Question

我知道什么是前进和跨越边缘。但我发现很难在程序中实现它们以找到给定图形中的所有前向和交叉边缘。

在这方面的任何帮助将不胜感激。

Answer 1

您可以使用DFS横向对所有图形边缘进行分类：

DFS-Visit(u)         ▷ with edge classification. G must be a directed graph

1.        color[u] ← GRAY
2.        time ← time + 1
3.        d[u] ← time
4.        for each vertex v adjacent to u
5.            do if color[v] ← BLACK
6.                then if d[u] < d[v]
7.                            then Classify (u, v) as a forward edge
8.                            else Classify (u, v) as a cross edge
9.                        if color[v] ← GRAY
10.                            then Classify (u, v) as a back edge
11.                       if color[v] ← WHITE
12.                            then π[v] ← u
13.                                 Classify (u, v) as a tree edge
14.                                 DFS-Visit(v)
15.        color[u] ← BLACK
16.        time ← time + 1
17.        f[u] ← time

正如您所见here。

Answer 2

您也可以使用时钟而不是颜色。看起来更容易。这是实现这一目标的方法：但是我会在c中发布答案，因为我还不知道c ++，所以你必须将它转换为c ++。

void DFS(Graph* G){             
int v;

for (v=0; v < G->n; v++)
  visited[v]=FALSE;

for (v=0; v < G->n; v++){
  if (!visited[v])
    Traverse(G, v);
 }

}

void Traverse(Graph* Gr, int v){                
int w;
Edge *current;

start[v]=clock;                             //We are going to classify the edges by the time they were visited
clock++;
visited[v]=TRUE;

current=Gr->stpoint[v];

while (current){
    w=current->vertex;

    if (!visited[w]) {                          
        printf("%d %d: Tree edge\n",v,w);       //If w is not visited then mark v-w as a tree edge
        if(!current)
            Traverse(Gr, w);
    }
    else{

        if((start[v] > start[w]) && (end[v] < end[w]))      //v was visited after w
            printf("%d %d: Back edge\n",v,w);
        else if ((start[v] < start[w]) && (end[v] > end[w]))    //v was visited before w
            printf("%d %d: Forward edge\n",v,w);
        else if ((start[v] > start[w]) && (end[v] > end[w]))    //
            printf("%d %d: Cross edge\n",v,w);

    }
    end[v]=clock;
    clock++;
    current=current->next;
 }

}

如何在图形中查找所有前向和交叉边缘

2 个答案: