# test_matching.py - unit tests for bipartite matching algorithms
#
# Copyright 2015 Jeffrey Finkelstein <jeffrey.finkelstein@gmail.com>,
# Copyright 2019 Søren Fuglede Jørgensen
#
# This file is part of NetworkX.
#
# NetworkX is distributed under a BSD license; see LICENSE.txt for more
# information.
"""Unit tests for the :mod:`networkx.algorithms.bipartite.matching` module."""
import itertools

import networkx as nx

import pytest

from networkx.algorithms.bipartite.matching import eppstein_matching
from networkx.algorithms.bipartite.matching import hopcroft_karp_matching
from networkx.algorithms.bipartite.matching import maximum_matching
from networkx.algorithms.bipartite.matching import minimum_weight_full_matching
from networkx.algorithms.bipartite.matching import to_vertex_cover


class TestMatching():
    """Tests for bipartite matching algorithms."""

    def setup(self):
        """Creates a bipartite graph for use in testing matching algorithms.

        The bipartite graph has a maximum cardinality matching that leaves
        vertex 1 and vertex 10 unmatched. The first six numbers are the left
        vertices and the next six numbers are the right vertices.

        """
        self.simple_graph = nx.complete_bipartite_graph(2, 3)
        self.simple_solution = {0: 2, 1: 3, 2: 0, 3: 1}

        edges = [(0, 7), (0, 8), (2, 6), (2, 9), (3, 8), (4, 8), (4, 9),
                 (5, 11)]
        self.top_nodes = set(range(6))
        self.graph = nx.Graph()
        self.graph.add_nodes_from(range(12))
        self.graph.add_edges_from(edges)

        # Example bipartite graph from issue 2127
        G = nx.Graph()
        G.add_nodes_from([
            (1, 'C'), (1, 'B'), (0, 'G'), (1, 'F'),
            (1, 'E'), (0, 'C'), (1, 'D'), (1, 'I'),
            (0, 'A'), (0, 'D'), (0, 'F'), (0, 'E'),
            (0, 'H'), (1, 'G'), (1, 'A'), (0, 'I'),
            (0, 'B'), (1, 'H'),
        ])
        G.add_edge((1, 'C'), (0, 'A'))
        G.add_edge((1, 'B'), (0, 'A'))
        G.add_edge((0, 'G'), (1, 'I'))
        G.add_edge((0, 'G'), (1, 'H'))
        G.add_edge((1, 'F'), (0, 'A'))
        G.add_edge((1, 'F'), (0, 'C'))
        G.add_edge((1, 'F'), (0, 'E'))
        G.add_edge((1, 'E'), (0, 'A'))
        G.add_edge((1, 'E'), (0, 'C'))
        G.add_edge((0, 'C'), (1, 'D'))
        G.add_edge((0, 'C'), (1, 'I'))
        G.add_edge((0, 'C'), (1, 'G'))
        G.add_edge((0, 'C'), (1, 'H'))
        G.add_edge((1, 'D'), (0, 'A'))
        G.add_edge((1, 'I'), (0, 'A'))
        G.add_edge((1, 'I'), (0, 'E'))
        G.add_edge((0, 'A'), (1, 'G'))
        G.add_edge((0, 'A'), (1, 'H'))
        G.add_edge((0, 'E'), (1, 'G'))
        G.add_edge((0, 'E'), (1, 'H'))
        self.disconnected_graph = G

    def check_match(self, matching):
        """Asserts that the matching is what we expect from the bipartite graph
        constructed in the :meth:`setup` fixture.

        """
        # For the sake of brevity, rename `matching` to `M`.
        M = matching
        matched_vertices = frozenset(itertools.chain(*M.items()))
        # Assert that the maximum number of vertices (10) is matched.
        assert matched_vertices == frozenset(range(12)) - {1, 10}
        # Assert that no vertex appears in two edges, or in other words, that
        # the matching (u, v) and (v, u) both appear in the matching
        # dictionary.
        assert all(u == M[M[u]] for u in range(12) if u in M)

    def check_vertex_cover(self, vertices):
        """Asserts that the given set of vertices is the vertex cover we
        expected from the bipartite graph constructed in the :meth:`setup`
        fixture.

        """
        # By Konig's theorem, the number of edges in a maximum matching equals
        # the number of vertices in a minimum vertex cover.
        assert len(vertices) == 5
        # Assert that the set is truly a vertex cover.
        for (u, v) in self.graph.edges():
            assert u in vertices or v in vertices
        # TODO Assert that the vertices are the correct ones.

    def test_eppstein_matching(self):
        """Tests that David Eppstein's implementation of the Hopcroft--Karp
        algorithm produces a maximum cardinality matching.

        """
        self.check_match(eppstein_matching(self.graph, self.top_nodes))

    def test_hopcroft_karp_matching(self):
        """Tests that the Hopcroft--Karp algorithm produces a maximum
        cardinality matching in a bipartite graph.

        """
        self.check_match(hopcroft_karp_matching(self.graph, self.top_nodes))

    def test_to_vertex_cover(self):
        """Test for converting a maximum matching to a minimum vertex cover."""
        matching = maximum_matching(self.graph, self.top_nodes)
        vertex_cover = to_vertex_cover(self.graph, matching, self.top_nodes)
        self.check_vertex_cover(vertex_cover)

    def test_eppstein_matching_simple(self):
        match = eppstein_matching(self.simple_graph)
        assert match == self.simple_solution

    def test_hopcroft_karp_matching_simple(self):
        match = hopcroft_karp_matching(self.simple_graph)
        assert match == self.simple_solution

    def test_eppstein_matching_disconnected(self):
        with pytest.raises(nx.AmbiguousSolution):
            match = eppstein_matching(self.disconnected_graph)

    def test_hopcroft_karp_matching_disconnected(self):
        with pytest.raises(nx.AmbiguousSolution):
            match = hopcroft_karp_matching(self.disconnected_graph)

    def test_issue_2127(self):
        """Test from issue 2127"""
        # Build the example DAG
        G = nx.DiGraph()
        G.add_edge("A", "C")
        G.add_edge("A", "B")
        G.add_edge("C", "E")
        G.add_edge("C", "D")
        G.add_edge("E", "G")
        G.add_edge("E", "F")
        G.add_edge("G", "I")
        G.add_edge("G", "H")

        tc = nx.transitive_closure(G)
        btc = nx.Graph()

        # Create a bipartite graph based on the transitive closure of G
        for v in tc.nodes():
            btc.add_node((0, v))
            btc.add_node((1, v))

        for u, v in tc.edges():
            btc.add_edge((0, u), (1, v))

        top_nodes = {n for n in btc if n[0] == 0}
        matching = hopcroft_karp_matching(btc, top_nodes)
        vertex_cover = to_vertex_cover(btc, matching, top_nodes)
        independent_set = set(G) - {v for _, v in vertex_cover}
        assert {'B', 'D', 'F', 'I', 'H'} == independent_set

    def test_vertex_cover_issue_2384(self):
        G = nx.Graph([(0, 3), (1, 3), (1, 4), (2, 3)])
        matching = maximum_matching(G)
        vertex_cover = to_vertex_cover(G, matching)
        for u, v in G.edges():
            assert u in vertex_cover or v in vertex_cover

    def test_unorderable_nodes(self):
        a = object()
        b = object()
        c = object()
        d = object()
        e = object()
        G = nx.Graph([(a, d), (b, d), (b, e), (c, d)])
        matching = maximum_matching(G)
        vertex_cover = to_vertex_cover(G, matching)
        for u, v in G.edges():
            assert u in vertex_cover or v in vertex_cover


def test_eppstein_matching():
    """Test in accordance to issue #1927"""
    G = nx.Graph()
    G.add_nodes_from(['a', 2, 3, 4], bipartite=0)
    G.add_nodes_from([1, 'b', 'c'], bipartite=1)
    G.add_edges_from([('a', 1), ('a', 'b'), (2, 'b'),
                      (2, 'c'), (3, 'c'), (4, 1)])
    matching = eppstein_matching(G)
    assert len(matching) == len(maximum_matching(G))
    assert all(x in set(matching.keys()) for x in set(matching.values()))


class TestMinimumWeightFullMatching(object):

    @classmethod
    def setup_class(cls):
        global scipy
        scipy = pytest.importorskip('scipy')

    def test_minimum_weight_full_matching_square(self):
        G = nx.complete_bipartite_graph(3, 3)
        G.add_edge(0, 3, weight=400)
        G.add_edge(0, 4, weight=150)
        G.add_edge(0, 5, weight=400)
        G.add_edge(1, 3, weight=400)
        G.add_edge(1, 4, weight=450)
        G.add_edge(1, 5, weight=600)
        G.add_edge(2, 3, weight=300)
        G.add_edge(2, 4, weight=225)
        G.add_edge(2, 5, weight=300)
        matching = minimum_weight_full_matching(G)
        assert matching == {0: 4, 1: 3, 2: 5, 4: 0, 3: 1, 5: 2}

    def test_minimum_weight_full_matching_smaller_left(self):
        G = nx.complete_bipartite_graph(3, 4)
        G.add_edge(0, 3, weight=400)
        G.add_edge(0, 4, weight=150)
        G.add_edge(0, 5, weight=400)
        G.add_edge(0, 6, weight=1)
        G.add_edge(1, 3, weight=400)
        G.add_edge(1, 4, weight=450)
        G.add_edge(1, 5, weight=600)
        G.add_edge(1, 6, weight=2)
        G.add_edge(2, 3, weight=300)
        G.add_edge(2, 4, weight=225)
        G.add_edge(2, 5, weight=290)
        G.add_edge(2, 6, weight=3)
        matching = minimum_weight_full_matching(G)
        assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1}

    def test_minimum_weight_full_matching_smaller_top_nodes_right(self):
        G = nx.complete_bipartite_graph(3, 4)
        G.add_edge(0, 3, weight=400)
        G.add_edge(0, 4, weight=150)
        G.add_edge(0, 5, weight=400)
        G.add_edge(0, 6, weight=1)
        G.add_edge(1, 3, weight=400)
        G.add_edge(1, 4, weight=450)
        G.add_edge(1, 5, weight=600)
        G.add_edge(1, 6, weight=2)
        G.add_edge(2, 3, weight=300)
        G.add_edge(2, 4, weight=225)
        G.add_edge(2, 5, weight=290)
        G.add_edge(2, 6, weight=3)
        matching = minimum_weight_full_matching(G, top_nodes=[3, 4, 5, 6])
        assert matching == {0: 4, 1: 6, 2: 5, 4: 0, 5: 2, 6: 1}

    def test_minimum_weight_full_matching_smaller_right(self):
        G = nx.complete_bipartite_graph(4, 3)
        G.add_edge(0, 4, weight=400)
        G.add_edge(0, 5, weight=400)
        G.add_edge(0, 6, weight=300)
        G.add_edge(1, 4, weight=150)
        G.add_edge(1, 5, weight=450)
        G.add_edge(1, 6, weight=225)
        G.add_edge(2, 4, weight=400)
        G.add_edge(2, 5, weight=600)
        G.add_edge(2, 6, weight=290)
        G.add_edge(3, 4, weight=1)
        G.add_edge(3, 5, weight=2)
        G.add_edge(3, 6, weight=3)
        matching = minimum_weight_full_matching(G)
        assert matching == {1: 4, 2: 6, 3: 5, 4: 1, 5: 3, 6: 2}

    def test_minimum_weight_full_matching_negative_weights(self):
        G = nx.complete_bipartite_graph(2, 2)
        G.add_edge(0, 2, weight=-2)
        G.add_edge(0, 3, weight=0.2)
        G.add_edge(1, 2, weight=-2)
        G.add_edge(1, 3, weight=0.3)
        matching = minimum_weight_full_matching(G)
        assert matching == {0: 3, 1: 2, 2: 1, 3: 0}

    def test_minimum_weight_full_matching_different_weight_key(self):
        G = nx.complete_bipartite_graph(2, 2)
        G.add_edge(0, 2, mass=2)
        G.add_edge(0, 3, mass=0.2)
        G.add_edge(1, 2, mass=1)
        G.add_edge(1, 3, mass=2)
        matching = minimum_weight_full_matching(G, weight='mass')
        assert matching == {0: 3, 1: 2, 2: 1, 3: 0}

    def test_minimum_weight_full_matching_requires_complete_input(self):
        with pytest.raises(ValueError):
            G = nx.Graph()
            G.add_nodes_from([1, 2, 3, 4], bipartite=0)
            G.add_nodes_from(['a', 'b', 'c'], bipartite=1)
            G.add_edges_from([(1, 'a'), (1, 'b'), (2, 'b'),
                              (2, 'c'), (3, 'c'), (4, 'a')])
            minimum_weight_full_matching(G)