dfn[u]: 表示节点u的搜索优先级 low[u]: 表示节点u,通过其本身或其子节点能到达的最小有搜索优先级 low[u] = Min{ 1. dfn[u] 其本身搜索优先级 2. Min{ low[v] } 其子节点v能到达的最小优先级 3. Min( dfn[v] ) 其通过回边(u,v),其中v为u的祖先节点,的优先级 }
一 无向图
1. 割点
又名关键点,若删除该点与其发出的边.则整个图不连通.
当前顶点u是一个关键点的充要条件是:
1. 若顶点U是根,则其必定包含两个以上的子节点. (因为若只有一个.删除了U之后,图仍然连通)
2. 若顶点U不是根, 则当 dfn[u] <= low[v] , (其中V是U的子孙节点). 因为V无法通过其本身或子孙到达U或者U更高级的点.所以删除U后,图不连通.
poj 1523 SPF
#include<cstdio> #include<cstdlib> #include<cstring> #include<algorithm> using namespace std; const int N = 1010; int edge[N][N]; int n, son; int subnet[N], dfn[N], low[N], tmpdfn; bool vis[N]; void init(){ tmpdfn = 1; son = 0; memset(dfn,0,sizeof(dfn)); memset(low,0,sizeof(low)); memset(vis,0,sizeof(vis)); memset(subnet,0,sizeof(subnet)); low[1] = dfn[1] = 1; vis[1] = true; } void dfs(int u){ // printf("u = %d\n", u ); for(int v = 1; v <= n; v++) { if( edge[u][v] ){ if( !vis[v] ){ vis[v] = true; dfn[v] = low[v] = ++tmpdfn; dfs( v ); low[u] = min( low[u], low[v] ); if( low[v] >= dfn[u] ){ if( u != 1 ) subnet[u]++; else son++; } } else low[u] = min( low[u], dfn[v] ); } } } int main(){ // freopen("1.in","r",stdin); int Case = 0; while( 1 ){ int u, v; n = 0; scanf("%d", &u); if( u == 0 ) break; memset(edge,0,sizeof(edge)); scanf("%d",&v); if( u > n ) n = u; if( v > n ) n = v; edge[u][v] = edge[v][u] = 1; while(1){ scanf("%d",&u); if( u == 0 ) break; scanf("%d",&v); if(u > n) n = u; if(v > n) n = v; edge[u][v] = edge[v][u] = 1; } if( Case ) puts(""); printf("Network #%d\n", ++Case); init(); dfs(1); if( son > 1 ) subnet[1] = son-1; bool find = false; for(int i = 1; i <= n; i++) { if( subnet[i] ){ find = true; printf(" SPF node %d leaves %d subnets\n", i, subnet[i]+1); } } if( !find ) printf(" No SPF nodes\n"); } return 0; }