edges(15)
before = g.to_adjacency_matrix()
g.save("test", "im")
g.load("test.im")
after = g.to_adjacency_matrix()
assert before == after
def get_k_regular_graph(size, k, connected=False) -> SimpleGraph:
"""Graf z wierzchołkami o tym samym stopniu"""
seq = [k for _ in range(size)]
g = SimpleGraph().from_graph_sequence(seq)
if connected:
if k < 2 and size != 2:
raise ValueError("Nie da się stworzyć zadanego grafu.")
while True:
if g.is_connected_graph():
break
g.randomize(size)
return g
def test_incidence_matrix(self):
g = SimpleGraph(8)
g.add_random_edges(15)
before = g.to_adjacency_list()
g.from_incidence_matrix(g.to_incidence_matrix())
after = g.to_adjacency_list()
assert before == after
def load_graph_to_work_on(args):
g = SimpleGraph()
if args.load:
g.load(args.load)
elif args.n:
g.add_nodes(int(args.n))
if args.l:
g.add_random_edges(int(args.l))
elif args.p:
g.connect_random(float(args.p))
return g
def simulated_annealing(g: SimpleGraph,
MAX_IT=None,
P: List[int] = None,
save=False):
if not g.is_complete():
return ValueError("Do tego algorytmu graf musi być pełny.")
if P is None:
P = [n for n in range(1, len(g) + 1)]
random.shuffle(P)
if MAX_IT is None:
MAX_IT = len(g)
adj_m = g.to_adjacency_matrix()
d = circuit_length(adj_m, P)
for i in range(100, 0, -1):
T = 0.001 * i**2
for _ in range(MAX_IT):
# switch: a-b c-d --> a-c b-d
_, b, c, _ = _choose_nodes(P)
P[b], P[c] = P[c], P[b]
d_new = circuit_length(adj_m, P)
if d_new < d:
d = d_new
else:
r = random.random()
if r < math.exp(-(d_new - d) / T):
d = d_new
else:
# switch back
P[b], P[c] = P[c], P[b]
if save:
x = [g.x[n - 1] for n in P]
y = [g.y[n - 1] for n in P]
# connect first and last point
x.append(g.x[P[0] - 1])
y.append(g.y[P[0] - 1])
plt.plot(x, y, "-o")
plt.title(f"MAX_IT={MAX_IT}, d={d:.3f}")
plt.xlabel("x")
plt.ylabel("y")
plt.savefig("SA.png")
plt.clf()
return P
def test_is_connected_graph(self):
g = SimpleGraph(4)
g.connect(1, 2)
g.connect(3, 4)
assert not g.is_connected_graph()
g.connect(2, 3)
assert g.is_connected_graph()
def test_add_random_edges(self):
g = SimpleGraph(8) # 8 vertices => max 28 edges
g.add_random_edges(8)
assert len(g.edges) == 8
g.add_random_edges(20)
assert len(g.edges) == 28
with pytest.raises(ValueError):
g.add_random_edges(1)
def test_adjacency_matrix(self):
g = SimpleGraph(8)
g.add_random_edges(15)
before = g.to_adjacency_matrix()
g.from_adjacency_matrix(before)
after = g.to_adjacency_matrix()
assert before == after
def find_hamiltonian_circuit(g: SimpleGraph) -> List[Node]:
"""Znajduje losowy cykl Hamiltona w grafie"""
g = copy.deepcopy(g)
if not g.is_connected_graph():
raise ValueError(f"Graf nie jest spójny:\n{g}")
stack = [random.choice(tuple(g.nodes))]
solution = hamilton_search_r(g, stack)
return solution
def hamilton_search_r(g: SimpleGraph, stack: List[Node]) -> List[Node]:
# Zawiera wszystkie wierzcholki
if set(stack) == g.nodes:
# Istnieje połączenie między pierwszym a ostatnim
if g.is_connected(stack[0], stack[-1]):
return stack
else:
stack.pop
return []
else:
for neighbour in g.node_neighbours(stack[-1]):
if neighbour in stack:
continue
stack.append(neighbour)
if hamilton_search_r(g, stack):
return stack
raise ValueError(f"Graf nie jest Hamiltonowski:\n{g}")
def get_eulerian_graph(size: int = None) -> SimpleGraph:
"""Losowy graf Eulerowski"""
if size is None:
size = random.randint(2, 16)
while True:
seq = []
for d in range(size):
d = random.randint(2, size - 1)
seq.append(d - d % 2)
if is_valid_graph_sequence(seq):
break
g = SimpleGraph().from_graph_sequence(seq)
while True:
if g.is_connected_graph():
break
g.randomize(size)
return g
def find_eulerian_trail(g: SimpleGraph) -> List[Node]:
"""Znajduje losowy cykl Eulera w grafie"""
if not g.is_eulerian():
raise ValueError(f"Nie jest to graf Eulerowski\n{g}")
solution = []
stack = [random.choice(tuple(g.nodes))]
while len(stack) != 0:
current_vertex = stack[-1]
if g.node_degree(current_vertex) == 0:
solution.append(current_vertex)
stack.pop()
else:
next_vertex = random.choice(tuple(
g.node_edges(current_vertex))).end
g.disconnect(current_vertex, next_vertex)
stack.append(next_vertex)
return solution
def test_connect(self):
g = SimpleGraph(8)
n1 = 1
n2 = 2
g.connect(n1, n2)
assert g.is_connected(n1, n2)
assert g.is_connected(n2, n1)
g.disconnect(n1, n2)
assert not g.is_connected(n1, n2)
assert not g.is_connected(n2, n1)
def get_minimum_spanning_tree_kruskal(g: SimpleGraph) -> SimpleGraph:
"""
Przyjmuje graf
Zwraca jego minimalne drzewo rozpinające
Korzysta z algorytmu kruskala
"""
# minimum spanning tree
mst = SimpleGraph(len(g))
Q = []
for edge in g.edges:
Q.append(edge)
while Q and not mst.is_connected_graph():
Q.sort(key=lambda e: e.weight)
current_edge = Q.pop(0)
comps = mst.components()
if comps[current_edge.begin] != comps[current_edge.end]:
mst.edges.add(current_edge)
return mst
def get_random_2D_graph(
size=20, x_min=-50, x_max=50, y_min=-50, y_max=50
) -> SimpleGraph:
filename = f"{size}_coordinates.tmp"
with open(filename, "w") as f:
for _ in range(size):
x = random.randint(x_min, x_max)
y = random.randint(y_min, y_max)
f.write(f"{x} {y}\n")
g = SimpleGraph().from_coordinates(filename)
return g
def test_from_graph_sequence(self):
g = SimpleGraph()
g.from_graph_sequence([4, 3, 3, 2, 2, 1, 1])
assert g.to_adjacency_list() == {
1: {2, 3, 4, 5},
2: {1, 3, 4},
3: {1, 2, 5},
4: {1, 2},
5: {1, 3},
6: {7},
7: {6},
}
assert g.graph_sequence() == [4, 3, 3, 2, 2, 1, 1]
with pytest.raises(ValueError):
g.from_graph_sequence([4, 3, 3, 2, 2, 1])
def example03():
"""Największa wspólna składowa"""
g = SimpleGraph().from_graph_sequence([4, 3, 3, 2, 2, 1, 1])
g.save(filename="graph3", file_format="png", color_components=True)
pprint(g.component_list())
print(f"Największa składowa: {g.largest_component()}")
def example02():
"""Randomizacja"""
g = SimpleGraph().from_graph_sequence([4, 3, 3, 2, 2, 1, 1])
g.save(filename="graph2_before", file_format="png")
g.randomize(100)
g.save(filename="graph2_after", file_format="png")
def test_breadth_first_search(self, graph, source, target, trail):
g = SimpleGraph().from_adjacency_list(graph)
tr = get_trail_to_node(breadth_first_search(g, source, target), target)
assert tr == trail
def test_minimax_get_graph_center(self, graph, minimax_center):
g = SimpleGraph().from_adjacency_matrix(graph)
assert get_minimax_graph_center(g) == minimax_center
def get_random_graph(max_size=20) -> SimpleGraph:
size = random.randint(2, max_size)
g = SimpleGraph(size)
g.connect_random(random.random())
return g
def load_graph_to_work_on(args):
g = SimpleGraph()
if args.load:
g.load(args.load)
elif args.n:
g.add_nodes(int(args.n))
if args.l:
g.add_random_edges(int(args.l))
elif args.p:
g.connect_random(float(args.p))
if args.w is not None:
if args.w[0]:
g.assign_random_weights(int(args.w[0][0]), int(args.w[0][1]))
else:
g.assign_random_weights()
return g