POJ1523 SPF （求割点——塔扬算法）

 

顶点u是割点的充要条件是：u是深度优先树上有两个以上子女的的根，或者不是根时有一个子女w满足low[w]>=dfn[u]，

low[u]是从u到u的子孙出发通过back edge 可达的最低深度优先数。

low[u]=min{

dfn[u],

min{ low[w] | w是u的一个子女}，

min{dfn[v] | v是u邻接，且(u,v)是一条回边}

}

//Tarjan  for solving cut-vertex on undirection graph
#include <cstdio>
#include <string.h>
#define min(a,b) ((a)>(b)?(b):(a))
#define max(a,b) ((a)>(b)?(a):(b))

const int maxn=1002;
int map[maxn][maxn];
int vis[maxn];
int dfn[maxn],low[maxn];
int nodes,tmpdfn;
int son , subnets[maxn];//
int cas=0;
void dfs (int u)
{
    for (int v=1 ; v<=nodes ; v++)
    {
        if(map[u][v])
        {
            if(!vis[v])//v is not visited ,v is u's son
            {
                vis[v]=1;
                dfn[v]=low[v]= (++tmpdfn);
                dfs(v);
                low[u]=min(low[v],low[u]);
                if(low[v]>=dfn[u])
                {
                    if(u!=1)subnets[u]++;
                    if(u==1)son++;
                }
            }
            else low[u]=min(low[u],dfn[v]);//v has already visited ,<v,u> is a back edge
        }
    }
}
void init ()
{
    low[1]=dfn[1]=1;
    tmpdfn=1;
    son=0;
    memset (vis,0,sizeof(vis));
    vis[1]=1;
    memset (subnets,0,sizeof(subnets));
}

int main ()
{
    int u,v,i;
    bool find ;
    while (scanf("%d",&u),u)
    {
        memset(map,0,sizeof(map));
        nodes=0;
        nodes=max(nodes,u);
        scanf("%d",&v);
        nodes=max(nodes,v);
        map[u][v]=map[v][u]=1;
        while (scanf("%d",&u),u)
        {
            scanf("%d",&v);
            nodes=max(nodes,u);
            nodes=max(nodes,v);
            map[u][v]=map[v][u]=1;
        }
        if(cas>=1)printf("\n");
        printf("Network #%d\n",++cas);
        init ();
        //printf("%d\n",nodes);
        dfs(1);
        if(son>1) subnets[1]=son-1;
        find=0 ;
        for (i=1 ; i<=nodes ; ++i)
        {
            if(subnets[i])
            {
                find=1 ;
                printf("  SPF node %d leaves %d subnets\n",i,subnets[i]+1);
            }
        }
        if(!find)printf("  No SPF nodes\n");
    }
    return 0;
}