内容目录
这题是点双连通分量,我一开始写成边的……
首先点双连通分量可能重叠……(1,2) (2,3) (3,1) (3,4) (4,5) (5,6) (3.6)
这时有(1,2,3)和(3,4,5,6)两组双连通分量
故一定要在Tarjen里判……另外Stack存边时注意特判(Stack不能为空)
当dfs[k]<=low[i] 时 就找到了点双连通分量 (这是点双连通)
请注意在推送(k,i)后遍历得到的一堆边(包括(k,i))组成了一组点双连通分量
两个重要定理:
(1) 如果一个双连通分量内的某些顶点在一个奇圈中(即双连通分量含有奇圈),那么这个双连通分量的其他顶点也在某个奇圈中;
(2) 如果一个双连通分量含有奇圈,则他必定不是一个二分图。反过来也成立,这是一个充要条件。
Program P2942; const maxn=1050; maxm=1000000; Var n,m,i,j,x,y:longint; b:array[1..maxn,1..maxn] of boolean; color,c,dfs,low:array[1..maxn] of longint; attend,flag:array[1..maxn] of boolean; size,time,totssc:longint; stack:array[0..maxm,1..2] of longint; function min(a,b:longint):longint; begin if a<b then exit(a) else exit(b); end; function is_Binary(k,col:longint):boolean; var i,j:longint; begin color[k]:=col; for i:=1 to n do if (flag[i]) and (b[k,i]) then begin if color[i]=0 then begin if not(is_binary(i,3-col)) then exit(false); end else if color[k]=color[i] then exit(false); end; exit(true); end; procedure tarjen(k,father:longint); var i,j:longint; begin inc(time); dfs[k]:=time; low[k]:=time; c[k]:=1; for i:=1 to n do if (b[k,i]) and (dfs[k]>dfs[i]) and (i<>father) then begin if dfs[i]=0 then begin inc(size); stack[size,1]:=k; stack[size,2]:=i; tarjen(i,k); low[k]:=min(low[k],low[i]); if dfs[k]<=low[i] then begin fillchar(flag,sizeof(flag),false); fillchar(color,sizeof(color),false); while (size>0) do begin flag[stack[size,1]]:=true; flag[stack[size,2]]:=true; dec(size); if (stack[size+1,1]=k) and (stack[size+1,2]=i) then break; end; if not(is_binary(k,1)) then begin for j:=1 to n do if flag[j] then attend[j]:=true; end; end; end else if c[i]=1 then low[k]:=min(low[k],dfs[i]); end; c[k]:=2; end; function main:longint; var i,j,tot:longint; begin fillchar(dfs,sizeof(dfs),0); fillchar(low,sizeof(low),0); fillchar(c,sizeof(c),0); fillchar(attend,sizeof(attend),false); fillchar(flag,sizeof(flag),false); fillchar(color,sizeof(color),0); fillchar(stack,sizeof(stack),0); size:=0;time:=0; for i:=1 to n do if (dfs[i]=0) then begin tarjen(i,0); end; tot:=0; for i:=1 to n do if attend[i] then inc(tot); exit(n-tot); end; begin while not seekeof do begin read(n,m); if (n=0) and (m=0) then break; fillchar(b,sizeof(b),true); for i:=1 to n do b[i,i]:=false; for i:=1 to m do begin read(x,y); b[x,y]:=false; b[y,x]:=false; end; writeln(main); end; end.