import pytest

from math import sqrt

import networkx as nx
from networkx.utils import pairwise


def dist(a, b):
    """Returns the Euclidean distance between points `a` and `b`."""
    return sqrt(sum((x1 - x2) ** 2 for x1, x2 in zip(a, b)))


class TestAStar:

    @classmethod
    def setup_class(cls):
        edges = [('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)]
        cls.XG = nx.DiGraph()
        cls.XG.add_weighted_edges_from(edges)

    def test_multiple_optimal_paths(self):
        """Tests that A* algorithm finds any of multiple optimal paths"""
        heuristic_values = {"a": 1.35, "b": 1.18, "c": 0.67, "d": 0}

        def h(u, v):
            return heuristic_values[u]

        graph = nx.Graph()
        points = ["a", "b", "c", "d"]
        edges = [("a", "b", 0.18), ("a", "c", 0.68),
                 ("b", "c", 0.50), ("c", "d", 0.67)]

        graph.add_nodes_from(points)
        graph.add_weighted_edges_from(edges)

        path1 = ["a", "c", "d"]
        path2 = ["a", "b", "c", "d"]
        assert nx.astar_path(graph, "a", "d", h) in (path1, path2)

    def test_astar_directed(self):
        assert nx.astar_path(self.XG, 's', 'v') == ['s', 'x', 'u', 'v']
        assert nx.astar_path_length(self.XG, 's', 'v') == 9

    def test_astar_multigraph(self):
        G = nx.MultiDiGraph(self.XG)
        pytest.raises(nx.NetworkXNotImplemented, nx.astar_path, G, 's', 'v')
        pytest.raises(nx.NetworkXNotImplemented, nx.astar_path_length,
                      G, 's', 'v')

    def test_astar_undirected(self):
        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
        GG['y']['v']['weight'] = 2
        assert nx.astar_path(GG, 's', 'v') == ['s', 'x', 'u', 'v']
        assert nx.astar_path_length(GG, 's', 'v') == 8

    def test_astar_directed2(self):
        XG2 = nx.DiGraph()
        edges = [(1, 4, 1), (4, 5, 1), (5, 6, 1), (6, 3, 1), (1, 3, 50),
                 (1, 2, 100), (2, 3, 100)]
        XG2.add_weighted_edges_from(edges)
        assert nx.astar_path(XG2, 1, 3) == [1, 4, 5, 6, 3]

    def test_astar_undirected2(self):
        XG3 = nx.Graph()
        edges = [(0, 1, 2), (1, 2, 12), (2, 3, 1), (3, 4, 5), (4, 5, 1),
                 (5, 0, 10)]
        XG3.add_weighted_edges_from(edges)
        assert nx.astar_path(XG3, 0, 3) == [0, 1, 2, 3]
        assert nx.astar_path_length(XG3, 0, 3) == 15

    def test_astar_undirected3(self):
        XG4 = nx.Graph()
        edges = [(0, 1, 2), (1, 2, 2), (2, 3, 1), (3, 4, 1), (4, 5, 1),
                 (5, 6, 1), (6, 7, 1), (7, 0, 1)]
        XG4.add_weighted_edges_from(edges)
        assert nx.astar_path(XG4, 0, 2) == [0, 1, 2]
        assert nx.astar_path_length(XG4, 0, 2) == 4

    """ Tests that A* finds correct path when multiple paths exist
        and the best one is not expanded first (GH issue #3464)
    """
    def test_astar_directed3(self):
        heuristic_values = {"n5": 36, "n2": 4, "n1": 0, "n0": 0}

        def h(u, v):
            return heuristic_values[u]

        edges = [("n5", "n1", 11), ("n5", "n2", 9),
                 ("n2", "n1", 1), ("n1", "n0", 32)]
        graph = nx.DiGraph()
        graph.add_weighted_edges_from(edges)
        answer = ["n5", "n2", "n1", "n0"]
        assert nx.astar_path(graph, "n5", "n0", h) == answer

    """ Tests that that parent is not wrongly overridden when a
        node is re-explored multiple times.
    """
    def test_astar_directed4(self):
        edges = [("a", "b", 1), ("a", "c", 1), ("b", "d", 2),
                 ("c", "d", 1), ("d", "e", 1)]
        graph = nx.DiGraph()
        graph.add_weighted_edges_from(edges)
        assert nx.astar_path(graph, "a", "e") == ["a", "c", "d", "e"]

# >>> MXG4=NX.MultiGraph(XG4)
# >>> MXG4.add_edge(0,1,3)
# >>> NX.dijkstra_path(MXG4,0,2)
# [0, 1, 2]

    def test_astar_w1(self):
        G = nx.DiGraph()
        G.add_edges_from([('s', 'u'), ('s', 'x'), ('u', 'v'), ('u', 'x'),
                          ('v', 'y'), ('x', 'u'), ('x', 'w'), ('w', 'v'),
                          ('x', 'y'), ('y', 's'), ('y', 'v')])
        assert nx.astar_path(G, 's', 'v') == ['s', 'u', 'v']
        assert nx.astar_path_length(G, 's', 'v') == 2

    def test_astar_nopath(self):
        with pytest.raises(nx.NodeNotFound):
            nx.astar_path(self.XG, 's', 'moon')

    def test_cycle(self):
        C = nx.cycle_graph(7)
        assert nx.astar_path(C, 0, 3) == [0, 1, 2, 3]
        assert nx.dijkstra_path(C, 0, 4) == [0, 6, 5, 4]

    def test_unorderable_nodes(self):
        """Tests that A* accommodates nodes that are not orderable.

        For more information, see issue #554.

        """
        # TODO In Python 3, instances of the `object` class are
        # unorderable by default, so we wouldn't need to define our own
        # class here, we could just instantiate an instance of the
        # `object` class. However, we still support Python 2; when
        # support for Python 2 is dropped, this test can be simplified
        # by replacing `Unorderable()` by `object()`.
        class Unorderable(object):

            def __le__(self):
                raise NotImplemented

            def __ge__(self):
                raise NotImplemented

        # Create the cycle graph on four nodes, with nodes represented
        # as (unorderable) Python objects.
        nodes = [Unorderable() for n in range(4)]
        G = nx.Graph()
        G.add_edges_from(pairwise(nodes, cyclic=True))
        path = nx.astar_path(G, nodes[0], nodes[2])
        assert len(path) == 3