text: import random
  
  import pytest
  
  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
  from networkx.utils import pairwise
  
  
  class TestIsSimplePath:
      """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 not 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 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 not nx.is_simple_path(G, ["not a node"])
  
      def test_simple_path(self):
          G = nx.path_graph(2)
          assert nx.is_simple_path(G, [0, 1])
  
      def test_non_simple_path(self):
          G = nx.path_graph(2)
          assert not nx.is_simple_path(G, [0, 1, 0])
  
      def test_cycle(self):
          G = nx.cycle_graph(3)
          assert not nx.is_simple_path(G, [0, 1, 2, 0])
  
      def test_missing_node(self):
          G = nx.path_graph(2)
          assert not nx.is_simple_path(G, [0, 2])
  
      def test_directed_path(self):
          G = nx.DiGraph([(0, 1), (1, 2)])
          assert nx.is_simple_path(G, [0, 1, 2])
  
      def test_directed_non_path(self):
          G = nx.DiGraph([(0, 1), (1, 2)])
          assert not nx.is_simple_path(G, [2, 1, 0])
  
      def test_directed_cycle(self):
          G = nx.DiGraph([(0, 1), (1, 2), (2, 0)])
          assert not nx.is_simple_path(G, [0, 1, 2, 0])
  
      def test_multigraph(self):
          G = nx.MultiGraph([(0, 1), (0, 1)])
          assert nx.is_simple_path(G, [0, 1])
  
      def test_multidigraph(self):
          G = nx.MultiDiGraph([(0, 1), (0, 1), (1, 0), (1, 0)])
          assert 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 {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 {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 {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 {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 {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 {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 {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 {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 list(paths) == []
  
  
  def test_all_simple_paths_cutoff():
      G = nx.complete_graph(4)
      paths = nx.all_simple_paths(G, 0, 1, cutoff=1)
      assert {tuple(p) for p in paths} == {(0, 1)}
      paths = nx.all_simple_paths(G, 0, 1, cutoff=2)
      assert {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 {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 {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 {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 list(paths) == []
      nx.add_path(G, [3, 1, 10, 2])
      paths = list(nx.all_simple_paths(G, 1, 2))
      assert len(paths) == 3
      assert {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 len(paths) == 2
      assert {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 {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 list(paths) == []
  
  
  def test_all_simple_paths_corner_cases():
      assert list(nx.all_simple_paths(nx.empty_graph(2), 0, 0)) == []
      assert list(nx.all_simple_paths(nx.empty_graph(2), 0, 1)) == []
      assert 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]) - {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 sorted(paths) == sorted(exact)
  
  
  def test_cutoff_zero():
      G = nx.complete_graph(4)
      paths = nx.all_simple_paths(G, 0, 3, cutoff=0)
      assert list(list(p) for p in paths) == []
      paths = nx.all_simple_paths(nx.MultiGraph(G), 0, 3, cutoff=0)
      assert list(list(p) for p in paths) == []
  
  
  def test_source_missing():
      with pytest.raises(nx.NodeNotFound):
          G = nx.Graph()
          nx.add_path(G, [1, 2, 3])
          list(nx.all_simple_paths(nx.MultiGraph(G), 0, 3))
  
  
  def test_target_missing():
      with pytest.raises(nx.NodeNotFound):
          G = nx.Graph()
          nx.add_path(G, [1, 2, 3])
          list(nx.all_simple_paths(nx.MultiGraph(G), 1, 4))
  
  
  # Tests for all_simple_edge_paths
  def test_all_simple_edge_paths():
      G = nx.path_graph(4)
      paths = nx.all_simple_edge_paths(G, 0, 3)
      assert {tuple(p) for p in paths} == {((0, 1), (1, 2), (2, 3))}
  
  
  def test_all_simple_edge_paths_with_two_targets_emits_two_paths():
      G = nx.path_graph(4)
      G.add_edge(2, 4)
      paths = nx.all_simple_edge_paths(G, 0, [3, 4])
      assert {tuple(p) for p in paths} == {
          ((0, 1), (1, 2), (2, 3)),
          ((0, 1), (1, 2), (2, 4)),
      }
  
  
  def test_digraph_all_simple_edge_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_edge_paths(G, 0, [3, 4])
      assert {tuple(p) for p in paths} == {
          ((0, 1), (1, 2), (2, 3)),
          ((0, 1), (1, 2), (2, 4)),
      }
  
  
  def test_all_simple_edge_paths_with_two_targets_cutoff():
      G = nx.path_graph(4)
      G.add_edge(2, 4)
      paths = nx.all_simple_edge_paths(G, 0, [3, 4], cutoff=3)
      assert {tuple(p) for p in paths} == {
          ((0, 1), (1, 2), (2, 3)),
          ((0, 1), (1, 2), (2, 4)),
      }
  
  
  def test_digraph_all_simple_edge_paths_with_two_targets_cutoff():
      G = nx.path_graph(4, create_using=nx.DiGraph())
      G.add_edge(2, 4)
      paths = nx.all_simple_edge_paths(G, 0, [3, 4], cutoff=3)
      assert {tuple(p) for p in paths} == {
          ((0, 1), (1, 2), (2, 3)),
          ((0, 1), (1, 2), (2, 4)),
      }
  
  
  def test_all_simple_edge_paths_with_two_targets_in_line_emits_two_paths():
      G = nx.path_graph(4)
      paths = nx.all_simple_edge_paths(G, 0, [2, 3])
      assert {tuple(p) for p in paths} == {((0, 1), (1, 2)), ((0, 1), (1, 2), (2, 3))}
  
  
  def test_all_simple_edge_paths_ignores_cycle():
      G = nx.cycle_graph(3, create_using=nx.DiGraph())
      G.add_edge(1, 3)
      paths = nx.all_simple_edge_paths(G, 0, 3)
      assert {tuple(p) for p in paths} == {((0, 1), (1, 3))}
  
  
  def test_all_simple_edge_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_edge_paths(G, 0, [2, 3])
      assert {tuple(p) for p in paths} == {((0, 1), (1, 2)), ((0, 1), (1, 3))}
  
  
  def test_all_simple_edge_paths_source_target():
      G = nx.path_graph(4)
      paths = nx.all_simple_edge_paths(G, 1, 1)
      assert list(paths) == []
  
  
  def test_all_simple_edge_paths_cutoff():
      G = nx.complete_graph(4)
      paths = nx.all_simple_edge_paths(G, 0, 1, cutoff=1)
      assert {tuple(p) for p in paths} == {((0, 1),)}
      paths = nx.all_simple_edge_paths(G, 0, 1, cutoff=2)
      assert {tuple(p) for p in paths} == {((0, 1),), ((0, 2), (2, 1)), ((0, 3), (3, 1))}
  
  
  def test_all_simple_edge_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_edge_paths(G, 1, [2, 3])
      assert {tuple(p) for p in paths} == {
          ((1, 2),),
          ((1, 3), (3, 4), (4, 2)),
          ((1, 5), (5, 4), (4, 2)),
          ((1, 3),),
          ((1, 2), (2, 3)),
          ((1, 5), (5, 4), (4, 3)),
          ((1, 5), (5, 4), (4, 2), (2, 3)),
      }
      paths = nx.all_simple_edge_paths(G, 1, [2, 3], cutoff=3)
      assert {tuple(p) for p in paths} == {
          ((1, 2),),
          ((1, 3), (3, 4), (4, 2)),
          ((1, 5), (5, 4), (4, 2)),
          ((1, 3),),
          ((1, 2), (2, 3)),
          ((1, 5), (5, 4), (4, 3)),
      }
      paths = nx.all_simple_edge_paths(G, 1, [2, 3], cutoff=2)
      assert {tuple(p) for p in paths} == {((1, 2),), ((1, 3),), ((1, 2), (2, 3))}
  
  
  def test_all_simple_edge_paths_multigraph():
      G = nx.MultiGraph([(1, 2), (1, 2)])
      paths = nx.all_simple_edge_paths(G, 1, 1)
      assert list(paths) == []
      nx.add_path(G, [3, 1, 10, 2])
      paths = list(nx.all_simple_edge_paths(G, 1, 2))
      assert len(paths) == 3
      assert {tuple(p) for p in paths} == {
          ((1, 2, 0),),
          ((1, 2, 1),),
          ((1, 10, 0), (10, 2, 0)),
      }
  
  
  def test_all_simple_edge_paths_multigraph_with_cutoff():
      G = nx.MultiGraph([(1, 2), (1, 2), (1, 10), (10, 2)])
      paths = list(nx.all_simple_edge_paths(G, 1, 2, cutoff=1))
      assert len(paths) == 2
      assert {tuple(p) for p in paths} == {((1, 2, 0),), ((1, 2, 1),)}
  
  
  def test_all_simple_edge_paths_directed():
      G = nx.DiGraph()
      nx.add_path(G, [1, 2, 3])
      nx.add_path(G, [3, 2, 1])
      paths = nx.all_simple_edge_paths(G, 1, 3)
      assert {tuple(p) for p in paths} == {((1, 2), (2, 3))}
  
  
  def test_all_simple_edge_paths_empty():
      G = nx.path_graph(4)
      paths = nx.all_simple_edge_paths(G, 0, 3, cutoff=2)
      assert list(paths) == []
  
  
  def test_all_simple_edge_paths_corner_cases():
      assert list(nx.all_simple_edge_paths(nx.empty_graph(2), 0, 0)) == []
      assert list(nx.all_simple_edge_paths(nx.empty_graph(2), 0, 1)) == []
      assert list(nx.all_simple_edge_paths(nx.path_graph(9), 0, 8, 0)) == []
  
  
  def hamiltonian_edge_path(G, source):
      source = arbitrary_element(G)
      neighbors = set(G[source]) - {source}
      n = len(G)
      for target in neighbors:
          for path in nx.all_simple_edge_paths(G, source, target):
              if len(path) == n - 1:
                  yield path
  
  
  def test_hamiltonian__edge_path():
      from itertools import permutations
  
      G = nx.complete_graph(4)
      paths = hamiltonian_edge_path(G, 0)
      exact = [list(pairwise([0] + list(p))) for p in permutations([1, 2, 3], 3)]
      assert sorted(exact) == [p for p in sorted(paths)]
  
  
  def test_edge_cutoff_zero():
      G = nx.complete_graph(4)
      paths = nx.all_simple_edge_paths(G, 0, 3, cutoff=0)
      assert list(list(p) for p in paths) == []
      paths = nx.all_simple_edge_paths(nx.MultiGraph(G), 0, 3, cutoff=0)
      assert list(list(p) for p in paths) == []
  
  
  def test_edge_source_missing():
      with pytest.raises(nx.NodeNotFound):
          G = nx.Graph()
          nx.add_path(G, [1, 2, 3])
          list(nx.all_simple_edge_paths(nx.MultiGraph(G), 0, 3))
  
  
  def test_edge_target_missing():
      with pytest.raises(nx.NodeNotFound):
          G = nx.Graph()
          nx.add_path(G, [1, 2, 3])
          list(nx.all_simple_edge_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 next(paths) == [1, 2, 3, 4, 8, 12]
      assert next(paths) == [1, 5, 6, 7, 8, 12]
      assert [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 [path for path in paths] == [[0, 1, 2, 3]]
  
  
  def test_shortest_simple_paths_directed_with_weight_fucntion():
      def cost(u, v, x):
          return 1
  
      G = cnlti(nx.grid_2d_graph(4, 4), first_label=1, ordering="sorted")
      paths = nx.shortest_simple_paths(G, 1, 12)
      assert next(paths) == [1, 2, 3, 4, 8, 12]
      assert next(paths) == [1, 5, 6, 7, 8, 12]
      assert [
          len(path) for path in nx.shortest_simple_paths(G, 1, 12, weight=cost)
      ] == sorted([len(path) for path in nx.all_simple_paths(G, 1, 12)])
  
  
  def test_shortest_simple_paths_with_weight_fucntion():
      def cost(u, v, x):
          return 1
  
      G = nx.cycle_graph(7, create_using=nx.DiGraph())
      paths = nx.shortest_simple_paths(G, 0, 3, weight=cost)
      assert [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 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 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 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 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 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 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 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 paths == solution
  
  
  def test_ssp_source_missing():
      with pytest.raises(nx.NodeNotFound):
          G = nx.Graph()
          nx.add_path(G, [1, 2, 3])
          list(nx.shortest_simple_paths(G, 0, 3))
  
  
  def test_ssp_target_missing():
      with pytest.raises(nx.NodeNotFound):
          G = nx.Graph()
          nx.add_path(G, [1, 2, 3])
          list(nx.shortest_simple_paths(G, 1, 4))
  
  
  def test_ssp_multigraph():
      with pytest.raises(nx.NetworkXNotImplemented):
          G = nx.MultiGraph()
          nx.add_path(G, [1, 2, 3])
          list(nx.shortest_simple_paths(G, 1, 4))
  
  
  def test_ssp_source_missing2():
      with pytest.raises(nx.NetworkXNoPath):
          G = nx.Graph()
          nx.add_path(G, [0, 1, 2])
          nx.add_path(G, [3, 4, 5])
          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 path == [0, 1, 2, 3]
      length, path = _bidirectional_shortest_path(cycle, 0, 3, ignore_nodes=[1])
      assert 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 path in [[1, 0, 3], [1, 2, 3]]
      length, path = _bidirectional_shortest_path(wheel, 1, 3, ignore_nodes=[0])
      assert path == [1, 2, 3]
      length, path = _bidirectional_shortest_path(wheel, 1, 3, ignore_nodes=[0, 2])
      assert path == [1, 5, 4, 3]
      length, path = _bidirectional_shortest_path(
          wheel, 1, 3, ignore_edges=[(1, 0), (5, 0), (2, 3)]
      )
      assert 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 path == [0, 1, 2, 3]
      pytest.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 path == [0, 1, 2, 3]
      pytest.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])
      pytest.raises(
          nx.NetworkXNoPath, _bidirectional_shortest_path, G, 1, 2, ignore_nodes=[1]
      )
      pytest.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])
      pytest.raises(
          nx.NetworkXNoPath, _bidirectional_shortest_path, G, 1, 2, ignore_nodes=[1, 2]
      )
  
  
  def validate_path(G, s, t, soln_len, path):
      assert path[0] == s
      assert path[-1] == t
      assert 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 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")])
      )
      pytest.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)])
      )
      pytest.raises(
          nx.NetworkXNoPath,
          _bidirectional_dijkstra,
          XG3,
          0,
          3,
          ignore_nodes=[1],
          ignore_edges=[(5, 4)],
      )
  
  
  def test_bidirectional_dijkstra_no_path():
      with pytest.raises(nx.NetworkXNoPath):
          G = nx.Graph()
          nx.add_path(G, [1, 2, 3])
          nx.add_path(G, [4, 5, 6])
          _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])
      pytest.raises(nx.NetworkXNoPath, _bidirectional_dijkstra, G, 1, 2, ignore_nodes=[1])
      pytest.raises(nx.NetworkXNoPath, _bidirectional_dijkstra, G, 1, 2, ignore_nodes=[2])
      pytest.raises(
          nx.NetworkXNoPath, _bidirectional_dijkstra, G, 1, 2, ignore_nodes=[1, 2]
      )
  