import random

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

import networkx as nx
from networkx import convert_node_labels_to_integers as cnlti
from networkx.algorithms.simple_paths import _bidirectional_dijkstra
from networkx.algorithms.simple_paths import _bidirectional_shortest_path
from networkx.utils import arbitrary_element


class TestIsSimplePath(object):
    """Unit tests for the
    :func:`networkx.algorithms.simple_paths.is_simple_path` function.

    """

    def test_empty_list(self):
        """Tests that the empty list is not a valid path, since there
        should be a one-to-one correspondence between paths as lists of
        nodes and paths as lists of edges.

        """
        G = nx.trivial_graph()
        assert_false(nx.is_simple_path(G, []))

    def test_trivial_path(self):
        """Tests that the trivial path, a path of length one, is
        considered a simple path in a graph.

        """
        G = nx.trivial_graph()
        assert_true(nx.is_simple_path(G, [0]))

    def test_trivial_nonpath(self):
        """Tests that a list whose sole element is an object not in the
        graph is not considered a simple path.

        """
        G = nx.trivial_graph()
        assert_false(nx.is_simple_path(G, ['not a node']))

    def test_simple_path(self):
        G = nx.path_graph(2)
        assert_true(nx.is_simple_path(G, [0, 1]))

    def test_non_simple_path(self):
        G = nx.path_graph(2)
        assert_false(nx.is_simple_path(G, [0, 1, 0]))

    def test_cycle(self):
        G = nx.cycle_graph(3)
        assert_false(nx.is_simple_path(G, [0, 1, 2, 0]))

    def test_missing_node(self):
        G = nx.path_graph(2)
        assert_false(nx.is_simple_path(G, [0, 2]))

    def test_directed_path(self):
        G = nx.DiGraph([(0, 1), (1, 2)])
        assert_true(nx.is_simple_path(G, [0, 1, 2]))

    def test_directed_non_path(self):
        G = nx.DiGraph([(0, 1), (1, 2)])
        assert_false(nx.is_simple_path(G, [2, 1, 0]))

    def test_directed_cycle(self):
        G = nx.DiGraph([(0, 1), (1, 2), (2, 0)])
        assert_false(nx.is_simple_path(G, [0, 1, 2, 0]))

    def test_multigraph(self):
        G = nx.MultiGraph([(0, 1), (0, 1)])
        assert_true(nx.is_simple_path(G, [0, 1]))

    def test_multidigraph(self):
        G = nx.MultiDiGraph([(0, 1), (0, 1), (1, 0), (1, 0)])
        assert_true(nx.is_simple_path(G, [0, 1]))


# Tests for all_simple_paths
def test_all_simple_paths():
    G = nx.path_graph(4)
    paths = nx.all_simple_paths(G, 0, 3)
    assert_equal(set(tuple(p) for p in paths), {(0, 1, 2, 3)})


def test_all_simple_paths_with_two_targets_emits_two_paths():
    G = nx.path_graph(4)
    G.add_edge(2, 4)
    paths = nx.all_simple_paths(G, 0, [3, 4])
    assert_equal(set(tuple(p) for p in paths), {(0, 1, 2, 3), (0, 1, 2, 4)})


def test_digraph_all_simple_paths_with_two_targets_emits_two_paths():
    G = nx.path_graph(4, create_using=nx.DiGraph())
    G.add_edge(2, 4)
    paths = nx.all_simple_paths(G, 0, [3, 4])
    assert_equal(set(tuple(p) for p in paths), {(0, 1, 2, 3), (0, 1, 2, 4)})


def test_all_simple_paths_with_two_targets_cutoff():
    G = nx.path_graph(4)
    G.add_edge(2, 4)
    paths = nx.all_simple_paths(G, 0, [3, 4], cutoff=3)
    assert_equal(set(tuple(p) for p in paths), {(0, 1, 2, 3), (0, 1, 2, 4)})


def test_digraph_all_simple_paths_with_two_targets_cutoff():
    G = nx.path_graph(4, create_using=nx.DiGraph())
    G.add_edge(2, 4)
    paths = nx.all_simple_paths(G, 0, [3, 4], cutoff=3)
    assert_equal(set(tuple(p) for p in paths), {(0, 1, 2, 3), (0, 1, 2, 4)})


def test_all_simple_paths_with_two_targets_in_line_emits_two_paths():
    G = nx.path_graph(4)
    paths = nx.all_simple_paths(G, 0, [2, 3])
    assert_equal(set(tuple(p) for p in paths), {(0, 1, 2), (0, 1, 2, 3)})


def test_all_simple_paths_ignores_cycle():
    G = nx.cycle_graph(3, create_using=nx.DiGraph())
    G.add_edge(1, 3)
    paths = nx.all_simple_paths(G, 0, 3)
    assert_equal(set(tuple(p) for p in paths), {(0, 1, 3)})


def test_all_simple_paths_with_two_targets_inside_cycle_emits_two_paths():
    G = nx.cycle_graph(3, create_using=nx.DiGraph())
    G.add_edge(1, 3)
    paths = nx.all_simple_paths(G, 0, [2, 3])
    assert_equal(set(tuple(p) for p in paths), {(0, 1, 2), (0, 1, 3)})


def test_all_simple_paths_source_target():
    G = nx.path_graph(4)
    paths = nx.all_simple_paths(G, 1, 1)
    assert_equal(paths, [])


def test_all_simple_paths_cutoff():
    G = nx.complete_graph(4)
    paths = nx.all_simple_paths(G, 0, 1, cutoff=1)
    assert_equal(set(tuple(p) for p in paths), {(0, 1)})
    paths = nx.all_simple_paths(G, 0, 1, cutoff=2)
    assert_equal(set(tuple(p) for p in paths), {(0, 1), (0, 2, 1), (0, 3, 1)})


def test_all_simple_paths_on_non_trivial_graph():
    ''' you may need to draw this graph to make sure it is reasonable '''
    G = nx.path_graph(5, create_using=nx.DiGraph())
    G.add_edges_from([(0, 5), (1, 5), (1, 3), (5, 4), (4, 2), (4, 3)])
    paths = nx.all_simple_paths(G, 1, [2, 3])
    assert_equal(set(tuple(p) for p in paths), {
        (1, 2), (1, 3, 4, 2), (1, 5, 4, 2), (1, 3), (1, 2, 3), (1, 5, 4, 3),
        (1, 5, 4, 2, 3)})
    paths = nx.all_simple_paths(G, 1, [2, 3], cutoff=3)
    assert_equal(set(tuple(p) for p in paths), {
        (1, 2), (1, 3, 4, 2), (1, 5, 4, 2), (1, 3), (1, 2, 3), (1, 5, 4, 3)})
    paths = nx.all_simple_paths(G, 1, [2, 3], cutoff=2)
    assert_equal(set(tuple(p) for p in paths), {(1, 2), (1, 3), (1, 2, 3)})


def test_all_simple_paths_multigraph():
    G = nx.MultiGraph([(1, 2), (1, 2)])
    paths = nx.all_simple_paths(G, 1, 1)
    assert_equal(paths, [])
    nx.add_path(G, [3, 1, 10, 2])
    paths = list(nx.all_simple_paths(G, 1, 2))
    assert_equal(len(paths), 3)
    assert_equal(set(tuple(p) for p in paths), {(1, 2), (1, 2), (1, 10, 2)})


def test_all_simple_paths_multigraph_with_cutoff():
    G = nx.MultiGraph([(1, 2), (1, 2), (1, 10), (10, 2)])
    paths = list(nx.all_simple_paths(G, 1, 2, cutoff=1))
    assert_equal(len(paths), 2)
    assert_equal(set(tuple(p) for p in paths), {(1, 2), (1, 2)})


def test_all_simple_paths_directed():
    G = nx.DiGraph()
    nx.add_path(G, [1, 2, 3])
    nx.add_path(G, [3, 2, 1])
    paths = nx.all_simple_paths(G, 1, 3)
    assert_equal(set(tuple(p) for p in paths), {(1, 2, 3)})


def test_all_simple_paths_empty():
    G = nx.path_graph(4)
    paths = nx.all_simple_paths(G, 0, 3, cutoff=2)
    assert_equal(list(paths), [])


def test_all_simple_paths_corner_cases():
    assert_equal(list(nx.all_simple_paths(nx.empty_graph(2), 0, 0)), [])
    assert_equal(list(nx.all_simple_paths(nx.empty_graph(2), 0, 1)), [])
    assert_equal(list(nx.all_simple_paths(nx.path_graph(9), 0, 8, 0)), [])


def hamiltonian_path(G, source):
    source = arbitrary_element(G)
    neighbors = set(G[source]) - set([source])
    n = len(G)
    for target in neighbors:
        for path in nx.all_simple_paths(G, source, target):
            if len(path) == n:
                yield path


def test_hamiltonian_path():
    from itertools import permutations
    G = nx.complete_graph(4)
    paths = [list(p) for p in hamiltonian_path(G, 0)]
    exact = [[0] + list(p) for p in permutations([1, 2, 3], 3)]
    assert_equal(sorted(paths), sorted(exact))


def test_cutoff_zero():
    G = nx.complete_graph(4)
    paths = nx.all_simple_paths(G, 0, 3, cutoff=0)
    assert_equal(list(list(p) for p in paths), [])
    paths = nx.all_simple_paths(nx.MultiGraph(G), 0, 3, cutoff=0)
    assert_equal(list(list(p) for p in paths), [])


@raises(nx.NodeNotFound)
def test_source_missing():
    G = nx.Graph()
    nx.add_path(G, [1, 2, 3])
    paths = list(nx.all_simple_paths(nx.MultiGraph(G), 0, 3))


@raises(nx.NodeNotFound)
def test_target_missing():
    G = nx.Graph()
    nx.add_path(G, [1, 2, 3])
    paths = list(nx.all_simple_paths(nx.MultiGraph(G), 1, 4))


# Tests for shortest_simple_paths
def test_shortest_simple_paths():
    G = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted")
    paths = nx.shortest_simple_paths(G, 1, 12)
    assert_equal(next(paths), [1, 2, 3, 4, 8, 12])
    assert_equal(next(paths), [1, 5, 6, 7, 8, 12])
    assert_equal([len(path) for path in nx.shortest_simple_paths(G, 1, 12)],
                 sorted([len(path) for path in nx.all_simple_paths(G, 1, 12)]))


def test_shortest_simple_paths_directed():
    G = nx.cycle_graph(7, create_using=nx.DiGraph())
    paths = nx.shortest_simple_paths(G, 0, 3)
    assert_equal([path for path in paths], [[0, 1, 2, 3]])


def test_Greg_Bernstein():
    g1 = nx.Graph()
    g1.add_nodes_from(["N0", "N1", "N2", "N3", "N4"])
    g1.add_edge("N4", "N1", weight=10.0, capacity=50, name="L5")
    g1.add_edge("N4", "N0", weight=7.0, capacity=40, name="L4")
    g1.add_edge("N0", "N1", weight=10.0, capacity=45, name="L1")
    g1.add_edge("N3", "N0", weight=10.0, capacity=50, name="L0")
    g1.add_edge("N2", "N3", weight=12.0, capacity=30, name="L2")
    g1.add_edge("N1", "N2", weight=15.0, capacity=42, name="L3")
    solution = [['N1', 'N0', 'N3'], ['N1', 'N2', 'N3'], ['N1', 'N4', 'N0', 'N3']]
    result = list(nx.shortest_simple_paths(g1, 'N1', 'N3', weight='weight'))
    assert_equal(result, solution)


def test_weighted_shortest_simple_path():
    def cost_func(path):
        return sum(G.adj[u][v]['weight'] for (u, v) in zip(path, path[1:]))

    G = nx.complete_graph(5)
    weight = {(u, v): random.randint(1, 100) for (u, v) in G.edges()}
    nx.set_edge_attributes(G, weight, 'weight')
    cost = 0
    for path in nx.shortest_simple_paths(G, 0, 3, weight='weight'):
        this_cost = cost_func(path)
        assert_true(cost <= this_cost)
        cost = this_cost


def test_directed_weighted_shortest_simple_path():
    def cost_func(path):
        return sum(G.adj[u][v]['weight'] for (u, v) in zip(path, path[1:]))

    G = nx.complete_graph(5)
    G = G.to_directed()
    weight = {(u, v): random.randint(1, 100) for (u, v) in G.edges()}
    nx.set_edge_attributes(G, weight, 'weight')
    cost = 0
    for path in nx.shortest_simple_paths(G, 0, 3, weight='weight'):
        this_cost = cost_func(path)
        assert_true(cost <= this_cost)
        cost = this_cost


def test_weighted_shortest_simple_path_issue2427():
    G = nx.Graph()
    G.add_edge('IN', 'OUT', weight=2)
    G.add_edge('IN', 'A', weight=1)
    G.add_edge('IN', 'B', weight=2)
    G.add_edge('B', 'OUT', weight=2)
    assert_equal(list(nx.shortest_simple_paths(G, 'IN', 'OUT', weight="weight")),
                 [['IN', 'OUT'], ['IN', 'B', 'OUT']])
    G = nx.Graph()
    G.add_edge('IN', 'OUT', weight=10)
    G.add_edge('IN', 'A', weight=1)
    G.add_edge('IN', 'B', weight=1)
    G.add_edge('B', 'OUT', weight=1)
    assert_equal(list(nx.shortest_simple_paths(G, 'IN', 'OUT', weight="weight")),
                 [['IN', 'B', 'OUT'], ['IN', 'OUT']])


def test_directed_weighted_shortest_simple_path_issue2427():
    G = nx.DiGraph()
    G.add_edge('IN', 'OUT', weight=2)
    G.add_edge('IN', 'A', weight=1)
    G.add_edge('IN', 'B', weight=2)
    G.add_edge('B', 'OUT', weight=2)
    assert_equal(list(nx.shortest_simple_paths(G, 'IN', 'OUT', weight="weight")),
                 [['IN', 'OUT'], ['IN', 'B', 'OUT']])
    G = nx.DiGraph()
    G.add_edge('IN', 'OUT', weight=10)
    G.add_edge('IN', 'A', weight=1)
    G.add_edge('IN', 'B', weight=1)
    G.add_edge('B', 'OUT', weight=1)
    assert_equal(list(nx.shortest_simple_paths(G, 'IN', 'OUT', weight="weight")),
                 [['IN', 'B', 'OUT'], ['IN', 'OUT']])


def test_weight_name():
    G = nx.cycle_graph(7)
    nx.set_edge_attributes(G, 1, 'weight')
    nx.set_edge_attributes(G, 1, 'foo')
    G.adj[1][2]['foo'] = 7
    paths = list(nx.shortest_simple_paths(G, 0, 3, weight='foo'))
    solution = [[0, 6, 5, 4, 3], [0, 1, 2, 3]]
    assert_equal(paths, solution)


@raises(nx.NodeNotFound)
def test_ssp_source_missing():
    G = nx.Graph()
    nx.add_path(G, [1, 2, 3])
    paths = list(nx.shortest_simple_paths(G, 0, 3))


@raises(nx.NodeNotFound)
def test_ssp_target_missing():
    G = nx.Graph()
    nx.add_path(G, [1, 2, 3])
    paths = list(nx.shortest_simple_paths(G, 1, 4))


@raises(nx.NetworkXNotImplemented)
def test_ssp_multigraph():
    G = nx.MultiGraph()
    nx.add_path(G, [1, 2, 3])
    paths = list(nx.shortest_simple_paths(G, 1, 4))


@raises(nx.NetworkXNoPath)
def test_ssp_source_missing():
    G = nx.Graph()
    nx.add_path(G, [0, 1, 2])
    nx.add_path(G, [3, 4, 5])
    paths = list(nx.shortest_simple_paths(G, 0, 3))


def test_bidirectional_shortest_path_restricted_cycle():
    cycle = nx.cycle_graph(7)
    length, path = _bidirectional_shortest_path(cycle, 0, 3)
    assert_equal(path, [0, 1, 2, 3])
    length, path = _bidirectional_shortest_path(cycle, 0, 3, ignore_nodes=[1])
    assert_equal(path, [0, 6, 5, 4, 3])


def test_bidirectional_shortest_path_restricted_wheel():
    wheel = nx.wheel_graph(6)
    length, path = _bidirectional_shortest_path(wheel, 1, 3)
    assert_true(path in [[1, 0, 3], [1, 2, 3]])
    length, path = _bidirectional_shortest_path(wheel, 1, 3, ignore_nodes=[0])
    assert_equal(path, [1, 2, 3])
    length, path = _bidirectional_shortest_path(wheel, 1, 3, ignore_nodes=[0, 2])
    assert_equal(path, [1, 5, 4, 3])
    length, path = _bidirectional_shortest_path(wheel, 1, 3,
                                                ignore_edges=[(1, 0), (5, 0), (2, 3)])
    assert_true(path in [[1, 2, 0, 3], [1, 5, 4, 3]])


def test_bidirectional_shortest_path_restricted_directed_cycle():
    directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph())
    length, path = _bidirectional_shortest_path(directed_cycle, 0, 3)
    assert_equal(path, [0, 1, 2, 3])
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_shortest_path,
        directed_cycle,
        0, 3,
        ignore_nodes=[1],
    )
    length, path = _bidirectional_shortest_path(directed_cycle, 0, 3,
                                                ignore_edges=[(2, 1)])
    assert_equal(path, [0, 1, 2, 3])
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_shortest_path,
        directed_cycle,
        0, 3,
        ignore_edges=[(1, 2)],
    )


def test_bidirectional_shortest_path_ignore():
    G = nx.Graph()
    nx.add_path(G, [1, 2])
    nx.add_path(G, [1, 3])
    nx.add_path(G, [1, 4])
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_shortest_path,
        G,
        1, 2,
        ignore_nodes=[1],
    )
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_shortest_path,
        G,
        1, 2,
        ignore_nodes=[2],
    )
    G = nx.Graph()
    nx.add_path(G, [1, 3])
    nx.add_path(G, [1, 4])
    nx.add_path(G, [3, 2])
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_shortest_path,
        G,
        1, 2,
        ignore_nodes=[1, 2],
    )


def validate_path(G, s, t, soln_len, path):
    assert_equal(path[0], s)
    assert_equal(path[-1], t)
    assert_equal(soln_len, sum(G[u][v].get('weight', 1)
                               for u, v in zip(path[:-1], path[1:])))


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


def test_bidirectional_dijksta_restricted():
    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)])

    XG3 = nx.Graph()
    XG3.add_weighted_edges_from([[0, 1, 2], [1, 2, 12],
                                 [2, 3, 1], [3, 4, 5],
                                 [4, 5, 1], [5, 0, 10]])
    validate_length_path(XG, 's', 'v', 9,
                         *_bidirectional_dijkstra(XG, 's', 'v'))
    validate_length_path(XG, 's', 'v', 10,
                         *_bidirectional_dijkstra(XG, 's', 'v', ignore_nodes=['u']))
    validate_length_path(XG, 's', 'v', 11,
                         *_bidirectional_dijkstra(XG, 's', 'v', ignore_edges=[('s', 'x')]))
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_dijkstra,
        XG,
        's', 'v',
        ignore_nodes=['u'],
        ignore_edges=[('s', 'x')],
    )
    validate_length_path(XG3, 0, 3, 15, *_bidirectional_dijkstra(XG3, 0, 3))
    validate_length_path(XG3, 0, 3, 16,
                         *_bidirectional_dijkstra(XG3, 0, 3, ignore_nodes=[1]))
    validate_length_path(XG3, 0, 3, 16,
                         *_bidirectional_dijkstra(XG3, 0, 3, ignore_edges=[(2, 3)]))
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_dijkstra,
        XG3,
        0, 3,
        ignore_nodes=[1],
        ignore_edges=[(5, 4)],
    )


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


def test_bidirectional_dijkstra_ignore():
    G = nx.Graph()
    nx.add_path(G, [1, 2, 10])
    nx.add_path(G, [1, 3, 10])
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_dijkstra,
        G,
        1, 2,
        ignore_nodes=[1],
    )
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_dijkstra,
        G,
        1, 2,
        ignore_nodes=[2],
    )
    assert_raises(
        nx.NetworkXNoPath,
        _bidirectional_dijkstra,
        G,
        1, 2,
        ignore_nodes=[1, 2],
    )
