Python Graph.build方法代码示例

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
    def test_bellman_ford_with_non_negative_cycle(self):
        """ Given the following graph from the lecture:
                  -2
            (a)-------->(b)
            ^|           |
             |           |
             4\       -1/
               \       /
                \(c)</
                 /  \
               2/    \-3
              v/      \v
             (x)       (y)
              \^       /^
               \      /
               1\    /-4
                 \  /
                 (z)
        And and a vertex (s) that is connected to all other vertices through
        edges of cost 0.
        """
        g = Graph.build(edges=[('a', 'b', -2), ('c', 'a', 4), ('b', 'c', -1),
                ('c', 'x', 2), ('c', 'y', -3), ('z', 'x', 1), ('z', 'y', -4)],
                directed=True)
        g.add_vertex('s')
        for vertex in g.get_vertices():
            g.add_edge(('s', vertex, 0))

        (costs, __) = shortest_path(g, 's', return_paths=False)
        expected_costs = {'a': 0, 'c': -3, 'b': -2, 's': 0,'y': -6, 'x': -1,'z': 0}
        self.assertEqual(costs, expected_costs,
            'should produce the correct costs')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
def kruskal_union_find_mst(graph):
    """ Uses Kruskel's greedy algorithm to compute the MST of graph.

    Running time: O(m*log n) - where m is the number of edges and n is the
        number of vertices.

    Params:
        graph: object, instance of src.graph.Graph

    Returns:
        object, src.graph.Graph instance reperesenting the MST.
    """
    mst_edges = []
    edges = graph.get_edges()
    num_vertices = len(graph.get_vertices())

    edges = graph.get_edges()
    edges.sort(key=lambda e: e[2])

    union_find = UnionFind()

    index = 0
    while index < num_vertices:
        edge = edges[index]
        [tail, head, value] = graph.split_edge(edge)
        index += 1

        if union_find.find(head) == union_find.find(tail):
            continue
        else:
            union_find.union(head, tail)
        mst_edges.append(edge)

    mst = Graph.build(edges=mst_edges, directed=False)
    return mst

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
    def test_johnson(self):
        """ Given the following graph from the lecture:
                  -2
            (a)-------->(b)
            ^|           |
             |           |
             4\       -1/
               \       /
                \(c)</
                 /  \
               2/    \-3
              v/      \v
             (x)       (y)
              \^       /^
               \      /
               1\    /-4
                 \  /
                 (z)
        """
        g = Graph.build(edges=[('a', 'b', -2), ('c', 'a', 4), ('b', 'c', -1),
                ('c', 'x', 2), ('c', 'y', -3), ('z', 'x', 1), ('z', 'y', -4)],
                directed=True)

        actual = johnson(g)
        expected = {
            'a': {'a': 0, 'c': -3, 'b': -2, 'y': -6, 'x': -1, 'z': INF},
            'c': {'a': 4, 'c': 0, 'b': 2, 'y': -3, 'x': 2, 'z': INF},
            'b': {'a': 3, 'c': -1, 'b': 0, 'y': -4, 'x': 1, 'z': INF},
            'y': {'a': INF, 'c': INF, 'b': INF, 'y': 0, 'x': INF, 'z': INF},
            'x': {'a': INF, 'c': INF, 'b': INF, 'y': INF, 'x': 0, 'z': INF},
            'z': {'a': INF, 'c': INF, 'b': INF, 'y': -4, 'x': 1, 'z': 0}
        }
        self.assertEqual(actual, expected,
            'should return correct all pairs shortest path distances')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
    def test_scc(self):
        """ Given the following graph it computes SCCs in it.

             />(2)---------->(8)----------v
            /   |               \     /->(10)
          (1)   |                v  /      |
            ^\  v          /---->(9)<-\    v
              \(3)----->(4)            \-(11)
                 \      ^| \            /^
                  \    / |  v         /
                   >(5)  |   (7)----/
                      ^\ |   /
                        \v  v
                         (6)
        """
        g = Graph.build(edges=[(1,2), (3,2), (2,3), (3,4), (3,5), (5,4),
                               (4,6), (4,7), (7,6), (6,5), (4,9), (7, 11),
                               (11,9), (9,10), (10,11), (2,8), (8,9), (8,10)],
                        directed=True)
        connected_components = scc(g)
        expected = [[8], [1], [2, 3], [9, 10, 11], [4, 5, 6, 7]]

        self.assertEqual(len(connected_components), len(expected),
                'should return the same number of components')
        for component in connected_components:
            self.assertIn(component, expected,
                'should detect strongly connected components')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
    def test_shortest_path_heap_case3(self):
        """ Compute a shortest path using the heap implementation. """
        g = Graph.build(edges=[
            ('a','b',1),('a','c',4),('a','d',4),('b','c',1),('c','d',1)],
            directed=True)

        shortest_path = shortest_path_heap(g, 'a')
        self.assertEqual(shortest_path['d'], 3)

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
    def test_cluster_graph(self):
        """ The graph is specified in distances but it should look something
        like this:
        | *a
        |                                *e
        |                          *c
        |
        |
        |
        |
        |                          *d
        |                                *f
        | *b
        +--------------------------------------------->
        """
        g = Graph.build(edges=[
            ('a', 'e', 8), ('a', 'c', 7), ('a', 'd', 9), ('a', 'f', 10), ('a', 'b', 8),
            ('e', 'f', 6), ('e', 'd', 5), ('e', 'b', 10), ('e', 'c', 1),
            ('c', 'f', 5), ('c', 'd', 4), ('c', 'b', 9),
            ('d', 'f', 1), ('d', 'b', 7),
            ('f', 'b', 8)
        ], directed=False)

        (clusters, distances) = cluster_graph(g, 4)
        expectedClusters = {
            'a': ['a'],
            'c': ['c', 'e'],
            'b': ['b'],
            'd': ['d', 'f']
        }
        expectedDistances = {
            ('b', 'c'): 9,
            ('c', 'd'): 4,
            ('a', 'd'): 9,
            ('a', 'b'): 8,
            ('a', 'c'): 7,
            ('b', 'd'): 7
        }
        self.assertEqual(clusters, expectedClusters,
            'should return correct clusters')
        self.assertEqual(distances, expectedDistances,
            'should compute distances')

        (clusters, distances) = cluster_graph(g, 3)
        expectedClusters = {
            'a': ['a'],
            'b': ['b'],
            'c': ['c', 'e', 'd', 'f']
        }
        expectedDistances = {
            ('b', 'c'): 7,
            ('a', 'b'): 8,
            ('a', 'c'): 7
        }
        self.assertEqual(clusters, expectedClusters,
            'should return correct clusters')
        self.assertEqual(distances, expectedDistances,
            'should compute distances')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
def prims_heap_mst(graph):
    """ Computes minimal spanning tree using a heap data structure to store
    unexplored vertices.

    The difference is that it maintains the frontier of the explored MST in a
    heap, as such always computing the min vertex in O(logm), where m is the
    number of edges.

    The heap is used to store the vertices not the edges as in the previous
    implementation. The heap maintains two invariants:
    1. elements in the heap are vertices not yet explored
    2. keys under which each vertex is stored in the heap is the minimum weight
    of an edge incident on the vertex whose tail is already in the MST.

    Complexity: O(m*log n), m - number of edges, n - number of vertices

    Args:
        graph: object, data structure to hold the graph data.

    Returns:
        A Graph instance reperesenting the MST.
    """
    mst_vertices = []
    mst_edges = []
    INF = float('inf')
    vertices = graph.get_vertices()
    num_vertices = len(vertices)

    frontier = VertexHeap.heapify([(v, INF) for v in vertices])
    vertex = random.choice(graph.get_vertices())
    frontier.remove(vertex)

    # This dict stores for each vertex the neighbour with the smallest edge,
    # and the edge cost. Format {vertex: (incident_vertex, edge_cost)}
    vertices = {}

    while vertex:
        mst_vertices.append(vertex)
        if len(mst_vertices) == num_vertices:
            break

        for edge in graph.egress(vertex):
            [__, head, cost] = graph.split_edge(edge)
            if head not in mst_vertices:
                [__, head_key] = frontier.remove(head)
                min_cost = min(cost, head_key)
                frontier.insert((head, min_cost))
                if min_cost < head_key:
                    vertices[head] = (vertex, cost)

        # Extract the vertex with min cost and compute it's associated min edge.
        (head, __) = frontier.extract_min()
        (tail, cost) = vertices[head]
        mst_edges.append((tail, head, cost))
        vertex = head

    mst = Graph.build(edges=mst_edges, directed=False)
    return mst

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
    def test_contract(self):
        g = Graph.build(edges=[(1,2), (2,3), (3,1)])
        g = contract(g, (1,2))

        self.assertIn('1_2', g.table, '1 and 2 have fused')
        self.assertIn(3, g.table['1_2'], '1 and 2 have fused')
        self.assertIn(3, g.table, '1 and 2 have fused')
        self.assertIn('1_2', g.table[3], '1 and 2 have fused')
        self.assertNotIn(2, g.get_vertices(), 'no more 2 vertex')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
 def test_get_sync_vertices(self):
     """ Given the graph below it should find 1 and 2 as sync vertices:
     (1) <- (3)
            /
     (2) <-/
     """
     g = Graph.build(edges=[(3,1), (3,2)], directed=True)
     actual = get_sync_vertices(g)
     expected = [1, 2]
     self.assertEqual(actual, expected, 'found sync vertices')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
    def test_shortest_path_naive_case1(self):
        """ Compute a shortest path using the heap implementation. """
        g = Graph.build(edges=[
            ('a','c',3),('c','b',10),('a','b',15),('d','b',9),
            ('a','d',4),('d','f',7),('d','e',3),('e','g',1),
            ('e','f',5),('g','f',2),('f','b',1)],
            directed=True)

        shortest_path = shortest_path_naive(g, 'a')
        self.assertEqual(shortest_path['g'], 8)
        self.assertEqual(shortest_path['b'], 11)

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
 def test_randomized_cut(self):
     """ Tests that the following graph is split correctly.
     (a)--(c)
      |  / |
     (b)--(d)
     """
     g = Graph.build(edges = [('a', 'b'), ('a', 'c'),
                              ('b', 'c'), ('b', 'd'),
                              ('c', 'd')])
     compacted = randomized_cut(g)
     self.assertEqual(len(compacted.get_vertices()), 2,
             'should have compacted to only 2 vertices')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
 def test_topological_ordering(self):
     """ Given the following graph:
       /-->(b)-->\
     (a)         (d)
       \-->(c)-->/
     """
     g = Graph.build(edges=[('a','b'), ('a', 'c'), ('b', 'd'), ('c', 'd')],
                     directed=True)
     ordering = dfs_loop(g)
     self.assertEqual(ordering['a'], 1)
     self.assertIn(ordering['b'], [2,3])
     self.assertIn(ordering['c'], [2,3])
     self.assertEqual(ordering['d'], 4)

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
 def test_kruskal_suboptimal_mst_2(self):
     g = Graph.build(edges=[('a', 'b', 3), ('a', 'f', 2), ('f', 'g', 7),
             ('b', 'd', 16), ('d', 'e', 11), ('f', 'e', 1), ('g', 'e', 6),
             ('g', 'h', 15), ('e', 'h', 5), ('b', 'c', 17), ('c', 'd', 8),
             ('d', 'i', 4), ('c', 'i', 18), ('e', 'i', 10), ('h', 'i', 12),
             ('i', 'j', 9), ('h', 'j', 13)],
         directed=False)
     mst = kruskal_suboptimal_mst(g)
     expected = sorted([('a', 'b', 3), ('a', 'f', 2), ('e', 'f', 1),
             ('e', 'g', 6), ('e', 'h', 5), ('e', 'i', 10), ('d', 'i', 4),
             ('c', 'd', 8), ('i', 'j', 9)])
     actual = sorted(mst.get_edges())
     self.assertEqual(actual, expected, 'should compute the correct mst')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
 def test_randomized_cut_for_larger_graph(self):
     """ Test minimum cut for a larger graph.
     (a)--(b)--(e)--(f)
      |  X |    |  X |
     (c)--(d)--(g)--(h)
     """
     g = Graph.build(edges = [('a', 'b'), ('a', 'c'), ('a', 'd'),
                              ('b', 'c'), ('b', 'd'), ('b', 'e'),
                              ('c', 'd'), ('d', 'g'),
                              ('e', 'g'), ('e', 'f'), ('e', 'h'),
                              ('f', 'g'), ('f', 'h'), ('g', 'h')])
     compacted = randomized_cut(g)
     self.assertEqual(len(compacted.get_vertices()), 2,
             'should have compacted to only 2 vertices')

# 需要导入模块: from src.graph import Graph [as 别名]
# 或者: from src.graph.Graph import build [as 别名]
    def test_get_frontier(self):
        """ Makes sure frontier edges are correctly picked.
            (1)--->(2)
             |      |
             V      V
            (3)<---(4)
        """
        g = Graph.build(edges=[(1,2), (1,3), (2,4), (4,3)], directed=True)
        explored_vertices = [1,3]

        actual = get_frontier(g, explored_vertices)
        expected = set([(1,2,True)])
        self.assertEqual(actual, expected, 'should only return the only node ' \
                                      'reachable that has not yet been visited')