Vehicle-cpp/hkpc/software/networkx/algorithms/tests/test_matching.py

import math
from itertools import permutations

from pytest import raises

import networkx as nx
from networkx.algorithms.matching import matching_dict_to_set
from networkx.utils import edges_equal


class TestMaxWeightMatching:
    """Unit tests for the
    :func:`~networkx.algorithms.matching.max_weight_matching` function.

    """

    def test_trivial1(self):
        """Empty graph"""
        G = nx.Graph()
        assert nx.max_weight_matching(G) == set()
        assert nx.min_weight_matching(G) == set()

    def test_selfloop(self):
        G = nx.Graph()
        G.add_edge(0, 0, weight=100)
        assert nx.max_weight_matching(G) == set()
        assert nx.min_weight_matching(G) == set()

    def test_single_edge(self):
        G = nx.Graph()
        G.add_edge(0, 1)
        assert edges_equal(
            nx.max_weight_matching(G), matching_dict_to_set({0: 1, 1: 0})
        )
        assert edges_equal(
            nx.min_weight_matching(G), matching_dict_to_set({0: 1, 1: 0})
        )

    def test_two_path(self):
        G = nx.Graph()
        G.add_edge("one", "two", weight=10)
        G.add_edge("two", "three", weight=11)
        assert edges_equal(
            nx.max_weight_matching(G),
            matching_dict_to_set({"three": "two", "two": "three"}),
        )
        assert edges_equal(
            nx.min_weight_matching(G),
            matching_dict_to_set({"one": "two", "two": "one"}),
        )

    def test_path(self):
        G = nx.Graph()
        G.add_edge(1, 2, weight=5)
        G.add_edge(2, 3, weight=11)
        G.add_edge(3, 4, weight=5)
        assert edges_equal(
            nx.max_weight_matching(G), matching_dict_to_set({2: 3, 3: 2})
        )
        assert edges_equal(
            nx.max_weight_matching(G, 1), matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3})
        )
        assert edges_equal(
            nx.min_weight_matching(G), matching_dict_to_set({1: 2, 3: 4})
        )
        assert edges_equal(
            nx.min_weight_matching(G, 1), matching_dict_to_set({1: 2, 3: 4})
        )

    def test_square(self):
        G = nx.Graph()
        G.add_edge(1, 4, weight=2)
        G.add_edge(2, 3, weight=2)
        G.add_edge(1, 2, weight=1)
        G.add_edge(3, 4, weight=4)
        assert edges_equal(
            nx.max_weight_matching(G), matching_dict_to_set({1: 2, 3: 4})
        )
        assert edges_equal(
            nx.min_weight_matching(G), matching_dict_to_set({1: 4, 2: 3})
        )

    def test_edge_attribute_name(self):
        G = nx.Graph()
        G.add_edge("one", "two", weight=10, abcd=11)
        G.add_edge("two", "three", weight=11, abcd=10)
        assert edges_equal(
            nx.max_weight_matching(G, weight="abcd"),
            matching_dict_to_set({"one": "two", "two": "one"}),
        )
        assert edges_equal(
            nx.min_weight_matching(G, weight="abcd"),
            matching_dict_to_set({"three": "two"}),
        )

    def test_floating_point_weights(self):
        G = nx.Graph()
        G.add_edge(1, 2, weight=math.pi)
        G.add_edge(2, 3, weight=math.exp(1))
        G.add_edge(1, 3, weight=3.0)
        G.add_edge(1, 4, weight=math.sqrt(2.0))
        assert edges_equal(
            nx.max_weight_matching(G), matching_dict_to_set({1: 4, 2: 3, 3: 2, 4: 1})
        )
        assert edges_equal(
            nx.min_weight_matching(G), matching_dict_to_set({1: 4, 2: 3, 3: 2, 4: 1})
        )

    def test_negative_weights(self):
        G = nx.Graph()
        G.add_edge(1, 2, weight=2)
        G.add_edge(1, 3, weight=-2)
        G.add_edge(2, 3, weight=1)
        G.add_edge(2, 4, weight=-1)
        G.add_edge(3, 4, weight=-6)
        assert edges_equal(
            nx.max_weight_matching(G), matching_dict_to_set({1: 2, 2: 1})
        )
        assert edges_equal(
            nx.max_weight_matching(G, maxcardinality=True),
            matching_dict_to_set({1: 3, 2: 4, 3: 1, 4: 2}),
        )
        assert edges_equal(
            nx.min_weight_matching(G), matching_dict_to_set({1: 2, 3: 4})
        )

    def test_s_blossom(self):
        """Create S-blossom and use it for augmentation:"""
        G = nx.Graph()
        G.add_weighted_edges_from([(1, 2, 8), (1, 3, 9), (2, 3, 10), (3, 4, 7)])
        answer = matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3})
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

        G.add_weighted_edges_from([(1, 6, 5), (4, 5, 6)])
        answer = matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1})
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_s_t_blossom(self):
        """Create S-blossom, relabel as T-blossom, use for augmentation:"""
        G = nx.Graph()
        G.add_weighted_edges_from(
            [(1, 2, 9), (1, 3, 8), (2, 3, 10), (1, 4, 5), (4, 5, 4), (1, 6, 3)]
        )
        answer = matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1})
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

        G.add_edge(4, 5, weight=3)
        G.add_edge(1, 6, weight=4)
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

        G.remove_edge(1, 6)
        G.add_edge(3, 6, weight=4)
        answer = matching_dict_to_set({1: 2, 2: 1, 3: 6, 4: 5, 5: 4, 6: 3})
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_nested_s_blossom(self):
        """Create nested S-blossom, use for augmentation:"""

        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 9),
                (1, 3, 9),
                (2, 3, 10),
                (2, 4, 8),
                (3, 5, 8),
                (4, 5, 10),
                (5, 6, 6),
            ]
        )
        dict_format = {1: 3, 2: 4, 3: 1, 4: 2, 5: 6, 6: 5}
        expected = {frozenset(e) for e in matching_dict_to_set(dict_format)}
        answer = {frozenset(e) for e in nx.max_weight_matching(G)}
        assert answer == expected
        answer = {frozenset(e) for e in nx.min_weight_matching(G)}
        assert answer == expected

    def test_nested_s_blossom_relabel(self):
        """Create S-blossom, relabel as S, include in nested S-blossom:"""
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 10),
                (1, 7, 10),
                (2, 3, 12),
                (3, 4, 20),
                (3, 5, 20),
                (4, 5, 25),
                (5, 6, 10),
                (6, 7, 10),
                (7, 8, 8),
            ]
        )
        answer = matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3, 5: 6, 6: 5, 7: 8, 8: 7})
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_nested_s_blossom_expand(self):
        """Create nested S-blossom, augment, expand recursively:"""
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 8),
                (1, 3, 8),
                (2, 3, 10),
                (2, 4, 12),
                (3, 5, 12),
                (4, 5, 14),
                (4, 6, 12),
                (5, 7, 12),
                (6, 7, 14),
                (7, 8, 12),
            ]
        )
        answer = matching_dict_to_set({1: 2, 2: 1, 3: 5, 4: 6, 5: 3, 6: 4, 7: 8, 8: 7})
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_s_blossom_relabel_expand(self):
        """Create S-blossom, relabel as T, expand:"""
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 23),
                (1, 5, 22),
                (1, 6, 15),
                (2, 3, 25),
                (3, 4, 22),
                (4, 5, 25),
                (4, 8, 14),
                (5, 7, 13),
            ]
        )
        answer = matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4})
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_nested_s_blossom_relabel_expand(self):
        """Create nested S-blossom, relabel as T, expand:"""
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 19),
                (1, 3, 20),
                (1, 8, 8),
                (2, 3, 25),
                (2, 4, 18),
                (3, 5, 18),
                (4, 5, 13),
                (4, 7, 7),
                (5, 6, 7),
            ]
        )
        answer = matching_dict_to_set({1: 8, 2: 3, 3: 2, 4: 7, 5: 6, 6: 5, 7: 4, 8: 1})
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_nasty_blossom1(self):
        """Create blossom, relabel as T in more than one way, expand,
        augment:
        """
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 45),
                (1, 5, 45),
                (2, 3, 50),
                (3, 4, 45),
                (4, 5, 50),
                (1, 6, 30),
                (3, 9, 35),
                (4, 8, 35),
                (5, 7, 26),
                (9, 10, 5),
            ]
        )
        ansdict = {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9}
        answer = matching_dict_to_set(ansdict)
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_nasty_blossom2(self):
        """Again but slightly different:"""
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 45),
                (1, 5, 45),
                (2, 3, 50),
                (3, 4, 45),
                (4, 5, 50),
                (1, 6, 30),
                (3, 9, 35),
                (4, 8, 26),
                (5, 7, 40),
                (9, 10, 5),
            ]
        )
        ans = {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9}
        answer = matching_dict_to_set(ans)
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_nasty_blossom_least_slack(self):
        """Create blossom, relabel as T, expand such that a new
        least-slack S-to-free dge is produced, augment:
        """
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 45),
                (1, 5, 45),
                (2, 3, 50),
                (3, 4, 45),
                (4, 5, 50),
                (1, 6, 30),
                (3, 9, 35),
                (4, 8, 28),
                (5, 7, 26),
                (9, 10, 5),
            ]
        )
        ans = {1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4, 9: 10, 10: 9}
        answer = matching_dict_to_set(ans)
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_nasty_blossom_augmenting(self):
        """Create nested blossom, relabel as T in more than one way"""
        # expand outer blossom such that inner blossom ends up on an
        # augmenting path:
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 45),
                (1, 7, 45),
                (2, 3, 50),
                (3, 4, 45),
                (4, 5, 95),
                (4, 6, 94),
                (5, 6, 94),
                (6, 7, 50),
                (1, 8, 30),
                (3, 11, 35),
                (5, 9, 36),
                (7, 10, 26),
                (11, 12, 5),
            ]
        )
        ans = {
            1: 8,
            2: 3,
            3: 2,
            4: 6,
            5: 9,
            6: 4,
            7: 10,
            8: 1,
            9: 5,
            10: 7,
            11: 12,
            12: 11,
        }
        answer = matching_dict_to_set(ans)
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_nasty_blossom_expand_recursively(self):
        """Create nested S-blossom, relabel as S, expand recursively:"""
        G = nx.Graph()
        G.add_weighted_edges_from(
            [
                (1, 2, 40),
                (1, 3, 40),
                (2, 3, 60),
                (2, 4, 55),
                (3, 5, 55),
                (4, 5, 50),
                (1, 8, 15),
                (5, 7, 30),
                (7, 6, 10),
                (8, 10, 10),
                (4, 9, 30),
            ]
        )
        ans = {1: 2, 2: 1, 3: 5, 4: 9, 5: 3, 6: 7, 7: 6, 8: 10, 9: 4, 10: 8}
        answer = matching_dict_to_set(ans)
        assert edges_equal(nx.max_weight_matching(G), answer)
        assert edges_equal(nx.min_weight_matching(G), answer)

    def test_wrong_graph_type(self):
        error = nx.NetworkXNotImplemented
        raises(error, nx.max_weight_matching, nx.MultiGraph())
        raises(error, nx.max_weight_matching, nx.MultiDiGraph())
        raises(error, nx.max_weight_matching, nx.DiGraph())
        raises(error, nx.min_weight_matching, nx.DiGraph())


class TestIsMatching:
    """Unit tests for the
    :func:`~networkx.algorithms.matching.is_matching` function.

    """

    def test_dict(self):
        G = nx.path_graph(4)
        assert nx.is_matching(G, {0: 1, 1: 0, 2: 3, 3: 2})

    def test_empty_matching(self):
        G = nx.path_graph(4)
        assert nx.is_matching(G, set())

    def test_single_edge(self):
        G = nx.path_graph(4)
        assert nx.is_matching(G, {(1, 2)})

    def test_edge_order(self):
        G = nx.path_graph(4)
        assert nx.is_matching(G, {(0, 1), (2, 3)})
        assert nx.is_matching(G, {(1, 0), (2, 3)})
        assert nx.is_matching(G, {(0, 1), (3, 2)})
        assert nx.is_matching(G, {(1, 0), (3, 2)})

    def test_valid_matching(self):
        G = nx.path_graph(4)
        assert nx.is_matching(G, {(0, 1), (2, 3)})

    def test_invalid_input(self):
        error = nx.NetworkXError
        G = nx.path_graph(4)
        # edge to node not in G
        raises(error, nx.is_matching, G, {(0, 5), (2, 3)})
        # edge not a 2-tuple
        raises(error, nx.is_matching, G, {(0, 1, 2), (2, 3)})
        raises(error, nx.is_matching, G, {(0,), (2, 3)})

    def test_selfloops(self):
        error = nx.NetworkXError
        G = nx.path_graph(4)
        # selfloop for node not in G
        raises(error, nx.is_matching, G, {(5, 5), (2, 3)})
        # selfloop edge not in G
        assert not nx.is_matching(G, {(0, 0), (1, 2), (2, 3)})
        # selfloop edge in G
        G.add_edge(0, 0)
        assert not nx.is_matching(G, {(0, 0), (1, 2)})

    def test_invalid_matching(self):
        G = nx.path_graph(4)
        assert not nx.is_matching(G, {(0, 1), (1, 2), (2, 3)})

    def test_invalid_edge(self):
        G = nx.path_graph(4)
        assert not nx.is_matching(G, {(0, 3), (1, 2)})
        raises(nx.NetworkXError, nx.is_matching, G, {(0, 55)})

        G = nx.DiGraph(G.edges)
        assert nx.is_matching(G, {(0, 1)})
        assert not nx.is_matching(G, {(1, 0)})


class TestIsMaximalMatching:
    """Unit tests for the
    :func:`~networkx.algorithms.matching.is_maximal_matching` function.

    """

    def test_dict(self):
        G = nx.path_graph(4)
        assert nx.is_maximal_matching(G, {0: 1, 1: 0, 2: 3, 3: 2})

    def test_invalid_input(self):
        error = nx.NetworkXError
        G = nx.path_graph(4)
        # edge to node not in G
        raises(error, nx.is_maximal_matching, G, {(0, 5)})
        raises(error, nx.is_maximal_matching, G, {(5, 0)})
        # edge not a 2-tuple
        raises(error, nx.is_maximal_matching, G, {(0, 1, 2), (2, 3)})
        raises(error, nx.is_maximal_matching, G, {(0,), (2, 3)})

    def test_valid(self):
        G = nx.path_graph(4)
        assert nx.is_maximal_matching(G, {(0, 1), (2, 3)})

    def test_not_matching(self):
        G = nx.path_graph(4)
        assert not nx.is_maximal_matching(G, {(0, 1), (1, 2), (2, 3)})
        assert not nx.is_maximal_matching(G, {(0, 3)})
        G.add_edge(0, 0)
        assert not nx.is_maximal_matching(G, {(0, 0)})

    def test_not_maximal(self):
        G = nx.path_graph(4)
        assert not nx.is_maximal_matching(G, {(0, 1)})


class TestIsPerfectMatching:
    """Unit tests for the
    :func:`~networkx.algorithms.matching.is_perfect_matching` function.

    """

    def test_dict(self):
        G = nx.path_graph(4)
        assert nx.is_perfect_matching(G, {0: 1, 1: 0, 2: 3, 3: 2})

    def test_valid(self):
        G = nx.path_graph(4)
        assert nx.is_perfect_matching(G, {(0, 1), (2, 3)})

    def test_valid_not_path(self):
        G = nx.cycle_graph(4)
        G.add_edge(0, 4)
        G.add_edge(1, 4)
        G.add_edge(5, 2)

        assert nx.is_perfect_matching(G, {(1, 4), (0, 3), (5, 2)})

    def test_invalid_input(self):
        error = nx.NetworkXError
        G = nx.path_graph(4)
        # edge to node not in G
        raises(error, nx.is_perfect_matching, G, {(0, 5)})
        raises(error, nx.is_perfect_matching, G, {(5, 0)})
        # edge not a 2-tuple
        raises(error, nx.is_perfect_matching, G, {(0, 1, 2), (2, 3)})
        raises(error, nx.is_perfect_matching, G, {(0,), (2, 3)})

    def test_selfloops(self):
        error = nx.NetworkXError
        G = nx.path_graph(4)
        # selfloop for node not in G
        raises(error, nx.is_perfect_matching, G, {(5, 5), (2, 3)})
        # selfloop edge not in G
        assert not nx.is_perfect_matching(G, {(0, 0), (1, 2), (2, 3)})
        # selfloop edge in G
        G.add_edge(0, 0)
        assert not nx.is_perfect_matching(G, {(0, 0), (1, 2)})

    def test_not_matching(self):
        G = nx.path_graph(4)
        assert not nx.is_perfect_matching(G, {(0, 3)})
        assert not nx.is_perfect_matching(G, {(0, 1), (1, 2), (2, 3)})

    def test_maximal_but_not_perfect(self):
        G = nx.cycle_graph(4)
        G.add_edge(0, 4)
        G.add_edge(1, 4)

        assert not nx.is_perfect_matching(G, {(1, 4), (0, 3)})


class TestMaximalMatching:
    """Unit tests for the
    :func:`~networkx.algorithms.matching.maximal_matching`.

    """

    def test_valid_matching(self):
        edges = [(1, 2), (1, 5), (2, 3), (2, 5), (3, 4), (3, 6), (5, 6)]
        G = nx.Graph(edges)
        matching = nx.maximal_matching(G)
        assert nx.is_maximal_matching(G, matching)

    def test_single_edge_matching(self):
        # In the star graph, any maximal matching has just one edge.
        G = nx.star_graph(5)
        matching = nx.maximal_matching(G)
        assert 1 == len(matching)
        assert nx.is_maximal_matching(G, matching)

    def test_self_loops(self):
        # Create the path graph with two self-loops.
        G = nx.path_graph(3)
        G.add_edges_from([(0, 0), (1, 1)])
        matching = nx.maximal_matching(G)
        assert len(matching) == 1
        # The matching should never include self-loops.
        assert not any(u == v for u, v in matching)
        assert nx.is_maximal_matching(G, matching)

    def test_ordering(self):
        """Tests that a maximal matching is computed correctly
        regardless of the order in which nodes are added to the graph.

        """
        for nodes in permutations(range(3)):
            G = nx.Graph()
            G.add_nodes_from(nodes)
            G.add_edges_from([(0, 1), (0, 2)])
            matching = nx.maximal_matching(G)
            assert len(matching) == 1
            assert nx.is_maximal_matching(G, matching)

    def test_wrong_graph_type(self):
        error = nx.NetworkXNotImplemented
        raises(error, nx.maximal_matching, nx.MultiGraph())
        raises(error, nx.maximal_matching, nx.MultiDiGraph())
        raises(error, nx.maximal_matching, nx.DiGraph())