UVALive 4839 HDU 3686 Traffic Real Time Query System

题意：给出一幅图，询问从一条边到另一条有几个点必被经过

没看题解思路完全不对。。似乎知道了tarjan的新姿势

思路：首先按边跑tarjan。然后记录一下每条边在哪一个块中，记录一下割点；

然后建图：对于每个割点所在的块中（每个割点肯定在多个块中），建一个新点跟它们连边；

然后就是一棵树啦，当然到树剖啦。然后询问就是统计一条链上的割点有多少啦

（缩点基本是抄袭）

代码：

#include <bits/stdc++.h>#define N 20009#define M 200009using namespace std;int first[N],number,x,y,n,m,dfn[N],low[N],sta[M];int ebelong[M],subnet[N],iscut[N],Number,First[N<<1];int top,cnt,taj,treecut[N<<1],vis[N<<1],Q,size[N<<1];int num[N<<1],deep[N<<1],Top[N<<1],father[N<<1],Mson[N<<1];vector<int> q[N];struct edge{int from,to,next,val,vis;void add(int x,int y,int z){from=x,to=y,next=first[x],first[x]=number,val=z,vis=0;}}e[M<<1];struct Edge{int to,next;void add(int x,int y){to=y,next=First[x],First[x]=Number;}}E[N<<3];void tarjan(int x){dfn[x]=low[x]=++cnt;for (int i=first[x];i;i=e[i].next)if (!e[i].vis){e[i].vis=e[i^1].vis=1;sta[++top]=i;if (!dfn[e[i].to]){tarjan(e[i].to);low[x]=min(low[x],low[e[i].to]);if (low[e[i].to]>=dfn[x]){++taj;subnet[x]++;iscut[x]=1;int y,j;do{j=sta[top--];q[e[j].from].push_back(taj);q[e[j].to].push_back(taj);ebelong[e[j].val]=taj;y=e[j].from;}while (y!=x);}}else low[x]=min(low[x],low[e[i].to]);}}void dfs(int x){vis[x]=1;for (int i=First[x];i;i=E[i].next)if (!vis[E[i].to]){num[E[i].to]=num[x];if (treecut[x]) num[E[i].to]++;dfs(E[i].to);}}void dfs1(int x){size[x]=1;deep[x]=deep[father[x]]+1;for (int i=First[x];i;i=E[i].next)if (E[i].to!=father[x]){father[E[i].to]=x;dfs1(E[i].to);size[x]+=size[E[i].to];if (size[E[i].to]>size[Mson[x]]) Mson[x]=E[i].to;}}void dfs2(int x,int y){Top[x]=y;if (Mson[x]) dfs2(Mson[x],y);for (int i=First[x];i;i=E[i].next)if (E[i].to!=father[x]&&E[i].to!=Mson[x])dfs2(E[i].to,E[i].to);}int lca(int x,int y){for (;Top[x]!=Top[y];x=father[Top[x]])if (deep[Top[x]]<deep[Top[y]]) swap(x,y);return deep[x]<deep[y]?x:y;}int main(){while (scanf("%d%d",&n,&m),n&&m){for (int i=1;i<=n;i++)first[i]=dfn[i]=low[i]=iscut[i]=subnet[i]=0;for (int i=1;i<=n;i++) q[i].clear();number=1,top=cnt=taj=Number=0;for (int i=1;i<=m;i++){scanf("%d%d",&x,&y);ebelong[i]=0;e[++number].add(x,y,i);e[++number].add(y,x,i);}for (int i=1;i<=n;i++)if (!dfn[i]){tarjan(i);subnet[i]--;if (subnet[i]<=0) iscut[i]=0;}for (int i=1;i<=taj+n;i++) First[i]=treecut[i]=0;for (int i=1;i<=n;i++)if (iscut[i]){sort(q[i].begin(),q[i].end());treecut[++taj]=1;E[++Number].add(taj,q[i][0]);E[++Number].add(q[i][0],taj);for (int j=1;j<q[i].size();j++)if (q[i][j-1]!=q[i][j]){E[++Number].add(taj,q[i][j]);E[++Number].add(q[i][j],taj);}}for (int i=1;i<=taj;i++)Mson[i]=deep[i]=num[i]=father[i]=Top[i]=vis[i]=size[i]=0;for (int i=1;i<=taj;i++)if (!vis[i]) dfs(i),dfs1(i),dfs2(i,i);scanf("%d",&Q);for (int i=1;i<=Q;i++){scanf("%d%d",&x,&y);x=ebelong[x],y=ebelong[y];if (!x||!y) puts("0");else{int z=lca(x,y);printf("%d\n",num[x]+num[y]-2*num[z]-treecut[z]);}}}return 0;}