割点，桥，双连通
计算割点和桥数的模板：
(基本上和强连通的tarjan算法一样)
var n,m,i,j,k,l,num,top,tot,co,ii,x,y,u,v,count,ans,cutedge,root:longint;
head,next,vet,low,dfn,color,d:array[0..400005] of longint;
visit,st,cut:array[0..400005] of boolean;
function min(a,b:longint):longint;
begin if a
procedure add(x,y:longint);
begin
inc(tot);
next[tot]:=head[x];head[x]:=tot;
vet[tot]:=y;
inc(tot);
next[tot]:=head[y];head[y]:=tot;
vet[tot]:=x;
end;
procedure tarjan(x,fa:longint);
var i,v,son:longint;
ok:boolean;
begin
inc(num);dfn[x]:=num;low[x]:=num;
son:=0;st[x]:=true;
i:=head[x];ok:=false;
while i<>0 do begin
v:=vet[i];
if (v=fa)and(not ok) then begin //回边的处理
ok:=true;i:=next[i];continue;
end;
if dfn[v]=0 then begin //v易打错成i
inc(son);
tarjan(v,x);//相较于强连通算法,因为是无向图,所以要记录父亲节点
if low[v]>dfn[x] then inc(cutedge); //从v出发不能回到x及x以前,则
if low[v]>=dfn[x] then cut[x]:=true; //从v出发不能回到x以前,则x为割点
low[x]:=min(low[v],low[x]);//容易打错的地方，v,x要特别注意
end
else if st[v] then low[x]:=min(low[x],dfn[v]);
i:=next[i];
end;
if x=root then begin
if son>1 then cut[x]:=true else cut[x]:=false;//根要特判
end;
st[x]:=false;//搜索过后要复原,使下一次能被搜到
end;
begin
readln(n,m);
for i:=1 to m do begin
readln(u,v);
ADD(u,v);
end;
for i:=1 to n do
if dfn[i]=0 then begin root:=i;tarjan(i,0);end;
for i:=1 to n do if cut[i] then inc(count);
writeln(count,' ',cutedge);
end
计算要使整个图变成双连通需要加的边数:
基本思路:先将双连通分量缩成点,计算度为1的leaf节点数count,ans=(count+1)>>1
var n,m,i,j,k,l,num,top,tot,co,ii,x,y,u,v,count,ans:longint;
head,next,vet,op,low,dfn,color,d,st:array[0..30005] of longint;
visit:array[0..30005] of boolean;
function min(a,b:longint):longint;
begin if athen exit(a);exit(b);end;
procedure add(x,y:longint);
begin
inc(tot);
next[tot]:=head[x];head[x]:=tot;
vet[tot]:=y;op[tot]:=tot+1;
inc(tot);
next[tot]:=head[y];head[y]:=tot;
vet[tot]:=x;op[tot]:=tot-1;
end;
procedure tarjan(x:longint);
var i,v:longint;
begin
inc(num);dfn[x]:=num;low[x]:=num;
inc(top);st[top]:=x;
i:=head[x];
while i<>0 do begin
if not visit[op[i]] then begin
visit[i]:=true;
v:=vet[i];
if dfn[v]=0 then begin
tarjan(v);
low[x]:=min(low[x],low[v]);
end
else low[x]:=min(low[x],dfn[v]);
end else visit[i]:=true;
i:=next[i];
end;
if dfn[x]=low[x] then begin //边双连通
inc(co);
while st[top]<>x do begin
color[st[top]]:=co;
dec(top);
end;
color[st[top]]:=co;
dec(top);
end;
end;
begin
readln(n,m);
for i:=1 to m do begin
readln(u,v);
ADD(u,v);
end;
for i:=1 to n do
if dfn[i]=0 then tarjan(i);
for i:=1 to n do begin
ii:=head[i];
while ii<>0 do begin
v:=vet[ii];
if color[v]<>color[i] then
inc(d[color[v]]);
ii:=next[ii];
end;
end;
for i:=1 to co do if d[i]=1 then inc(count);
ans:=(count+1)>>1;
writeln(ans);
end.