Graph theory Algorithm-tarjan template "shrinking point; cutting top; Double connecting component"

graph theory Algorithm-tarjan template "shrinking point; cutting top; Double connecting component" Tarjan Three algorithms for the small partners Tarjan Indent (strong connected component)

int N;int low[100010],dfn[100010];bool Ins[100010];int col[100010];//Record each point belongs to the strong connected component (i.e. dyeing) vector<int> map[100010]    ;stack<int> st;int tot;//Timestamp int colnum;//records the number of strongly connected components void Tarjan (int u) {low[u]=dfn[u]=++tot;    St.push (U);    Ins[u]=true;        for (int j=0;j<map[u].size (); j + +) {int v=map[u][j];            if (!dfn[v]) {Tarjan (v);        Low[u]=min (Low[u],low[v]);    } else if (Ins[v]) low[u]=min (Low[u],dfn[v]);                } if (Low[u]==dfn[u]) {///to which a new strong connected component colnum++ is found;        int temp;        int cont=0;            do {temp=st.top ();            St.pop ();                        Ins[temp]=false;                        The point of the same strong connected component is dyed to represent a col[temp]=colnum of the indentation point;    It is also possible to perform some other operations on the strongly connected component, such as saving the original node contained in the Indent (temp!=u).    }}void init () {memset (dfn,0,sizeof (DFN));    memset (low,0,sizeof (Low));    memset (col,0,sizeof (col)); memset (ins,false,sizeof (INS)); tot=colnum=0;}    void Solve () {init ();    for (int i=1;i<=n;i++) {if (!dfn[i]) Tarjan (i); }}

Tarjan Cutting Point (cutting top)

int n;vector<int> map[100010];int low[100010],dfn[100010];bool cut[1000010];//记录割点int tot;void tarjan(int u,int fa){    low[u]=dfn[u]=++tot;    int child=0;    for(int j=0;j<map[u].size();j++)    {        int v=map[u][j];        if(!dfn[v])        {            child++;            tarjan(v,u);            low[u]=min(low[u],low[v]);                        if(low[v]>=dfn[u])            cut[u]=true;        }                else if(dfn[v]<dfn[u]&&v!=fa)        low[u]=min(low[u],dfn[v]);    }        if(fa<0&&child==1)    cut[u]=false;}void init(){    memset(dfn,0,sizeof(dfn));    memset(low,0,sizeof(low));    memset(cut,false,sizeof(cut));    tot=0;}void solve(){        init();    for(int i=1;i<=n;i++)    {        if(!dfn[i])        tarjan(i，-1);        //**高亮**这里的第二个参数一定要设为负数    }    //cut[i]==true即表示i为割点}

Tarjan-Two connected components

int n;vector<int> map[100010];int low[100010],dfn[100010];bool cut[1000010];int bcc[1000010];int tot;int bcc_    cont//records the number of two connected components; struct Edge{int u,v};stack<edge> e;void tarjan (int u,int fa) {low[u]=dfn[u]=++tot;    int child=0;        for (int j=0;j<map[u].size (); j + +) {int v=map[u][j];                Edge e= (Edge) {u,v};            if (!dfn[v]) {E.push (E);            child++;            Tarjan (V,u);                        Low[u]=min (Low[u],low[v]);                if (Low[v]>=dfn[u]) {//To here a new double-connected component cut[u]=true is found;                    bcc_cont++: while (1) {Edge temp=e.top ();                                        E.pop ();                    if (Bccno[temp.u]!=bcc_cont) Bccno[temp.u]=bcc_cont;                                        if (Bccno[temp.v]!=bcc_cont) Bccno[temp.v]=bcc_cont; if (Temp.u==u& &temp.v==v) break;            }}} and else if (DFN[V]&LT;DFN[U]&AMP;&AMP;V!=FA) {E.push (E);        Low[u]=min (Low[u],dfn[v]); }} if (Fa<0&&child==1) Cut[u]=false;}    void Init () {memset (dfn,0,sizeof (DFN));    memset (low,0,sizeof (Low));    memset (bccno,0,sizeof (BCCNO)); tot=bcc_cont=0;}    void Solve () {init (); for (int i=1;i<=n;i++) {if (!dfn[i]) Tarjan (i,-1);//** Highlight * * The second argument here must be set to a negative number}}

In fact, three algorithms are basically the same way of thinking
After all, it's the same person who raised it.

Graph theory Algorithm-tarjan template "shrinking point; cutting top; Double connecting component"