Tarjan算法总结

Posted 2020-12-16 lslzf

边双联通分量

inline void Tarjan(int x,int inedge)
{
    dfn[x]=low[x]=++cnt;
    for(int i=Last[x];i;i=e[i].next)
    {
        int y=e[i].ver;
        if(!dfn[y])
        {
            Tarjan(y,i);
            low[x]=min(low[x],low[y]);
            if(low[y]>dfn[x])e[i].flag=e[i^1].flag=true;
        }
        else if(i!=(inedge^1))low[x]=min(low[x],dfn[y]);
    }
}
inline void dfs(int x)
{
    con[x]=tot;
    for(int i=Last[x];i;i=e[i].next)
    {
        if(e[i].flag)continue;
        int y=e[i].ver;
        if(!con[y])dfs(y);
    }
}
inline void colored(void)
{
    for(int i=1;i<=n;i++)
        if(!con[i])++tot,dfs(i);
}

点双连通分量

inline void Tarjan(int x,int root)
{
    dfn[x]=low[x]=++cnt;
    Stack.push(x);
    int flag=0;
    if(x==root&&!Last[x])
    {
        Stack.pop();T++;
        cut[x]=true;
        con[T].push_back(x);
        return;
    }
    for(int i=Last[x];i;i=e[i].next)
    {
        int y=e[i].ver;
        if(!dfn[y])
        {
            Tarjan(y,root);
            low[x]=min(low[x],low[y]);
            if(low[y]>=dfn[x])
            {
                int top=0;T++;
                while(top!=y)
                {
                    top=Stack.top();
                    Stack.pop();
                    con[T].push_back(top);
                }
                con[T].push_back(x);
                flag++;
                if(x!=root||flag>1)cut[x]=true;
            }
        }
        else low[x]=min(low[x],dfn[y]);
    }
}

强连通分量

void Tarjan(int x)
{
	dfn[x]=low[x]=++tim;
	s[++top]=x;
	for(int i=head[x];i;i=nxt[i]){
		int y=ver[i];
		if(!dfn[y]){
			Tarjan(y);
			low[x]=min(low[x],low[y]);
		}
		else if(!sccno[y]) low[x]=min(low[x],dfn[y]);
	}
	if(dfn[x]==low[x]){
		cnt++;
		while(1){
			int y=s[top--];
			sccno[y]=cnt;
			num[cnt]++;
			if(y==x) break;
		}
	}
}