使用Tarjan算法在图中枚举循环

Question

我试图使用Tarjan算法确定有向图中的周期,该算法在1972年Septermber的研究论文"有向图的基本电路的枚举"中提出.

我正在使用Python来编写算法代码,并使用邻接列表来跟踪节点之间的关系.

所以在下面的"G"中,节点0指向节点1,节点1指向节点4,6,7 ...等.

G = [[1], [4, 6, 7], [4, 6, 7], [4, 6, 7], [2, 3], [2, 3], [5, 8], [5, 8], [], []]
N = len(G)

points = []
marked_stack = []
marked = [False for x in xrange(0,N)]

g = None
def tarjan(s, v, f):
    global g
    points.append(v)
    marked_stack.append(v)
    marked[v] = True

    for w in G[v]:
        if w < s:            
            G[v].pop(G[v].index(w))
        elif w == s:
            print points
            f = True
        elif marked[w] == False:
            if f == g and f == False:
                f = False
            else:
                f = True
            tarjan(s, w, g)

    g = f

    if f == True:
        u = marked_stack.pop()
        while (u != v):
            marked[u] = False
            u = marked_stack.pop()
        #v is now deleted from mark stacked, and has been called u
        #unmark v
        marked[u] = False
    points.pop(points.index(v))

for i in xrange(0,N):
    marked[i] = False

for i in xrange(0,N):
    points = []
    tarjan(i,i, False)
    while (len(marked_stack) > 0):
        u = marked_stack.pop()
        marked[u] = False

Tarjan的算法检测以下周期:

[2,4]

[2,4,3,6,5]

[2,4,3,7,5]

[2,6,5]

[2,6,5,3,4]

[2,7,5]

[2,7,5,3,4]

[3,7,5]

我也完成了Tiernan的算法,它(正确地)找到了2个额外的周期:

[3,4]

[3,6,5]

我很感激任何帮助,找出为什么Tarjan跳过这两个周期.我的代码中可能存在问题吗？

Answer 1

在这些行中：

for w in G[v]:
    if w < s:            
        G[v].pop(G[v].index(w))

您正在遍历列表并从中弹出元素。这会阻止迭代按预期工作。

如果您更改代码以制作列表的副本，则会产生额外的循环：

for w in G[v][:]: