Python DiGraph.reverse_edge方法代码示例

# 需要导入模块: from sage.graphs.digraph import DiGraph [as 别名]
# 或者: from sage.graphs.digraph.DiGraph import reverse_edge [as 别名]

#.........这里部分代码省略.........


    EXAMPLES:

    A cycle has one possible (non-symmetric) strong orientation::

        sage: g = graphs.CycleGraph(4)
        sage: it = g.strong_orientations_iterator()
        sage: len(list(it))
        1

    A tree cannot be strongly oriented::

        sage: g = graphs.RandomTree(100)
        sage: len(list(g.strong_orientations_iterator()))
        0

    Neither can be a disconnected graph::

        sage: g = graphs.CompleteGraph(6)
        sage: g.add_vertex(7)
        sage: len(list(g.strong_orientations_iterator()))
        0

    TESTS:

        sage: g = graphs.CompleteGraph(2)
        sage: len(list(g.strong_orientations_iterator()))
        0

        sage: g = graphs.CubeGraph(3)
        sage: b = True
        sage: for orientedGraph in g.strong_orientations_iterator():
        ....:     if not orientedGraph.is_strongly_connected():
        ....:         b = False
        sage: b
        True

    The total number of strong orientations of a graph can be counted using
    the Tutte polynomial evaluated at points (0,2)::

        sage: g = graphs.PetersenGraph()
        sage: nr1 = len(list(g.strong_orientations_iterator()))
        sage: nr2 = g.tutte_polynomial()(0,2)
        sage: nr1 == nr2/2 # The Tutte polynomial counts also the symmetrical orientations
        True

    """
    # if the graph has a bridge or is disconnected,
    # then it cannot be strongly oriented
    if G.order() < 3 or not G.is_biconnected():
        return

    V = G.vertices()
    Dg = DiGraph([G.vertices(), G.edges()], pos=G.get_pos())

    # compute an arbitrary spanning tree of the undirected graph
    te = kruskal(G)
    treeEdges = [(u,v) for u,v,_ in te]
    A = [edge for edge in G.edges(labels=False) if edge not in treeEdges]

    # initialization of the first binary word 00...0
    # corresponding to the current orientation of the non-tree edges
    existingAedges = [0]*len(A)

    # Make the edges of the spanning tree doubly oriented
    for e in treeEdges:
        if Dg.has_edge(e):
            Dg.add_edge(e[1], e[0])
        else:
            Dg.add_edge(e)

    # Generate all orientations for non-tree edges (using Gray code)
    # Each of these orientations can be extended to a strong orientation
    # of G by orienting properly the tree-edges
    previousWord = 0
    i = 0

    # the orientation of one edge is fixed so we consider one edge less
    nr = 2**(len(A)-1)
    while i < nr:
        word = (i >> 1) ^ i
        bitChanged = word ^ previousWord
        
        bit = 0
        while bitChanged > 1:
            bitChanged >>= 1
            bit += 1

        previousWord = word
        if existingAedges[bit] == 0:
            Dg.reverse_edge(A[bit])
            existingAedges[bit] = 1
        else:
            Dg.reverse_edge(A[bit][1], A[bit][0])
            existingAedges[bit] = 0
        # launch the algorithm for enumeration of the solutions
        for sol in _strong_orientations_of_a_mixed_graph(Dg, V, treeEdges):
            yield sol
        i = i + 1