2208: [Jsoi2010]连通数 - BZOJ

Description

Input

输入数据第一行是图顶点的数量，一个正整数N。 接下来N行，每行N个字符。第i行第j列的1表示顶点i到j有边，0则表示无边。

Output

输出一行一个整数，表示该图的连通数。

Sample Input

3

010

001

100
Sample Output

9
HINT

对于100%的数据，N不超过2000。

看到这题然后马上打了一个tarjan

然后对每一个强连通分量dfs，A了之后感觉有点奇怪，这个复杂度是多少来着，我好像算不出来，果断百度题解

然后大囧。。。。。。怎么好像正解是tarjan+拓扑排序+状态压缩，只搜到了一个和我一样的做法

然后我想到这样做其实可以随随便便卡掉，还是n三方，于是又打了一遍正解，加个拓扑和状态压缩

 const
     maxn=;
 var
     first,c,sum,dfn,low,z:array[..maxn*]of longint;
     next,last:array[..maxn*maxn*]of longint;
     flag:array[..maxn*]of boolean;
     f:array[..maxn,..maxn]of boolean;
     n,cnt,tot,ans,time,s:longint;

 procedure insert(x,y:longint);
 begin
     inc(tot);
     last[tot]:=y;
     next[tot]:=first[x];
     first[x]:=tot;
 end;

 procedure dfs(x:longint);
 var
     i:longint;
 begin
     inc(time);
     dfn[x]:=time;
     low[x]:=time;
     inc(s);
     z[s]:=x;
     flag[x]:=true;
     i:=first[x];
     while i<> do
       begin
         if dfn[last[i]]= then
           begin
             dfs(last[i]);
             if low[last[i]]<low[x] then low[x]:=low[last[i]];
           end
         else
           if flag[last[i]] and (low[last[i]]<low[x]) then low[x]:=low[last[i]];
         i:=next[i];
       end;
     if low[x]=dfn[x] then
     begin
       inc(cnt);
       while z[s+]<>x do
         begin
           inc(sum[cnt]);
           c[z[s]]:=cnt;
           flag[z[s]]:=false;
           dec(s);
         end;
     end;
 end;

 procedure init;
 var
     i,j:longint;
     cc:char;
 begin
     readln(n);
     for i:= to n do
       begin
         for j:= to n do
           begin
             read(cc);
             if cc='' then insert(i,j);
           end;
         readln;
       end;
     for i:= to n do
       if dfn[i]= then dfs(i);
     for i:= to n do
       begin
         j:=first[i];
         while j<> do
           begin
             if f[c[i],c[last[j]]]=false then
             begin
               insert(n+c[i],n+c[last[j]]);
               f[c[i],c[last[j]]]:=true;
             end;
             j:=next[j];
           end;
       end;
 end;

 function dfs2(x:longint):longint;
 var
     i:longint;
 begin
     dfs2:=sum[x-n];
     flag[x]:=true;
     i:=first[x];
     while i<> do
       begin
         if flag[last[i]]=false then inc(dfs2,dfs2(last[i]));
         i:=next[i];
       end;
 end;

 procedure work;
 var
     i,j:longint;
 begin
     for i:= to cnt do
       begin
         for j:= to cnt do
           flag[j+n]:=false;
         inc(ans,sum[i]*dfs2(i+n));
       end;
     writeln(ans);
 end;

 begin
     init;
     work;
 end.

 const
     maxn=;
 var
     first,c,sum,dfn,low,z,d:array[..maxn*]of longint;
     next,last:array[..maxn*maxn*]of longint;
     flag:array[..maxn*]of boolean;
     ff:array[..maxn,..maxn]of boolean;
     n,cnt,tot,ans,time,s:longint;

 procedure insert(x,y:longint);
 begin
     inc(tot);
     last[tot]:=y;
     next[tot]:=first[x];
     first[x]:=tot;
 end;

 procedure dfs(x:longint);
 var
     i:longint;
 begin
     inc(time);
     dfn[x]:=time;
     low[x]:=time;
     inc(s);
     z[s]:=x;
     flag[x]:=true;
     i:=first[x];
     while i<> do
       begin
         if dfn[last[i]]= then
           begin
             dfs(last[i]);
             if low[last[i]]<low[x] then low[x]:=low[last[i]];
           end
         else
           if flag[last[i]] and (low[last[i]]<low[x]) then low[x]:=low[last[i]];
         i:=next[i];
       end;
     if low[x]=dfn[x] then
     begin
       inc(cnt);
       while z[s+]<>x do
         begin
           inc(sum[cnt]);
           c[z[s]]:=cnt;
           flag[z[s]]:=false;
           dec(s);
         end;
     end;
 end;

 procedure init;
 var
     i,j:longint;
     cc:char;
 begin
     readln(n);
     for i:= to n do
       begin
         for j:= to n do
           begin
             read(cc);
             if cc='' then insert(i,j);
           end;
         readln;
       end;
     for i:= to n do
       if dfn[i]= then dfs(i);
     for i:= to n do
       begin
         j:=first[i];
         while j<> do
           begin
             if (ff[c[i],c[last[j]]]=false) and (c[i]<>c[last[j]]) then
             begin
               insert(n+c[i],n+c[last[j]]);
               inc(d[c[last[j]]]);
               ff[c[i],c[last[j]]]:=true;
             end;
             j:=next[j];
           end;
       end;
 end;

 var
     q:array[..maxn]of longint;
     f:array[..maxn,..]of longint;
     l,r:longint;

 procedure work;
 var
     i,j,k,tmp:longint;
 begin
     l:=;
     r:=;
     for i:= to cnt do
       if d[i]= then
       begin
         inc(r);
         q[r]:=i;
       end;
     while l<=r do
       begin
         j:=first[q[l]+n];
         while j<> do
           begin
             dec(d[last[j]-n]);
             if d[last[j]-n]= then
             begin
               inc(r);
               q[r]:=last[j]-n;
             end;
             j:=next[j];
           end;
         inc(l);
       end;
     for i:=r downto  do
       begin
         f[q[i],q[i] div ]:=<<(q[i]mod );
         j:=first[q[i]+n];
         while j<> do
           begin
             for k:= to cnt div  do
               f[q[i],k]:=f[q[i],k]or f[last[j]-n,k];
             j:=next[j];
           end;
       end;
     for i:= to cnt do
       begin
         tmp:=;
         for j:= to cnt do
           if f[i,j div ] and (<<(j mod ))> then inc(tmp,sum[j]);
         inc(ans,tmp*sum[i]);
       end;
     writeln(ans);
 end;

 begin
     init;
     work;
 end.