import itertools
from nose.tools import assert_equal, assert_true, assert_false, assert_raises
import networkx as nx

from networkx.algorithms.flow import (edmonds_karp, preflow_push,
    shortest_augmenting_path) 

flow_funcs = [edmonds_karp, preflow_push, shortest_augmenting_path]

# connectivity functions not imported to the base namespace
from networkx.algorithms.connectivity import (local_edge_connectivity,
    local_node_connectivity)


msg = "Assertion failed in function: {0}"

# helper functions for tests
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."
                raise Exception(msg % max_attempts)
            else:
                attempts += 1


def test_average_connectivity():
    # figure 1 from:
    # Beineke, L., O. Oellermann, and R. Pippert (2002). The average 
    # connectivity of a graph. Discrete mathematics 252(1-3), 31-45
    # http://www.sciencedirect.com/science/article/pii/S0012365X01001807
    G1 = nx.path_graph(3)
    G1.add_edges_from([(1, 3),(1, 4)])
    G2 = nx.path_graph(3)
    G2.add_edges_from([(1, 3),(1, 4),(0, 3),(0, 4),(3, 4)])
    G3 = nx.Graph()
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        assert_equal(nx.average_node_connectivity(G1, **kwargs), 1,
                     msg=msg.format(flow_func.__name__))
        assert_equal(nx.average_node_connectivity(G2, **kwargs), 2.2,
                     msg=msg.format(flow_func.__name__))
        assert_equal(nx.average_node_connectivity(G3, **kwargs), 0,
                     msg=msg.format(flow_func.__name__))

def test_average_connectivity_directed():
    G = nx.DiGraph([(1,3),(1,4),(1,5)])
    for flow_func in flow_funcs:
        assert_equal(nx.average_node_connectivity(G), 0.25,
                     msg=msg.format(flow_func.__name__))

def test_articulation_points():
    Ggen = _generate_no_biconnected()
    for flow_func in flow_funcs:
        for i in range(3):
            G = next(Ggen)
            assert_equal(nx.node_connectivity(G, flow_func=flow_func), 1,
                         msg=msg.format(flow_func.__name__))

def test_brandes_erlebach():
    # Figure 1 chapter 7: Connectivity
    # http://www.informatik.uni-augsburg.de/thi/personen/kammer/Graph_Connectivity.pdf
    G = nx.Graph()
    G.add_edges_from([(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 6), (3, 4),
                      (3, 6), (4, 6), (4, 7), (5, 7), (6, 8), (6, 9), (7, 8),
                      (7, 10), (8, 11), (9, 10), (9, 11), (10, 11)])
    for flow_func in flow_funcs:
        kwargs = dict(flow_func=flow_func)
        assert_equal(3, local_edge_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, local_node_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.node_connectivity(G, 1, 11, **kwargs),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.edge_connectivity(G, **kwargs), # node 5 has degree 2
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.node_connectivity(G, **kwargs),
                     msg=msg.format(flow_func.__name__))

def test_white_harary_1():
    # Figure 1b white and harary (2001)
    # # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
    # A graph with high adhesion (edge connectivity) and low cohesion
    # (vertex connectivity)
    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
    G.remove_node(7)
    for i in range(4, 7):
        G.add_edge(0, i)
    G = nx.disjoint_union(G, nx.complete_graph(4))
    G.remove_node(G.order() - 1)
    for i in range(7, 10):
        G.add_edge(0, i)
    for flow_func in flow_funcs:
        assert_equal(1, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))

def test_white_harary_2():
    # Figure 8 white and harary (2001)
    # # http://eclectic.ss.uci.edu/~drwhite/sm-w23.PDF
    G = nx.disjoint_union(nx.complete_graph(4), nx.complete_graph(4))
    G.add_edge(0, 4)
    # kappa <= lambda <= delta
    assert_equal(3, min(nx.core_number(G).values()))
    for flow_func in flow_funcs:
        assert_equal(1, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(1, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))

def test_complete_graphs():
    for n in range(5, 20, 5):
        for flow_func in flow_funcs:
            G = nx.complete_graph(n)
            assert_equal(n-1, nx.node_connectivity(G, flow_func=flow_func),
                         msg=msg.format(flow_func.__name__))
            assert_equal(n-1, nx.node_connectivity(G.to_directed(),
                                                   flow_func=flow_func),
                         msg=msg.format(flow_func.__name__))
            assert_equal(n-1, nx.edge_connectivity(G, flow_func=flow_func),
                         msg=msg.format(flow_func.__name__))
            assert_equal(n-1, nx.edge_connectivity(G.to_directed(),
                                                   flow_func=flow_func),
                         msg=msg.format(flow_func.__name__))

def test_empty_graphs():
    for k in range(5, 25, 5):
        G = nx.empty_graph(k)
        for flow_func in flow_funcs:
            assert_equal(0, nx.node_connectivity(G, flow_func=flow_func),
                         msg=msg.format(flow_func.__name__))
            assert_equal(0, nx.edge_connectivity(G, flow_func=flow_func),
                         msg=msg.format(flow_func.__name__))

def test_petersen():
    G = nx.petersen_graph()
    for flow_func in flow_funcs:
        assert_equal(3, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))

def test_tutte():
    G = nx.tutte_graph()
    for flow_func in flow_funcs:
        assert_equal(3, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))

def test_dodecahedral():
    G = nx.dodecahedral_graph()
    for flow_func in flow_funcs:
        assert_equal(3, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(3, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))

def test_octahedral():
    G=nx.octahedral_graph()
    for flow_func in flow_funcs:
        assert_equal(4, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(4, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))

def test_icosahedral():
    G=nx.icosahedral_graph()
    for flow_func in flow_funcs:
        assert_equal(5, nx.node_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(5, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))

def test_missing_source():
    G = nx.path_graph(4)
    for flow_func in flow_funcs:
        assert_raises(nx.NetworkXError, nx.node_connectivity, G, 10, 1,
                      flow_func=flow_func)

def test_missing_target():
    G = nx.path_graph(4)
    for flow_func in flow_funcs:
        assert_raises(nx.NetworkXError, nx.node_connectivity, G, 1, 10,
                      flow_func=flow_func)

def test_edge_missing_source():
    G = nx.path_graph(4)
    for flow_func in flow_funcs:
        assert_raises(nx.NetworkXError, nx.edge_connectivity, G, 10, 1,
                      flow_func=flow_func)

def test_edge_missing_target():
    G = nx.path_graph(4)
    for flow_func in flow_funcs:
        assert_raises(nx.NetworkXError, nx.edge_connectivity, G, 1, 10,
                      flow_func=flow_func)

def test_not_weakly_connected():
    G = nx.DiGraph()
    G.add_path([1, 2, 3])
    G.add_path([4, 5])
    for flow_func in flow_funcs:
        assert_equal(nx.node_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__))
        assert_equal(nx.edge_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__))

def test_not_connected():
    G = nx.Graph()
    G.add_path([1, 2, 3])
    G.add_path([4, 5])
    for flow_func in flow_funcs:
        assert_equal(nx.node_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__))
        assert_equal(nx.edge_connectivity(G), 0,
                     msg=msg.format(flow_func.__name__))

def test_directed_edge_connectivity():
    G = nx.cycle_graph(10, create_using=nx.DiGraph()) # only one direction
    D = nx.cycle_graph(10).to_directed() # 2 reciprocal edges
    for flow_func in flow_funcs:
        assert_equal(1, nx.edge_connectivity(G, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(1, local_edge_connectivity(G, 1, 4, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(1, nx.edge_connectivity(G, 1, 4, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.edge_connectivity(D, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, local_edge_connectivity(D, 1, 4, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))
        assert_equal(2, nx.edge_connectivity(D, 1, 4, flow_func=flow_func),
                     msg=msg.format(flow_func.__name__))

def test_cutoff():
    G = nx.complete_graph(5)
    for local_func in [local_edge_connectivity, local_node_connectivity]:
        for flow_func in flow_funcs:
            if flow_func is preflow_push:
                # cutoff is not supported by preflow_push
                continue
            for cutoff in [3, 2, 1]:
                result = local_func(G, 0, 4, flow_func=flow_func, cutoff=cutoff)
                assert_equal(cutoff, result,
                             msg="cutoff error in {0}".format(flow_func.__name__))

def test_invalid_auxiliary():
    G = nx.complete_graph(5)
    assert_raises(nx.NetworkXError, local_node_connectivity, G, 0, 3,
                  auxiliary=G)

def test_interface_only_source():
    G = nx.complete_graph(5)
    for interface_func in [nx.node_connectivity, nx.edge_connectivity]:
        assert_raises(nx.NetworkXError, interface_func, G, s=0)

def test_interface_only_target():
    G = nx.complete_graph(5)
    for interface_func in [nx.node_connectivity, nx.edge_connectivity]:
        assert_raises(nx.NetworkXError, interface_func, G, t=3)

def test_edge_connectivity_flow_vs_stoer_wagner():
    graph_funcs = [
        nx.icosahedral_graph,
        nx.octahedral_graph,
        nx.dodecahedral_graph,
    ]
    for graph_func in graph_funcs:
        G = graph_func()
        assert_equal(nx.stoer_wagner(G)[0], nx.edge_connectivity(G))


class TestAllPairsNodeConnectivity:

    def setUp(self):
        self.path = nx.path_graph(7)
        self.directed_path = nx.path_graph(7, create_using=nx.DiGraph())
        self.cycle = nx.cycle_graph(7)
        self.directed_cycle = nx.cycle_graph(7, create_using=nx.DiGraph())
        self.gnp = nx.gnp_random_graph(30, 0.1)
        self.directed_gnp = nx.gnp_random_graph(30, 0.1, directed=True)
        self.K20 = nx.complete_graph(20)
        self.K10 = nx.complete_graph(10)
        self.K5 = nx.complete_graph(5)
        self.G_list = [self.path, self.directed_path, self.cycle,
            self.directed_cycle, self.gnp, self.directed_gnp, self.K10,
            self.K5, self.K20]

    def test_cycles(self):
        K_undir = nx.all_pairs_node_connectivity(self.cycle)
        for source in K_undir:
            for target, k in K_undir[source].items():
                assert_true(k == 2)
        K_dir = nx.all_pairs_node_connectivity(self.directed_cycle)
        for source in K_dir:
            for target, k in K_dir[source].items():
                assert_true(k == 1)

    def test_complete(self):
        for G in [self.K10, self.K5, self.K20]:
            K = nx.all_pairs_node_connectivity(G)
            for source in K:
                for target, k in K[source].items():
                    assert_true(k == len(G)-1)

    def test_paths(self):
        K_undir = nx.all_pairs_node_connectivity(self.path)
        for source in K_undir:
            for target, k in K_undir[source].items():
                assert_true(k == 1)
        K_dir = nx.all_pairs_node_connectivity(self.directed_path)
        for source in K_dir:
            for target, k in K_dir[source].items():
                if source < target:
                    assert_true(k == 1)
                else:
                    assert_true(k == 0)

    def test_all_pairs_connectivity_nbunch(self):
        G = nx.complete_graph(5)
        nbunch = [0, 2, 3]
        C = nx.all_pairs_node_connectivity(G, nbunch=nbunch)
        assert_equal(len(C), len(nbunch))

    def test_all_pairs_connectivity_icosahedral(self):
        G = nx.icosahedral_graph()
        C = nx.all_pairs_node_connectivity(G)
        assert_true(all(5 == C[u][v] for u, v in itertools.combinations(G, 2)))

    def test_all_pairs_connectivity(self):
        G = nx.Graph()
        nodes = [0, 1, 2, 3]
        G.add_path(nodes)
        A = {n: {} for n in G}
        for u, v in itertools.combinations(nodes,2):
            A[u][v] = A[v][u] = nx.node_connectivity(G, u, v)
        C = nx.all_pairs_node_connectivity(G)
        assert_equal(sorted((k, sorted(v)) for k, v in A.items()),
                     sorted((k, sorted(v)) for k, v in C.items()))

    def test_all_pairs_connectivity_directed(self):
        G = nx.DiGraph()
        nodes = [0, 1, 2, 3]
        G.add_path(nodes)
        A = {n: {} for n in G}
        for u, v in itertools.permutations(nodes, 2):
            A[u][v] = nx.node_connectivity(G, u, v)
        C = nx.all_pairs_node_connectivity(G)
        assert_equal(sorted((k, sorted(v)) for k, v in A.items()),
                     sorted((k, sorted(v)) for k, v in C.items()))

    def test_all_pairs_connectivity_nbunch(self):
        G = nx.complete_graph(5)
        nbunch = [0, 2, 3]
        A = {n: {} for n in nbunch}
        for u, v in itertools.combinations(nbunch, 2):
            A[u][v] = A[v][u] = nx.node_connectivity(G, u, v)
        C = nx.all_pairs_node_connectivity(G, nbunch=nbunch)
        assert_equal(sorted((k, sorted(v)) for k, v in A.items()),
                     sorted((k, sorted(v)) for k, v in C.items()))

    def test_all_pairs_connectivity_nbunch_iter(self):
        G = nx.complete_graph(5)
        nbunch = [0, 2, 3]
        A = {n: {} for n in nbunch}
        for u, v in itertools.combinations(nbunch, 2):
            A[u][v] = A[v][u] = nx.node_connectivity(G, u, v)
        C = nx.all_pairs_node_connectivity(G, nbunch=iter(nbunch))
        assert_equal(sorted((k, sorted(v)) for k, v in A.items()),
                     sorted((k, sorted(v)) for k, v in C.items()))
