def test_floyd_warshall_undirected_negative_weight_cycle(self) -> None:
g = MultiGraph([
("s", "t", 10),
("s", "y", 5),
("t", "y", -6),
("t", "x", 1),
("x", "z", 4),
("y", "t", 8),
("y", "x", 4),
("y", "z", 3),
("z", "s", 7),
("z", "x", 6),
])
with pytest.raises(NegativeWeightCycle):
floyd_warshall(g)
def test_floyd_warshall_negative_edge_weights(self) -> None:
g = DiGraph([
("s", "t", 10),
("s", "y", 5),
("t", "y", -6),
("t", "x", 1),
("x", "z", 4),
("y", "t", 8),
("y", "x", 4),
("y", "z", -3),
("z", "s", 7),
("z", "x", 6),
("a", "s", -100),
])
all_paths_dict: VertexDict[VertexDict[
ShortestPath[DiVertex]]] = floyd_warshall(g)
assert (len(all_paths_dict) == 6
), "all_paths_dict dictionary should have length equal to |V|."
assert len(all_paths_dict["s"]) == 6, (
"Each source in the shortest all_paths_dict dictionary should have "
"a destinations dictionary of length equal to |V|.")
assert all_paths_dict["a"][
"s"].length == -100, "Length of path a ~> s should be -100."
assert all_paths_dict["a"][
"t"].length == -90, "Length of path a ~> t should be -90."
assert (all_paths_dict["s"]["a"].length == INFINITY
), "Length of path s ~> a should be infinity."
assert (all_paths_dict["z"]["a"].length == INFINITY
), "Length of path z ~> a should be infinity."
assert not all_paths_dict["s"]["a"].is_destination_reachable(
), "'a' should not be reachable from 's'."
assert all_paths_dict["s"][
"s"].length == 0, "length of s path should be 0"
assert all_paths_dict["s"][
"t"].length == 10, "length of path s ~> t should be 10"
assert all_paths_dict["s"][
"x"].length == 7, "length of path s ~> x should be 7"
assert all_paths_dict["s"][
"y"].length == 4, "length of path s ~> y should be 4"
assert all_paths_dict["s"][
"z"].length == 1, "length of path s ~> z should be 1"
assert all_paths_dict["z"][
"s"].length == 7, "length of path z ~> s should be 7"
assert all_paths_dict["z"][
"t"].length == 17, "length of path z ~> t should be 17"
assert all_paths_dict["z"][
"x"].length == 6, "length of path z ~> x should be 6"
assert all_paths_dict["z"][
"y"].length == 11, "length of path z ~> y should be 11"
assert all_paths_dict["z"][
"z"].length == 0, "length of path z ~> z should be 0"
def test_floyd_warshall_path_reconstruction(self) -> None:
g = DiGraph([
("s", "t", 10),
("s", "y", 5),
("t", "y", 2),
("t", "x", 1),
("x", "z", 4),
("y", "t", 3),
("y", "x", 9),
("y", "z", 2),
("z", "s", 7),
("z", "x", 6),
("a", "s", -100),
])
all_paths_dict: VertexDict[VertexDict[
ShortestPath[DiVertex]]] = floyd_warshall(g, save_paths=True)
assert all_paths_dict["s"]["z"].path() == ["s", "y", "z"]
assert all_paths_dict["y"]["s"].path() == ["y", "z", "s"]
assert all_paths_dict["y"]["t"].path() == [
"y", "t"
], "path y ~> t should be [y, t]"
assert all_paths_dict["y"]["x"].path() == ["y", "t", "x"]
assert all_paths_dict["y"]["y"].path() == [
"y"
], "path y ~> y should be [y]"
assert all_paths_dict["y"]["z"].path() == [
"y", "z"
], "path y ~> z should be [y, z]"
assert all_paths_dict["y"]["a"].path(
) == [], "path y ~> a should be []"
path_s_z = reconstruct_path("s", "z", all_paths_dict)
assert path_s_z == all_paths_dict["s"]["z"].path()
path_y_s = reconstruct_path("y", "s", all_paths_dict)
assert path_y_s == all_paths_dict["y"]["s"].path()
path_y_t = reconstruct_path("y", "t", all_paths_dict)
assert path_y_t == all_paths_dict["y"]["t"].path()
path_y_x = reconstruct_path("y", "x", all_paths_dict)
assert path_y_x == all_paths_dict["y"]["x"].path()
path_y_y = reconstruct_path("y", "y", all_paths_dict)
assert path_y_y == all_paths_dict["y"]["y"].path()
path_y_z = reconstruct_path("y", "z", all_paths_dict)
assert path_y_z == all_paths_dict["y"]["z"].path()
path_y_a = reconstruct_path("y", "a", all_paths_dict)
assert path_y_a == all_paths_dict["y"]["a"].path()
def test_floyd_warshall_positive_edge_weights(self) -> None:
g = DiGraph([
("s", "t", 10),
("s", "y", 5),
("t", "y", 2),
("t", "x", 1),
("x", "z", 4),
("y", "t", 3),
("y", "x", 9),
("y", "z", 2),
("z", "s", 7),
("z", "x", 6),
])
all_paths_dict: VertexDict[VertexDict[
ShortestPath[DiVertex]]] = floyd_warshall(g)
assert len(
all_paths_dict
) == 5, "all_paths_dict dictionary should have length equal to |V|"
assert len(all_paths_dict["s"]) == 5, (
"Each source in the shortest all_paths_dict dictionary should have "
"a destinations dictionary of length equal to |V|.")
assert all_paths_dict["s"][
"s"].length == 0, "length of s ~> s path should be 0"
assert all_paths_dict["s"][
"t"].length == 8, "length of path s ~> t should be 8"
assert all_paths_dict["s"][
"x"].length == 9, "length of path s ~> x should be 9"
assert all_paths_dict["s"][
"y"].length == 5, "length of path s ~> y should be 5"
assert all_paths_dict["s"][
"z"].length == 7, "length of path s ~> z should be 7"
assert all_paths_dict["y"][
"t"].length == 3, "length of path y ~> t should be 3"
assert all_paths_dict["y"][
"x"].length == 4, "length of path y ~> x should be 4"
assert all_paths_dict["y"][
"s"].length == 9, "length of path y ~> s should be 9"
assert all_paths_dict["y"][
"z"].length == 2, "length of path y ~> z should be 2"
def test_floyd_warshall_undirected(self) -> None:
g = MultiGraph([
("s", "t", 10),
("s", "y", 5),
("t", "y", 6),
("t", "x", 1),
("x", "z", 4),
("y", "t", 8),
("y", "x", 4),
("y", "z", 3),
("z", "s", 7),
("z", "x", 6),
])
all_paths_dict: VertexDict[VertexDict[
ShortestPath[MultiVertex]]] = floyd_warshall(g)
assert (len(all_paths_dict) == 5
), "all_paths_dict dictionary should have length equal to |V|."
assert all_paths_dict["s"][
"s"].length == 0, "length of path s ~> s should be 0"
assert all_paths_dict["s"][
"t"].length == 10, "length of path s ~> t should be 10"
assert all_paths_dict["s"][
"x"].length == 9, "length of path s ~> x should be 9"
assert all_paths_dict["s"][
"y"].length == 5, "length of path s ~> y should be 5"
assert all_paths_dict["s"][
"z"].length == 7, "length of path s ~> z should be 7"
assert all_paths_dict["x"][
"s"].length == 9, "length of path x ~> s should be 9"
assert all_paths_dict["x"][
"t"].length == 1, "length of path x ~> t should be 1"
assert all_paths_dict["x"][
"x"].length == 0, "length of path x ~> x should be 0"
assert all_paths_dict["x"][
"y"].length == 4, "length of path x ~> y should be 5"
assert all_paths_dict["x"][
"z"].length == 4, "length of path x ~> z should be 7"
def test_floyd_warshall_save_paths(self) -> None:
g = DiGraph([
("s", "t", 10),
("s", "y", 5),
("t", "y", 2),
("t", "x", 1),
("x", "z", 4),
("y", "t", 3),
("y", "x", 9),
("y", "z", 2),
("z", "s", 7),
("z", "x", 6),
])
all_paths_dict: VertexDict[VertexDict[
ShortestPath[DiVertex]]] = floyd_warshall(g, save_paths=False)
assert all_paths_dict["s"]["z"].path() == []
assert all_paths_dict["y"]["s"].path() == []
assert all_paths_dict["y"]["t"].path() == []
assert all_paths_dict["y"]["x"].path() == []
assert all_paths_dict["y"]["y"].path() == []
assert all_paths_dict["y"]["z"].path() == []