Source: Internet
Author: User

Title Analysis: In an undirected graph, some points are painted black, so that when you delete any of the points in the graph, each connected component has at least one black point. At least a few black spots can be applied, and there are several options in case of minimum coating.

Problem Analysis: Obviously, must not be cut point. For each connected component, if there are 1 cut points, it must be applied to any point in the component except the cut point, if there are multiple (2 or more) cut points, then this component does not need coloring. If the whole picture is not cut point, then any choice of two points coloring, the reason to paint two, is to prevent the deletion of the electricity is black spot.

The code is as follows:

`# include<iostream># include<cstdio># include<stack># include<map># include<vector>#    include<cstring># include<algorithm>using namespace Std;const int maxn=100005;struct Edge{int u,v,nxt; Edge (int _u=0,int _v=0,int _nxt=0): U (_u), V (_v), NXT (_NXT) {}}; Edge E[maxn];int HEAD[MAXN],PRE[MAXN],ISCUT[MAXN],LOW[MAXN],BCCNO[MAXN],CNT,BCC_CNT,DFS_CNT;MAP&LT;INT,INT&GT;MP    ; stack<edge>s;vector<int>bcc[maxn];void Add (int u,int v) {e[cnt].v=v;    E[cnt].nxt=head[u]; head[u]=cnt++;}    void Read (int m,int &n) {mp.clear ();    int A, B;    cnt=n=0;    memset (head,-1,sizeof (head));        while (m--) {scanf ("%d%d", &a,&b);        if (mp[a]==0) mp[a]=++n;        if (mp[b]==0) mp[b]=++n;        Add (mp[a]-1,mp[b]-1);    Add (mp[b]-1,mp[a]-1);    }}void dfs (int u,int fa) {int child=0;    low[u]=pre[u]=++dfs_cnt;        for (int i=head[u];i!=-1;i=e[i].nxt) {int v=e[i].v; if (!pre[v]) {+ +Child            S.push (Edge (u,v));            DFS (V,U);            Low[u]=min (Low[v],low[u]);                if (Low[v]>=pre[u]) {iscut[u]=1;                Bcc[++bcc_cnt].clear ();                    while (1) {Edge x=s.top ();                    S.pop ();                        if (bccno[x.u]!=bcc_cnt) {bcc[bcc_cnt].push_back (X.U);                    bccno[x.u]=bcc_cnt;                        } if (bccno[x.v]!=bcc_cnt) {bcc[bcc_cnt].push_back (X.V);                    bccno[x.v]=bcc_cnt;                } if (x.u==u&&x.v==v) break;            }}}else if (PRE[V]&LT;PRE[U]&AMP;&AMP;V!=FA) {S.push (Edge (u,v));        Low[u]=min (Low[u],pre[v]); }} if (Fa<0&&child==1) iscut[u]=0;}    void findbcc (int n) {bcc_cnt=dfs_cnt=0;    memset (pre,0,sizeof (pre)); memset (low,0,sIzeof (low));    memset (iscut,0,sizeof (iscut));    memset (bccno,0,sizeof (BCCNO)); for (int i=0;i<n;++i) if (!pre[i]) DFS (i,-1);}    void solve (int k) {Long long ans1=0,ans2=1;        for (int i=1;i<=bcc_cnt;++i) {int ccnt=0;        for (int j=0;j<bcc[i].size (); ++j) if (Iscut[bcc[i][j]]) ++ccnt;    if (ccnt==1) ++ans1,ans2*= (Long Long) (Bcc[i].size ()-ccnt);    } if (bcc_cnt==1) ans1=2,ans2=bcc[1].size () * (Bcc[1].size ()-1)/2; printf ("Case%d:%lld%lld\n", k,ans1,ans2);}    int main () {int n,m,cas=0;        while (scanf ("%d", &m) &&m) {read (m,n);        FINDBCC (n);    Solve (++cas); } return 0;}`

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