pku1523 SPF

(1)求割点。割点距离各连通分支有一边距离（父子边），故使用<=
(2)求割边。割边两端点分别在两个连通分支之中，故使用<
(3)求去除割点u后形成的连通分支数。若dfn[u]<lowlink[v]，则uv为一割边，对应一个连通分支；若dfn[u]==lowlink[v]，则表示割点u和v所在的连通分支之间只有父子边uv相连，除掉后亦可得到一连通分支。

 

 

#include  < iostream >
using   namespace  std;

#define  MAXN 1001
#define  Min(a,b)(a<b?a:b)

int  p[MAXN],ecnt,dfn[MAXN],lowlink[MAXN],sign,subSCC[MAXN],root,odeg[MAXN],T;
bool  exist[MAXN],cut[MAXN];

struct  Edge{
     int  v,next;
}edg[ 10 * MAXN];

void  init(){
    sign = 0 ;
    ecnt = 0 ;
    memset(cut, false , sizeof (cut));
    memset(odeg, 0 , sizeof (odeg));
     // memset(subSCC,0,sizeof(subSCC));
    memset(exist, false , sizeof (exist));
    memset(p, - 1 , sizeof (p));
    memset(dfn, - 1 , sizeof (dfn));
     for ( int  i = 1 ;i < MAXN;i ++ )
        subSCC[i] = 1 ; /// /根所在的连通分支在dfs中没有被统计
}

void  dfs( int  pre, int  u){
     int  i,v;
    dfn[u] = lowlink[u] =++ sign;
     for (i = p[u];i !=- 1 ;i = edg[i].next){
        v = edg[i].v;
        odeg[u] ++ ;
         if (dfn[v] !=- 1 ){
             if (v != pre) // (2)
                lowlink[u] = Min(lowlink[u],dfn[v]);
        }
         else {
            dfs(u,v);
            lowlink[u] = Min(lowlink[u],lowlink[v]);
             // (1)
             if (u != root  &&  dfn[u] <= lowlink[v])
                cut[u] = true ; // cut[u]为true表示u为割点。这里改用计数器的话会重复计数
             else   if (u == root  &&  odeg[root] > 1 ) // DFS树的根r是割点的充要条件是：至少有2条以r为尾(从r出发)的父子边
                cut[u] = true ;
             // (2)
             // if(bfn[u]<lowlink[v])
             //     Brige[u,v] is true; // 边uv是桥
             // (3)
             if (u != root  &&  dfn[u] <= lowlink[v])
                subSCC[u] ++ ;
             else   if (u == root)
                subSCC[u] = odeg[u];
            
        }
    }
}
                



void  solve(){
     int  i;
     bool  ok = false ;
    root = 1 ;
     while ( ! exist[root])
        root ++ ;
     for (i = 1 ;i < MAXN;i ++ )
         if (exist[i]  &&  dfn[i] ==- 1 )
            dfs( - 1 ,i);

    printf( " Network #%d\n " ,T ++ );
     for (i = 1 ;i < MAXN;i ++ ){
         if (cut[i]){
            ok = true ;
            printf( "   SPF node %d leaves %d subnets\n " ,i,subSCC[i]);
        }
    }
     if ( ! ok){
        printf( "   No SPF nodes\n " );
    }
    printf( " \n " );
}

int  main(){
    T = 1 ;
     int  u,v;
     while (scanf( " %d " , & u)  &&  u){
        init();
        scanf( " %d " , & v);
        edg[ecnt].v = v;
        edg[ecnt].next = p[u];
        p[u] = ecnt ++ ;
        edg[ecnt].v = u;
        edg[ecnt].next = p[v];
        p[v] = ecnt ++ ;
        exist[u] = exist[v] = true ;
         while (scanf( " %d " , & u)  &&  u){
            scanf( " %d " , & v);
            edg[ecnt].v = v;
            edg[ecnt].next = p[u];
            p[u] = ecnt ++ ;
            edg[ecnt].v = u;
            edg[ecnt].next = p[v];
            p[v] = ecnt ++ ;
            exist[u] = exist[v] = true ;
        }
        solve();
    }
     return   0 ;
}