PKU1144 network

       本題考查的是尋找割點（也叫掛接點），運用DFS執行。

       每個節點我們除了需要用d來記錄它的時間戳，還需要low來記錄它及其後裔中最淺的反向邊指向。對於一個圖的割點，我們能發現如下充要條件：

（1）若u爲圖G搜索樹的根，當且僅當u在這棵搜索樹中有至少兩個兒子。

（2） 若u爲圖G搜索樹的非根結點，當且僅當u有一個子節點v，使其不存在從v或v的後裔中指向u的真祖先的反向邊。

program network; const root=1; maxn=101; type pointer=^node; node=record next:pointer; data:longint; end; var edge:array[0..maxn] of pointer; vis:array[0..maxn] of longint; cut:array[0..maxn] of boolean; d,low:array[0..maxn] of longint; n,ans,time:longint; function getmin(a,b:longint):longint; begin if a<b then exit(a); exit(b); end; procedure prework; var i:longint; begin ans:=0; time:=0; fillchar(vis,sizeof(vis),0); fillchar(cut,sizeof(cut),0); for i:=0 to maxn do edge[i]:=nil; end; procedure link(a,b:longint); var p:pointer; begin new(p); p^.data:=b; p^.next:=edge[a]; edge[a]:=p; end; procedure init; var u,v:longint; begin read(u); while u<>0 do begin while not eoln do begin read(v); link(u,v); link(v,u); end; read(u); end; end; procedure dfs(father,u:longint); var tot,v:longint; p:pointer; begin inc(vis[u]); tot:=0; inc(time); d[u]:=time; low[u]:=time; p:=edge[u]; while p<>nil do begin v:=p^.data; if (vis[v]=1) and (v<>father) then low[u]:=getmin(low[u],d[v]); if (vis[v]=0) then begin dfs(u,v); inc(tot); low[u]:=getmin(low[u],low[v]); if (u=root) and (tot>1) then cut[u]:=true else if (u<>root) and (low[v]>=d[u]) then cut[u]:=true; end; p:=p^.next; end; inc(vis[u]); end; procedure outit; var i:longint; begin for i:=1 to n do if cut[i] then inc(ans); writeln(ans); end; procedure bigmain; begin readln(n); while n<>0 do begin prework; init; dfs(0,root); outit; readln(n); end; end; begin assign(input,'a.in'); reset(input); assign(output,'a.out'); rewrite(output); bigmain; close(input); close(output); end.