# Jordi Torrents
# Test for k-cutsets
from operator import itemgetter
from nose.tools import assert_equal, assert_false, assert_true, assert_raises

import networkx as nx
from networkx.algorithms import flow
from networkx.algorithms.connectivity.kcutsets import _is_separating_set


flow_funcs = [
    flow.boykov_kolmogorov,
    flow.dinitz,
    flow.edmonds_karp,
    flow.preflow_push,
    flow.shortest_augmenting_path,
]


##
# Some nice synthetic graphs
##
def graph_example_1():
    G = nx.convert_node_labels_to_integers(nx.grid_graph([5, 5]),
                                           label_attribute='labels')
    rlabels = nx.get_node_attributes(G, 'labels')
    labels = dict((v, k) for k, v in rlabels.items())

    for nodes in [(labels[(0, 0)], labels[(1, 0)]),
                  (labels[(0, 4)], labels[(1, 4)]),
                  (labels[(3, 0)], labels[(4, 0)]),
                  (labels[(3, 4)], labels[(4, 4)])]:
        new_node = G.order() + 1
        # Petersen graph is triconnected
        P = nx.petersen_graph()
        G = nx.disjoint_union(G, P)
        # Add two edges between the grid and P
        G.add_edge(new_node + 1, nodes[0])
        G.add_edge(new_node, nodes[1])
        # K5 is 4-connected
        K = nx.complete_graph(5)
        G = nx.disjoint_union(G, K)
        # Add three edges between P and K5
        G.add_edge(new_node + 2, new_node + 11)
        G.add_edge(new_node + 3, new_node + 12)
        G.add_edge(new_node + 4, new_node + 13)
        # Add another K5 sharing a node
        G = nx.disjoint_union(G, K)
        nbrs = G[new_node + 10]
        G.remove_node(new_node + 10)
        for nbr in nbrs:
            G.add_edge(new_node + 17, nbr)
        G.add_edge(new_node + 16, new_node + 5)

    G.name = 'Example graph for connectivity'
    return G


def torrents_and_ferraro_graph():
    G = nx.convert_node_labels_to_integers(nx.grid_graph([5, 5]),
                                           label_attribute='labels')
    rlabels = nx.get_node_attributes(G, 'labels')
    labels = dict((v, k) for k, v in rlabels.items())

    for nodes in [(labels[(0, 4)], labels[(1, 4)]),
                  (labels[(3, 4)], labels[(4, 4)])]:
        new_node = G.order() + 1
        # Petersen graph is triconnected
        P = nx.petersen_graph()
        G = nx.disjoint_union(G, P)
        # Add two edges between the grid and P
        G.add_edge(new_node + 1, nodes[0])
        G.add_edge(new_node, nodes[1])
        # K5 is 4-connected
        K = nx.complete_graph(5)
        G = nx.disjoint_union(G, K)
        # Add three edges between P and K5
        G.add_edge(new_node + 2, new_node + 11)
        G.add_edge(new_node + 3, new_node + 12)
        G.add_edge(new_node + 4, new_node + 13)
        # Add another K5 sharing a node
        G = nx.disjoint_union(G, K)
        nbrs = G[new_node + 10]
        G.remove_node(new_node + 10)
        for nbr in nbrs:
            G.add_edge(new_node + 17, nbr)
        # Commenting this makes the graph not biconnected !!
        # This stupid mistake make one reviewer very angry :P
        G.add_edge(new_node + 16, new_node + 8)

    for nodes in [(labels[(0, 0)], labels[(1, 0)]),
                  (labels[(3, 0)], labels[(4, 0)])]:
        new_node = G.order() + 1
        # Petersen graph is triconnected
        P = nx.petersen_graph()
        G = nx.disjoint_union(G, P)
        # Add two edges between the grid and P
        G.add_edge(new_node + 1, nodes[0])
        G.add_edge(new_node, nodes[1])
        # K5 is 4-connected
        K = nx.complete_graph(5)
        G = nx.disjoint_union(G, K)
        # Add three edges between P and K5
        G.add_edge(new_node + 2, new_node + 11)
        G.add_edge(new_node + 3, new_node + 12)
        G.add_edge(new_node + 4, new_node + 13)
        # Add another K5 sharing two nodes
        G = nx.disjoint_union(G, K)
        nbrs = G[new_node + 10]
        G.remove_node(new_node + 10)
        for nbr in nbrs:
            G.add_edge(new_node + 17, nbr)
        nbrs2 = G[new_node + 9]
        G.remove_node(new_node + 9)
        for nbr in nbrs2:
            G.add_edge(new_node + 18, nbr)

    G.name = 'Example graph for connectivity'
    return G


# Helper function
def _check_separating_sets(G):
    for Gc in nx.connected_component_subgraphs(G):
        if len(Gc) < 3:
            continue
        node_conn = nx.node_connectivity(Gc)
        for cut in nx.all_node_cuts(Gc):
            assert_equal(node_conn, len(cut))
            H = Gc.copy()
            H.remove_nodes_from(cut)
            assert_false(nx.is_connected(H))


def test_torrents_and_ferraro_graph():
    G = torrents_and_ferraro_graph()
    _check_separating_sets(G)


def test_example_1():
    G = graph_example_1()
    _check_separating_sets(G)


def test_random_gnp():
    G = nx.gnp_random_graph(100, 0.1)
    _check_separating_sets(G)


def test_shell():
    constructor = [(20, 80, 0.8), (80, 180, 0.6)]
    G = nx.random_shell_graph(constructor)
    _check_separating_sets(G)


def test_configuration():
    deg_seq = nx.random_powerlaw_tree_sequence(100, tries=5000)
    G = nx.Graph(nx.configuration_model(deg_seq))
    G.remove_edges_from(nx.selfloop_edges(G))
    _check_separating_sets(G)


def test_karate():
    G = nx.karate_club_graph()
    _check_separating_sets(G)


def _generate_no_biconnected(max_attempts=50):
    attempts = 0
    while True:
        G = nx.fast_gnp_random_graph(100, 0.0575)
        if nx.is_connected(G) and not nx.is_biconnected(G):
            attempts = 0
            yield G
        else:
            if attempts >= max_attempts:
                msg = "Tried %d times: no suitable Graph." % attempts
                raise Exception(msg % max_attempts)
            else:
                attempts += 1


def test_articulation_points():
    Ggen = _generate_no_biconnected()
    for i in range(1):  # change 1 to 3 or more for more realizations.
        G = next(Ggen)
        articulation_points = list({a} for a in nx.articulation_points(G))
        for cut in nx.all_node_cuts(G):
            assert_true(cut in articulation_points)


def test_grid_2d_graph():
    # All minimum node cuts of a 2d grid
    # are the four pairs of nodes that are
    # neighbors of the four corner nodes.
    G = nx.grid_2d_graph(5, 5)
    solution = [
        set([(0, 1), (1, 0)]),
        set([(3, 0), (4, 1)]),
        set([(3, 4), (4, 3)]),
        set([(0, 3), (1, 4)]),
    ]
    for cut in nx.all_node_cuts(G):
        assert_true(cut in solution)


def test_disconnected_graph():
    G = nx.fast_gnp_random_graph(100, 0.01)
    cuts = nx.all_node_cuts(G)
    assert_raises(nx.NetworkXError, next, cuts)


def test_alternative_flow_functions():
    graph_funcs = [graph_example_1, nx.davis_southern_women_graph]
    for graph_func in graph_funcs:
        G = graph_func()
        node_conn = nx.node_connectivity(G)
        for flow_func in flow_funcs:
            for cut in nx.all_node_cuts(G, flow_func=flow_func):
                assert_equal(node_conn, len(cut))
                H = G.copy()
                H.remove_nodes_from(cut)
                assert_false(nx.is_connected(H))


def test_is_separating_set_complete_graph():
    G = nx.complete_graph(5)
    assert_true(_is_separating_set(G, {0, 1, 2, 3}))


def test_is_separating_set():
    for i in [5, 10, 15]:
        G = nx.star_graph(i)
        max_degree_node = max(G, key=G.degree)
        assert_true(_is_separating_set(G, {max_degree_node}))


def test_non_repeated_cuts():
    # The algorithm was repeating the cut {0, 1} for the giant biconnected
    # component of the Karate club graph.
    K = nx.karate_club_graph()
    G = max(list(nx.biconnected_component_subgraphs(K)), key=len)
    solution = [{32, 33}, {2, 33}, {0, 3}, {0, 1}, {29, 33}]
    cuts = list(nx.all_node_cuts(G))
    if len(solution) != len(cuts):
        print(nx.info(G))
        print("Solution: {}".format(solution))
        print("Result: {}".format(cuts))
    assert_true(len(solution) == len(cuts))
    for cut in cuts:
        assert_true(cut in solution)


def test_cycle_graph():
    G = nx.cycle_graph(5)
    solution = [{0, 2}, {0, 3}, {1, 3}, {1, 4}, {2, 4}]
    cuts = list(nx.all_node_cuts(G))
    assert_true(len(solution) == len(cuts))
    for cut in cuts:
        assert_true(cut in solution)


def test_complete_graph():
    G = nx.complete_graph(5)
    solution = [
        {0, 1, 2, 3},
        {0, 1, 2, 4},
        {0, 1, 3, 4},
        {0, 2, 3, 4},
        {1, 2, 3, 4},
    ]
    cuts = list(nx.all_node_cuts(G))
    assert_true(len(solution) == len(cuts))
    for cut in cuts:
        assert_true(cut in solution)