from itertools import permutations
import math

from nose.tools import assert_equal
from nose.tools import assert_false
from nose.tools import assert_true
import networkx as nx
from networkx.algorithms.matching import matching_dict_to_set
from networkx.testing import assert_edges_equal


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

    """

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

    def test_trivial2(self):
        """Self loop"""
        G = nx.Graph()
        G.add_edge(0, 0, weight=100)
        assert_equal(nx.max_weight_matching(G), set())

    def test_trivial3(self):
        """Single edge"""
        G = nx.Graph()
        G.add_edge(0, 1)
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({0: 1, 1: 0}))

    def test_trivial4(self):
        """Small graph"""
        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'}))

    def test_trivial5(self):
        """Path"""
        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}))

    def test_trivial6(self):
        """Small graph with arbitrary weight attribute"""
        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'}))

    def test_floating_point_weights(self):
        """Floating point weights"""
        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}))

    def test_negative_weights(self):
        """Negative weights"""
        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, 1),
                           matching_dict_to_set({1: 3, 2: 4, 3: 1, 4: 2}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3}))

        G.add_weighted_edges_from([(1, 6, 5), (4, 5, 6)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}))
        G.add_edge(4, 5, weight=3)
        G.add_edge(1, 6, weight=4)
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 5, 5: 4, 6: 1}))
        G.remove_edge(1, 6)
        G.add_edge(3, 6, weight=4)
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 2, 2: 1, 3: 6, 4: 5, 5: 4, 6: 3}))

    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)])
        assert_equal(nx.max_weight_matching(G),
                     matching_dict_to_set({1: 3, 2: 4, 3: 1, 4: 2, 5: 6, 6: 5}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 2, 2: 1, 3: 4, 4: 3, 5: 6, 6: 5, 7: 8, 8: 7}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 2, 2: 1, 3: 5, 4: 6, 5: 3, 6: 4, 7: 8, 8: 7}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7, 6: 1, 7: 5, 8: 4}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 8, 2: 3, 3: 2, 4: 7, 5: 6, 6: 5, 7: 4, 8: 1}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
                                                 6: 1, 7: 5, 8: 4, 9: 10, 10: 9}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
                                                 6: 1, 7: 5, 8: 4, 9: 10, 10: 9}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 6, 2: 3, 3: 2, 4: 8, 5: 7,
                                                 6: 1, 7: 5, 8: 4, 9: 10, 10: 9}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 8, 2: 3, 3: 2, 4: 6, 5: 9, 6: 4,
                                                 7: 10, 8: 1, 9: 5, 10: 7, 11: 12, 12: 11}))

    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)])
        assert_edges_equal(nx.max_weight_matching(G),
                           matching_dict_to_set({1: 2, 2: 1, 3: 5, 4: 9, 5: 3,
                                                 6: 7, 7: 6, 8: 10, 9: 4, 10: 8}))


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

    """

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

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

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

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

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

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


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

    """

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

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

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

    def test_not_maximal(self):
        G = nx.path_graph(4)
        assert_false(nx.is_maximal_matching(G, {(0, 1)}))


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

    """

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

    def test_valid(self):
        G = nx.path_graph(4)
        assert_true(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_true(nx.is_perfect_matching(G, {(1, 4), (0, 3), (5, 2)}))

    def test_not_matching(self):
        G = nx.path_graph(4)
        assert_false(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_false(nx.is_perfect_matching(G, {(1, 4), (0, 3)}))


class TestMaximalMatching(object):
    """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_true(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_equal(1, len(matching))
        assert_true(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_equal(len(matching), 1)
        # The matching should never include self-loops.
        assert_false(any(u == v for u, v in matching))
        assert_true(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_equal(len(matching), 1)
            assert_true(nx.is_maximal_matching(G, matching))