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

  1 const

  2     maxn=200;

  3 var

  4     first,c,sum,dfn,low,z:array[0..maxn*2]of longint;

  5     next,last:array[0..maxn*maxn*2]of longint;

  6     flag:array[0..maxn*2]of boolean;

  7     f:array[0..maxn,0..maxn]of boolean;

  8     n,cnt,tot,ans,time,s:longint;

  9 

 10 procedure insert(x,y:longint);

 11 begin

 12     inc(tot);

 13     last[tot]:=y;

 14     next[tot]:=first[x];

 15     first[x]:=tot;

 16 end;

 17 

 18 procedure dfs(x:longint);

 19 var

 20     i:longint;

 21 begin

 22     inc(time);

 23     dfn[x]:=time;

 24     low[x]:=time;

 25     inc(s);

 26     z[s]:=x;

 27     flag[x]:=true;

 28     i:=first[x];

 29     while i<>0 do

 30       begin

 31         if dfn[last[i]]=0 then

 32           begin

 33             dfs(last[i]);

 34             if low[last[i]]<low[x] then low[x]:=low[last[i]];

 35           end

 36         else

 37           if flag[last[i]] and (low[last[i]]<low[x]) then low[x]:=low[last[i]];

 38         i:=next[i];

 39       end;

 40     if low[x]=dfn[x] then

 41     begin

 42       inc(cnt);

 43       while z[s+1]<>x do

 44         begin

 45           inc(sum[cnt]);

 46           c[z[s]]:=cnt;

 47           flag[z[s]]:=false;

 48           dec(s);

 49         end;

 50     end;

 51 end;

 52 

 53 procedure init;

 54 var

 55     i,j:longint;

 56     cc:char;

 57 begin

 58     readln(n);

 59     for i:=1 to n do

 60       begin

 61         for j:=1 to n do

 62           begin

 63             read(cc);

 64             if cc='1' then insert(i,j);

 65           end;

 66         readln;

 67       end;

 68     for i:=1 to n do

 69       if dfn[i]=0 then dfs(i);

 70     for i:=1 to n do

 71       begin

 72         j:=first[i];

 73         while j<>0 do

 74           begin

 75             if f[c[i],c[last[j]]]=false then

 76             begin

 77               insert(n+c[i],n+c[last[j]]);

 78               f[c[i],c[last[j]]]:=true;

 79             end;

 80             j:=next[j];

 81           end;

 82       end;

 83 end;

 84 

 85 function dfs2(x:longint):longint;

 86 var

 87     i:longint;

 88 begin

 89     dfs2:=sum[x-n];

 90     flag[x]:=true;

 91     i:=first[x];

 92     while i<>0 do

 93       begin

 94         if flag[last[i]]=false then inc(dfs2,dfs2(last[i]));

 95         i:=next[i];

 96       end;

 97 end;

 98 

 99 procedure work;

100 var

101     i,j:longint;

102 begin

103     for i:=1 to cnt do

104       begin

105         for j:=1 to cnt do

106           flag[j+n]:=false;

107         inc(ans,sum[i]*dfs2(i+n));

108       end;

109     writeln(ans);

110 end;

111 

112 begin

113     init;

114     work;

115 end.

View Code

  1 const

  2     maxn=2020;

  3 var

  4     first,c,sum,dfn,low,z,d:array[0..maxn*2]of longint;

  5     next,last:array[0..maxn*maxn*2]of longint;

  6     flag:array[0..maxn*2]of boolean;

  7     ff:array[0..maxn,0..maxn]of boolean;

  8     n,cnt,tot,ans,time,s:longint;

  9 

 10 procedure insert(x,y:longint);

 11 begin

 12     inc(tot);

 13     last[tot]:=y;

 14     next[tot]:=first[x];

 15     first[x]:=tot;

 16 end;

 17 

 18 procedure dfs(x:longint);

 19 var

 20     i:longint;

 21 begin

 22     inc(time);

 23     dfn[x]:=time;

 24     low[x]:=time;

 25     inc(s);

 26     z[s]:=x;

 27     flag[x]:=true;

 28     i:=first[x];

 29     while i<>0 do

 30       begin

 31         if dfn[last[i]]=0 then

 32           begin

 33             dfs(last[i]);

 34             if low[last[i]]<low[x] then low[x]:=low[last[i]];

 35           end

 36         else

 37           if flag[last[i]] and (low[last[i]]<low[x]) then low[x]:=low[last[i]];

 38         i:=next[i];

 39       end;

 40     if low[x]=dfn[x] then

 41     begin

 42       inc(cnt);

 43       while z[s+1]<>x do

 44         begin

 45           inc(sum[cnt]);

 46           c[z[s]]:=cnt;

 47           flag[z[s]]:=false;

 48           dec(s);

 49         end;

 50     end;

 51 end;

 52 

 53 procedure init;

 54 var

 55     i,j:longint;

 56     cc:char;

 57 begin

 58     readln(n);

 59     for i:=1 to n do

 60       begin

 61         for j:=1 to n do

 62           begin

 63             read(cc);

 64             if cc='1' then insert(i,j);

 65           end;

 66         readln;

 67       end;

 68     for i:=1 to n do

 69       if dfn[i]=0 then dfs(i);

 70     for i:=1 to n do

 71       begin

 72         j:=first[i];

 73         while j<>0 do

 74           begin

 75             if (ff[c[i],c[last[j]]]=false) and (c[i]<>c[last[j]]) then

 76             begin

 77               insert(n+c[i],n+c[last[j]]);

 78               inc(d[c[last[j]]]);

 79               ff[c[i],c[last[j]]]:=true;

 80             end;

 81             j:=next[j];

 82           end;

 83       end;

 84 end;

 85 

 86 var

 87     q:array[0..maxn]of longint;

 88     f:array[0..maxn,0..70]of longint;

 89     l,r:longint;

 90 

 91 procedure work;

 92 var

 93     i,j,k,tmp:longint;

 94 begin

 95     l:=1;

 96     r:=0;

 97     for i:=1 to cnt do

 98       if d[i]=0 then

 99       begin

100         inc(r);

101         q[r]:=i;

102       end;

103     while l<=r do

104       begin

105         j:=first[q[l]+n];

106         while j<>0 do

107           begin

108             dec(d[last[j]-n]);

109             if d[last[j]-n]=0 then

110             begin

111               inc(r);

112               q[r]:=last[j]-n;

113             end;

114             j:=next[j];

115           end;

116         inc(l);

117       end;

118     for i:=r downto 1 do

119       begin

120         f[q[i],q[i] div 30]:=1<<(q[i]mod 30);

121         j:=first[q[i]+n];

122         while j<>0 do

123           begin

124             for k:=0 to cnt div 30 do

125               f[q[i],k]:=f[q[i],k]or f[last[j]-n,k];

126             j:=next[j];

127           end;

128       end;

129     for i:=1 to cnt do

130       begin

131         tmp:=0;

132         for j:=1 to cnt do

133           if f[i,j div 30] and (1<<(j mod 30))>0 then inc(tmp,sum[j]);

134         inc(ans,tmp*sum[i]);

135       end;

136     writeln(ans);

137 end;

138 

139 begin

140     init;

141     work;

142 end.

View Code