from __future__ import division

from nose.tools import assert_equal
from nose.tools import assert_true
from nose.tools import assert_false
from nose.tools import assert_raises
from nose.tools import raises

import networkx as nx
from networkx.utils import pairwise


def validate_path(G, s, t, soln_len, path):
    assert_equal(path[0], s)
    assert_equal(path[-1], t)
    if not G.is_multigraph():
        computed = sum(G[u][v].get('weight', 1) for u, v in pairwise(path))
        assert_equal(soln_len, computed)
    else:
        computed = sum(min(e.get('weight', 1) for e in G[u][v].values())
                       for u, v in pairwise(path))
        assert_equal(soln_len, computed)


def validate_length_path(G, s, t, soln_len, length, path):
    assert_equal(soln_len, length)
    validate_path(G, s, t, length, path)


class WeightedTestBase(object):
    """Base class for test classes that test functions for computing
    shortest paths in weighted graphs.

    """

    def setup(self):
        """Creates some graphs for use in the unit tests."""
        cnlti = nx.convert_node_labels_to_integers
        self.grid = cnlti(nx.grid_2d_graph(4, 4), first_label=1,
                          ordering="sorted")
        self.cycle = nx.cycle_graph(7)
        self.directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph())
        self.XG = nx.DiGraph()
        self.XG.add_weighted_edges_from([('s', 'u', 10), ('s', 'x', 5),
                                         ('u', 'v', 1), ('u', 'x', 2),
                                         ('v', 'y', 1), ('x', 'u', 3),
                                         ('x', 'v', 5), ('x', 'y', 2),
                                         ('y', 's', 7), ('y', 'v', 6)])
        self.MXG = nx.MultiDiGraph(self.XG)
        self.MXG.add_edge('s', 'u', weight=15)
        self.XG2 = nx.DiGraph()
        self.XG2.add_weighted_edges_from([[1, 4, 1], [4, 5, 1],
                                          [5, 6, 1], [6, 3, 1],
                                          [1, 3, 50], [1, 2, 100],
                                          [2, 3, 100]])

        self.XG3 = nx.Graph()
        self.XG3.add_weighted_edges_from([[0, 1, 2], [1, 2, 12],
                                          [2, 3, 1], [3, 4, 5],
                                          [4, 5, 1], [5, 0, 10]])

        self.XG4 = nx.Graph()
        self.XG4.add_weighted_edges_from([[0, 1, 2], [1, 2, 2],
                                          [2, 3, 1], [3, 4, 1],
                                          [4, 5, 1], [5, 6, 1],
                                          [6, 7, 1], [7, 0, 1]])
        self.MXG4 = nx.MultiGraph(self.XG4)
        self.MXG4.add_edge(0, 1, weight=3)
        self.G = nx.DiGraph()  # no weights
        self.G.add_edges_from([('s', 'u'), ('s', 'x'),
                               ('u', 'v'), ('u', 'x'),
                               ('v', 'y'), ('x', 'u'),
                               ('x', 'v'), ('x', 'y'),
                               ('y', 's'), ('y', 'v')])


class TestWeightedPath(WeightedTestBase):

    def test_dijkstra(self):
        from pprint import pprint 
        pprint(nx.single_source_dijkstra(self.XG, 's'))
        (D, P, K) = nx.single_source_dijkstra(self.XG, 's')
        validate_path(self.XG, 's', 'v', 9, P['v'])
        assert_equal(D['v'], 9)

        validate_path(
            self.XG, 's', 'v', 9, nx.single_source_dijkstra_path(self.XG, 's')['v'])
        assert_equal(dict(
            nx.single_source_dijkstra_path_length(self.XG, 's'))['v'], 9)

        validate_path(
            self.XG, 's', 'v', 9, nx.single_source_dijkstra(self.XG, 's')[1]['v'])
        validate_path(
            self.MXG, 's', 'v', 9, nx.single_source_dijkstra_path(self.MXG, 's')['v'])

        GG = self.XG.to_undirected()
        # make sure we get lower weight
        # to_undirected might choose either edge with weight 2 or weight 3
        GG['u']['x']['weight'] = 2
        (D, P, K) = nx.single_source_dijkstra(GG, 's')
        validate_path(GG, 's', 'v', 8, P['v'])
        assert_equal(D['v'], 8)     # uses lower weight of 2 on u<->x edge
        validate_path(GG, 's', 'v', 8, nx.dijkstra_path(GG, 's', 'v'))
        assert_equal(nx.dijkstra_path_length(GG, 's', 'v'), 8)

        validate_path(self.XG2, 1, 3, 4, nx.dijkstra_path(self.XG2, 1, 3))
        validate_path(self.XG3, 0, 3, 15, nx.dijkstra_path(self.XG3, 0, 3))
        assert_equal(nx.dijkstra_path_length(self.XG3, 0, 3), 15)
        validate_path(self.XG4, 0, 2, 4, nx.dijkstra_path(self.XG4, 0, 2))
        assert_equal(nx.dijkstra_path_length(self.XG4, 0, 2), 4)
        validate_path(self.MXG4, 0, 2, 4, nx.dijkstra_path(self.MXG4, 0, 2))
        validate_path(
            self.G, 's', 'v', 2, nx.single_source_dijkstra(self.G, 's', 'v')[1])
        validate_path(
            self.G, 's', 'v', 2, nx.single_source_dijkstra(self.G, 's')[1]['v'])

        validate_path(self.G, 's', 'v', 2, nx.dijkstra_path(self.G, 's', 'v'))
        assert_equal(nx.dijkstra_path_length(self.G, 's', 'v'), 2)

        # NetworkXError: node s not reachable from moon
        assert_raises(nx.NetworkXNoPath, nx.dijkstra_path, self.G, 's', 'moon')
        assert_raises(
            nx.NetworkXNoPath, nx.dijkstra_path_length, self.G, 's', 'moon')

        validate_path(self.cycle, 0, 3, 3, nx.dijkstra_path(self.cycle, 0, 3))
        validate_path(self.cycle, 0, 4, 3, nx.dijkstra_path(self.cycle, 0, 4))

        assert_equal(nx.single_source_dijkstra(self.cycle, 0, 0), (0, [0]))

    def test_bidirectional_dijkstra(self):
        validate_length_path(
            self.XG, 's', 'v', 9, *nx.bidirectional_dijkstra(self.XG, 's', 'v'))
        validate_length_path(
            self.G, 's', 'v', 2, *nx.bidirectional_dijkstra(self.G, 's', 'v'))
        validate_length_path(
            self.cycle, 0, 3, 3, *nx.bidirectional_dijkstra(self.cycle, 0, 3))
        validate_length_path(
            self.cycle, 0, 4, 3, *nx.bidirectional_dijkstra(self.cycle, 0, 4))
        validate_length_path(
            self.XG3, 0, 3, 15, *nx.bidirectional_dijkstra(self.XG3, 0, 3))
        validate_length_path(
            self.XG4, 0, 2, 4, *nx.bidirectional_dijkstra(self.XG4, 0, 2))

        # need more tests here
        P = nx.single_source_dijkstra_path(self.XG, 's')['v']
        validate_path(self.XG, 's', 'v', sum(self.XG[u][v]['weight'] for u, v in zip(
            P[:-1], P[1:])), nx.dijkstra_path(self.XG, 's', 'v'))

        # check absent source
        G = nx.path_graph(2)
        assert_raises(nx.NodeNotFound, nx.bidirectional_dijkstra, G, 3, 0)

    @raises(nx.NetworkXNoPath)
    def test_bidirectional_dijkstra_no_path(self):
        G = nx.Graph()
        nx.add_path(G, [1, 2, 3])
        nx.add_path(G, [4, 5, 6])
        path = nx.bidirectional_dijkstra(G, 1, 6)

    def test_absent_source(self):
        # the check is in _dijkstra_multisource, but this will provide
        # regression testing against later changes to any of the "client"
        # Dijkstra or Bellman-Ford functions
        G = nx.path_graph(2)
        for fn in (nx.dijkstra_path,
                   nx.dijkstra_path_length,
                   nx.single_source_dijkstra_path,
                   nx.single_source_dijkstra_path_length,
                   nx.single_source_dijkstra,
                   nx.dijkstra_predecessor_and_distance,):
            assert_raises(nx.NodeNotFound, fn, G, 3, 0)

    def test_dijkstra_predecessor1(self):
        G = nx.path_graph(4)
        assert_equal(nx.dijkstra_predecessor_and_distance(G, 0),
                     ({0: [], 1: [0], 2: [1], 3: [2]}, {0: 0, 1: 1, 2: 2, 3: 3}))

    def test_dijkstra_predecessor2(self):
        # 4-cycle
        G = nx.Graph([(0, 1), (1, 2), (2, 3), (3, 0)])
        pred, dist = nx.dijkstra_predecessor_and_distance(G, (0))
        assert_equal(pred[0], [])
        assert_equal(pred[1], [0])
        assert_true(pred[2] in [[1, 3], [3, 1]])
        assert_equal(pred[3], [0])
        assert_equal(dist, {0: 0, 1: 1, 2: 2, 3: 1})

    def test_dijkstra_predecessor3(self):
        XG = nx.DiGraph()
        XG.add_weighted_edges_from([('s', 'u', 10), ('s', 'x', 5),
                                    ('u', 'v', 1), ('u', 'x', 2),
                                    ('v', 'y', 1), ('x', 'u', 3),
                                    ('x', 'v', 5), ('x', 'y', 2),
                                    ('y', 's', 7), ('y', 'v', 6)])
        (P, D) = nx.dijkstra_predecessor_and_distance(XG, 's')
        assert_equal(P['v'], ['u'])
        assert_equal(D['v'], 9)
        (P, D) = nx.dijkstra_predecessor_and_distance(XG, 's', cutoff=8)
        assert_false('v' in D)

    def test_single_source_dijkstra_path_length(self):
        pl = nx.single_source_dijkstra_path_length
        assert_equal(dict(pl(self.MXG4, 0))[2], 4)
        spl = pl(self.MXG4, 0, cutoff=2)
        assert_false(2 in spl)

    def test_bidirectional_dijkstra_multigraph(self):
        G = nx.MultiGraph()
        G.add_edge('a', 'b', weight=10)
        G.add_edge('a', 'b', weight=100)
        dp = nx.bidirectional_dijkstra(G, 'a', 'b')
        assert_equal(dp, (10, ['a', 'b']))

    def test_dijkstra_pred_distance_multigraph(self):
        G = nx.MultiGraph()
        G.add_edge('a', 'b', key='short', foo=5, weight=100)
        G.add_edge('a', 'b', key='long', bar=1, weight=110)
        p, d = nx.dijkstra_predecessor_and_distance(G, 'a')
        assert_equal(p, {'a': [], 'b': ['a']})
        assert_equal(d, {'a': 0, 'b': 100})

    def test_negative_edge_cycle(self):
        G = nx.cycle_graph(5, create_using=nx.DiGraph())
        assert_equal(nx.negative_edge_cycle(G), False)
        G.add_edge(8, 9, weight=-7)
        G.add_edge(9, 8, weight=3)
        graph_size = len(G)
        assert_equal(nx.negative_edge_cycle(G), True)
        assert_equal(graph_size, len(G))
        assert_raises(ValueError, nx.single_source_dijkstra_path_length, G, 8)
        assert_raises(ValueError, nx.single_source_dijkstra, G, 8)
        assert_raises(ValueError, nx.dijkstra_predecessor_and_distance, G, 8)
        G.add_edge(9, 10)
        assert_raises(ValueError, nx.bidirectional_dijkstra, G, 8, 10)

    def test_weight_function(self):
        """Tests that a callable weight is interpreted as a weight
        function instead of an edge attribute.

        """
        # Create a triangle in which the edge from node 0 to node 2 has
        # a large weight and the other two edges have a small weight.
        G = nx.complete_graph(3)
        G.adj[0][2]['weight'] = 10
        G.adj[0][1]['weight'] = 1
        G.adj[1][2]['weight'] = 1
        # The weight function will take the multiplicative inverse of
        # the weights on the edges. This way, weights that were large
        # before now become small and vice versa.

        def weight(u, v, d, k): return 1 / d['weight']
        # The shortest path from 0 to 2 using the actual weights on the
        # edges should be [0, 1, 2].
        distance, path, keys = nx.single_source_dijkstra(G, 0, 2)
        assert_equal(distance, 2)
        assert_equal(path, [0, 1, 2])
        # However, with the above weight function, the shortest path
        # should be [0, 2], since that has a very small weight.
        distance, path, keys = nx.single_source_dijkstra(G, 0, 2, weight=weight)
        assert_equal(distance, 1 / 10)
        assert_equal(path, [0, 2])

    def test_all_pairs_dijkstra_path(self):
        cycle = nx.cycle_graph(7)
        p = dict(nx.all_pairs_dijkstra_path(cycle))
        assert_equal(p[0][3], [0, 1, 2, 3])

        cycle[1][2]['weight'] = 10
        p = dict(nx.all_pairs_dijkstra_path(cycle))
        assert_equal(p[0][3], [0, 6, 5, 4, 3])

    def test_all_pairs_dijkstra_path_length(self):
        cycle = nx.cycle_graph(7)
        pl = dict(nx.all_pairs_dijkstra_path_length(cycle))
        assert_equal(pl[0], {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1})

        cycle[1][2]['weight'] = 10
        pl = dict(nx.all_pairs_dijkstra_path_length(cycle))
        assert_equal(pl[0], {0: 0, 1: 1, 2: 5, 3: 4, 4: 3, 5: 2, 6: 1})

    def test_all_pairs_dijkstra(self):
        cycle = nx.cycle_graph(7)
        out = dict(nx.all_pairs_dijkstra(cycle))
        assert_equal(out[0][0], {0: 0, 1: 1, 2: 2, 3: 3, 4: 3, 5: 2, 6: 1})
        assert_equal(out[0][1][3], [0, 1, 2, 3])

        cycle[1][2]['weight'] = 10
        out = dict(nx.all_pairs_dijkstra(cycle))
        assert_equal(out[0][0], {0: 0, 1: 1, 2: 5, 3: 4, 4: 3, 5: 2, 6: 1})
        assert_equal(out[0][1][3], [0, 6, 5, 4, 3])


class TestDijkstraPathLength(object):
    """Unit tests for the :func:`networkx.dijkstra_path_length`
    function.

    """

    def test_weight_function(self):
        """Tests for computing the length of the shortest path using
        Dijkstra's algorithm with a user-defined weight function.

        """
        # Create a triangle in which the edge from node 0 to node 2 has
        # a large weight and the other two edges have a small weight.
        G = nx.complete_graph(3)
        G.adj[0][2]['weight'] = 10
        G.adj[0][1]['weight'] = 1
        G.adj[1][2]['weight'] = 1
        # The weight function will take the multiplicative inverse of
        # the weights on the edges. This way, weights that were large
        # before now become small and vice versa.

        def weight(u, v, d, k): return 1 / d['weight']
        # The shortest path from 0 to 2 using the actual weights on the
        # edges should be [0, 1, 2]. However, with the above weight
        # function, the shortest path should be [0, 2], since that has a
        # very small weight.
        length = nx.dijkstra_path_length(G, 0, 2, weight=weight)
        assert_equal(length, 1 / 10)


class TestMultiSourceDijkstra(object):
    """Unit tests for the multi-source dialect of Dijkstra's shortest
    path algorithms.

    """

    @raises(ValueError)
    def test_no_sources(self):
        nx.multi_source_dijkstra(nx.Graph(), {})

    @raises(ValueError)
    def test_path_no_sources(self):
        nx.multi_source_dijkstra_path(nx.Graph(), {})

    @raises(ValueError)
    def test_path_length_no_sources(self):
        nx.multi_source_dijkstra_path_length(nx.Graph(), {})

    def test_absent_source(self):
        G = nx.path_graph(2)
        for fn in (nx.multi_source_dijkstra_path,
                   nx.multi_source_dijkstra_path_length,
                   nx.multi_source_dijkstra,):
            assert_raises(nx.NodeNotFound, fn, G, [3], 0)

    def test_two_sources(self):
        edges = [(0, 1, 1), (1, 2, 1), (2, 3, 10), (3, 4, 1)]
        G = nx.Graph()
        G.add_weighted_edges_from(edges)
        sources = {0, 4}
        distances, paths, keys = nx.multi_source_dijkstra(G, sources)
        expected_distances = {0: 0, 1: 1, 2: 2, 3: 1, 4: 0}
        expected_paths = {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [4, 3], 4: [4]}
        assert_equal(distances, expected_distances)
        assert_equal(paths, expected_paths)

    def test_simple_paths(self):
        G = nx.path_graph(4)
        lengths = nx.multi_source_dijkstra_path_length(G, [0])
        assert_equal(lengths, {n: n for n in G})
        paths = nx.multi_source_dijkstra_path(G, [0])
        assert_equal(paths, {n: list(range(n + 1)) for n in G})


class TestBellmanFordAndGoldbergRadzik(WeightedTestBase):

    def test_single_node_graph(self):
        G = nx.DiGraph()
        G.add_node(0)
        assert_equal(nx.single_source_bellman_ford_path(G, 0), {0: [0]})
        assert_equal(nx.single_source_bellman_ford_path_length(G, 0), {0: 0})
        assert_equal(nx.single_source_bellman_ford(G, 0), ({0: 0}, {0: [0]}))
        assert_equal(nx.bellman_ford_predecessor_and_distance(G, 0), ({0: []}, {0: 0}))
        assert_equal(nx.goldberg_radzik(G, 0), ({0: None}, {0: 0}))

    def test_absent_source_bellman_ford(self):
        # the check is in _bellman_ford; this provides regression testing
        # against later changes to "client" Bellman-Ford functions
        G = nx.path_graph(2)
        for fn in (nx.bellman_ford_predecessor_and_distance,
                   nx.bellman_ford_path,
                   nx.bellman_ford_path_length,
                   nx.single_source_bellman_ford_path,
                   nx.single_source_bellman_ford_path_length,
                   nx.single_source_bellman_ford,):
            assert_raises(nx.NodeNotFound, fn, G, 3, 0)

    @raises(nx.NodeNotFound)
    def test_absent_source_goldberg_radzik(self):
        G = nx.path_graph(2)
        nx.goldberg_radzik(G, 3, 0)

    def test_negative_weight_cycle(self):
        G = nx.cycle_graph(5, create_using=nx.DiGraph())
        G.add_edge(1, 2, weight=-7)
        for i in range(5):
            assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, i)
            assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, i)
            assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, i)
            assert_raises(nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, i)
            assert_raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, i)
        G = nx.cycle_graph(5)  # undirected Graph
        G.add_edge(1, 2, weight=-3)
        for i in range(5):
            assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, i)
            assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, i)
            assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, i)
            assert_raises(nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, i)
            assert_raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, i)
        G = nx.DiGraph([(1, 1, {'weight': -1})])
        assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford_path, G, 1)
        assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford_path_length, G, 1)
        assert_raises(nx.NetworkXUnbounded, nx.single_source_bellman_ford, G, 1)
        assert_raises(nx.NetworkXUnbounded, nx.bellman_ford_predecessor_and_distance, G, 1)
        assert_raises(nx.NetworkXUnbounded, nx.goldberg_radzik, G, 1)
        # no negative cycle but negative weight
        G = nx.cycle_graph(5, create_using=nx.DiGraph())
        G.add_edge(1, 2, weight=-3)
        assert_equal(nx.single_source_bellman_ford_path(G, 0),
                     {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [0, 1, 2, 3], 4: [0, 1, 2, 3, 4]})
        assert_equal(nx.single_source_bellman_ford_path_length(G, 0),
                     {0: 0, 1: 1, 2: -2, 3: -1, 4: 0})
        assert_equal(nx.single_source_bellman_ford(G, 0),
                     ({0: 0, 1: 1, 2: -2, 3: -1, 4: 0},
                      {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [0, 1, 2, 3], 4: [0, 1, 2, 3, 4]}))
        assert_equal(nx.bellman_ford_predecessor_and_distance(G, 0),
                     ({0: [], 1: [0], 2: [1], 3: [2], 4: [3]},
                      {0: 0, 1: 1, 2: -2, 3: -1, 4: 0}))
        assert_equal(nx.goldberg_radzik(G, 0),
                     ({0: None, 1: 0, 2: 1, 3: 2, 4: 3},
                      {0: 0, 1: 1, 2: -2, 3: -1, 4: 0}))

    def test_not_connected(self):
        G = nx.complete_graph(6)
        G.add_edge(10, 11)
        G.add_edge(10, 12)
        assert_equal(nx.single_source_bellman_ford_path(G, 0),
                     {0: [0], 1: [0, 1], 2: [0, 2], 3: [0, 3], 4: [0, 4], 5: [0, 5]})
        assert_equal(nx.single_source_bellman_ford_path_length(G, 0),
                     {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1})
        assert_equal(nx.single_source_bellman_ford(G, 0),
                     ({0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1},
                      {0: [0], 1: [0, 1], 2: [0, 2], 3: [0, 3], 4: [0, 4], 5: [0, 5]}))
        assert_equal(nx.bellman_ford_predecessor_and_distance(G, 0),
                     ({0: [], 1: [0], 2: [0], 3: [0], 4: [0], 5: [0]},
                      {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}))
        assert_equal(nx.goldberg_radzik(G, 0),
                     ({0: None, 1: 0, 2: 0, 3: 0, 4: 0, 5: 0},
                      {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}))

        # not connected, with a component not containing the source that
        # contains a negative cost cycle.
        G = nx.complete_graph(6)
        G.add_edges_from([('A', 'B', {'load': 3}),
                          ('B', 'C', {'load': -10}),
                          ('C', 'A', {'load': 2})])
        assert_equal(nx.single_source_bellman_ford_path(G, 0, weight='load'),
                     {0: [0], 1: [0, 1], 2: [0, 2], 3: [0, 3], 4: [0, 4], 5: [0, 5]})
        assert_equal(nx.single_source_bellman_ford_path_length(G, 0, weight='load'),
                     {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1})
        assert_equal(nx.single_source_bellman_ford(G, 0, weight='load'),
                     ({0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1},
                      {0: [0], 1: [0, 1], 2: [0, 2], 3: [0, 3], 4: [0, 4], 5: [0, 5]}))
        assert_equal(nx.bellman_ford_predecessor_and_distance(G, 0, weight='load'),
                     ({0: [], 1: [0], 2: [0], 3: [0], 4: [0], 5: [0]},
                      {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}))
        assert_equal(nx.goldberg_radzik(G, 0, weight='load'),
                     ({0: None, 1: 0, 2: 0, 3: 0, 4: 0, 5: 0},
                      {0: 0, 1: 1, 2: 1, 3: 1, 4: 1, 5: 1}))

    def test_multigraph(self):
        assert_equal(nx.bellman_ford_path(self.MXG, 's', 'v'), ['s', 'x', 'u', 'v'])
        assert_equal(nx.bellman_ford_path_length(self.MXG, 's', 'v'), 9)
        assert_equal(nx.single_source_bellman_ford_path(self.MXG, 's')['v'], ['s', 'x', 'u', 'v'])
        assert_equal(nx.single_source_bellman_ford_path_length(self.MXG, 's')['v'], 9)
        D, P = nx.single_source_bellman_ford(self.MXG, 's', target='v')
        assert_equal(D, 9)
        assert_equal(P, ['s', 'x', 'u', 'v'])
        P, D = nx.bellman_ford_predecessor_and_distance(self.MXG, 's')
        assert_equal(P['v'], ['u'])
        assert_equal(D['v'], 9)
        P, D = nx.goldberg_radzik(self.MXG, 's')
        assert_equal(P['v'], 'u')
        assert_equal(D['v'], 9)
        assert_equal(nx.bellman_ford_path(self.MXG4, 0, 2), [0, 1, 2])
        assert_equal(nx.bellman_ford_path_length(self.MXG4, 0, 2), 4)
        assert_equal(nx.single_source_bellman_ford_path(self.MXG4, 0)[2], [0, 1, 2])
        assert_equal(nx.single_source_bellman_ford_path_length(self.MXG4, 0)[2], 4)
        D, P = nx.single_source_bellman_ford(self.MXG4, 0, target=2)
        assert_equal(D, 4)
        assert_equal(P, [0, 1, 2])
        P, D = nx.bellman_ford_predecessor_and_distance(self.MXG4, 0)
        assert_equal(P[2], [1])
        assert_equal(D[2], 4)
        P, D = nx.goldberg_radzik(self.MXG4, 0)
        assert_equal(P[2], 1)
        assert_equal(D[2], 4)

    def test_others(self):
        assert_equal(nx.bellman_ford_path(self.XG, 's', 'v'), ['s', 'x', 'u', 'v'])
        assert_equal(nx.bellman_ford_path_length(self.XG, 's', 'v'), 9)
        assert_equal(nx.single_source_bellman_ford_path(self.XG, 's')['v'], ['s', 'x', 'u', 'v'])
        assert_equal(nx.single_source_bellman_ford_path_length(self.XG, 's')['v'], 9)
        D, P = nx.single_source_bellman_ford(self.XG, 's', target='v')
        assert_equal(D, 9)
        assert_equal(P, ['s', 'x', 'u', 'v'])
        (P, D) = nx.bellman_ford_predecessor_and_distance(self.XG, 's')
        assert_equal(P['v'], ['u'])
        assert_equal(D['v'], 9)
        (P, D) = nx.goldberg_radzik(self.XG, 's')
        assert_equal(P['v'], 'u')
        assert_equal(D['v'], 9)

    def test_path_graph(self):
        G = nx.path_graph(4)
        assert_equal(nx.single_source_bellman_ford_path(G, 0),
                     {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [0, 1, 2, 3]})
        assert_equal(nx.single_source_bellman_ford_path_length(G, 0),
                     {0: 0, 1: 1, 2: 2, 3: 3})
        assert_equal(nx.single_source_bellman_ford(G, 0),
                     ({0: 0, 1: 1, 2: 2, 3: 3}, {0: [0], 1: [0, 1], 2: [0, 1, 2], 3: [0, 1, 2, 3]}))
        assert_equal(nx.bellman_ford_predecessor_and_distance(G, 0),
                     ({0: [], 1: [0], 2: [1], 3: [2]}, {0: 0, 1: 1, 2: 2, 3: 3}))
        assert_equal(nx.goldberg_radzik(G, 0),
                     ({0: None, 1: 0, 2: 1, 3: 2}, {0: 0, 1: 1, 2: 2, 3: 3}))
        assert_equal(nx.single_source_bellman_ford_path(G, 3),
                     {0: [3, 2, 1, 0], 1: [3, 2, 1], 2: [3, 2], 3: [3]})
        assert_equal(nx.single_source_bellman_ford_path_length(G, 3),
                     {0: 3, 1: 2, 2: 1, 3: 0})
        assert_equal(nx.single_source_bellman_ford(G, 3),
                     ({0: 3, 1: 2, 2: 1, 3: 0}, {0: [3, 2, 1, 0], 1: [3, 2, 1], 2: [3, 2], 3: [3]}))
        assert_equal(nx.bellman_ford_predecessor_and_distance(G, 3),
                     ({0: [1], 1: [2], 2: [3], 3: []}, {0: 3, 1: 2, 2: 1, 3: 0}))
        assert_equal(nx.goldberg_radzik(G, 3),
                     ({0: 1, 1: 2, 2: 3, 3: None}, {0: 3, 1: 2, 2: 1, 3: 0}))

    def test_4_cycle(self):
        # 4-cycle
        G = nx.Graph([(0, 1), (1, 2), (2, 3), (3, 0)])
        dist, path = nx.single_source_bellman_ford(G, 0)
        assert_equal(dist, {0: 0, 1: 1, 2: 2, 3: 1})
        assert_equal(path[0], [0])
        assert_equal(path[1], [0, 1])
        assert_true(path[2] in [[0, 1, 2], [0, 3, 2]])
        assert_equal(path[3], [0, 3])

        pred, dist = nx.bellman_ford_predecessor_and_distance(G, 0)
        assert_equal(pred[0], [])
        assert_equal(pred[1], [0])
        assert_true(pred[2] in [[1, 3], [3, 1]])
        assert_equal(pred[3], [0])
        assert_equal(dist, {0: 0, 1: 1, 2: 2, 3: 1})

        pred, dist = nx.goldberg_radzik(G, 0)
        assert_equal(pred[0], None)
        assert_equal(pred[1], 0)
        assert_true(pred[2] in [1, 3])
        assert_equal(pred[3], 0)
        assert_equal(dist, {0: 0, 1: 1, 2: 2, 3: 1})

    def test_negative_weight(self):
        G = nx.DiGraph()
        G.add_nodes_from('abcd')
        G.add_edge('a','d', weight = 0)
        G.add_edge('a','b', weight = 1)
        G.add_edge('b','c', weight = -3)
        G.add_edge('c','d', weight = 1)

        assert_equal(nx.bellman_ford_path(G, 'a', 'd'), ['a', 'b', 'c', 'd'])
        assert_equal(nx.bellman_ford_path_length(G, 'a', 'd'), -1)


class TestJohnsonAlgorithm(WeightedTestBase):

    @raises(nx.NetworkXError)
    def test_single_node_graph(self):
        G = nx.DiGraph()
        G.add_node(0)
        nx.johnson(G)

    def test_negative_cycle(self):
        G = nx.DiGraph()
        G.add_weighted_edges_from([('0', '3', 3), ('0', '1', -5), ('1', '0', -5),
                                   ('0', '2', 2), ('1', '2', 4),
                                   ('2', '3', 1)])
        assert_raises(nx.NetworkXUnbounded, nx.johnson, G)
        G = nx.Graph()
        G.add_weighted_edges_from([('0', '3', 3), ('0', '1', -5), ('1', '0', -5),
                                   ('0', '2', 2), ('1', '2', 4),
                                   ('2', '3', 1)])
        assert_raises(nx.NetworkXUnbounded, nx.johnson, G)

    def test_negative_weights(self):
        G = nx.DiGraph()
        G.add_weighted_edges_from([('0', '3', 3), ('0', '1', -5),
                                   ('0', '2', 2), ('1', '2', 4),
                                   ('2', '3', 1)])
        paths = nx.johnson(G)
        assert_equal(paths, {'1': {'1': ['1'], '3': ['1', '2', '3'],
                                   '2': ['1', '2']}, '0': {'1': ['0', '1'],
                                                           '0': ['0'], '3': ['0', '1', '2', '3'],
                                                           '2': ['0', '1', '2']}, '3': {'3': ['3']},
                             '2': {'3': ['2', '3'], '2': ['2']}})

    @raises(nx.NetworkXError)
    def test_unweighted_graph(self):
        G = nx.path_graph(5)
        nx.johnson(G)

    def test_graphs(self):
        validate_path(self.XG, 's', 'v', 9, nx.johnson(self.XG)['s']['v'])
        validate_path(self.MXG, 's', 'v', 9, nx.johnson(self.MXG)['s']['v'])
        validate_path(self.XG2, 1, 3, 4, nx.johnson(self.XG2)[1][3])
        validate_path(self.XG3, 0, 3, 15, nx.johnson(self.XG3)[0][3])
        validate_path(self.XG4, 0, 2, 4, nx.johnson(self.XG4)[0][2])
        validate_path(self.MXG4, 0, 2, 4, nx.johnson(self.MXG4)[0][2])
