1589: [Usaco2008 Dec]Trick or Treat on the Farm 采集糖果

1589: [Usaco2008 Dec]Trick or Treat on the Farm 采集糖果

Time Limit: 5 Sec  Memory Limit: 64 MB
Submit: 419  Solved: 232
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Description

每年万圣节，威斯康星的奶牛们都要打扮一番，出门在农场的N(1≤N≤100000)个牛棚里转悠，来采集糖果．她们每走到一个未曾经过的牛棚，就会采集这个棚里的1颗糖果． 农场不大，所以约翰要想尽法子让奶牛们得到快乐．他给每一个牛棚设置了一个“后继牛棚”．牛棚i的后继牛棚是Xi．他告诉奶牛们，她们到了一个牛棚之后，只要再往后继牛棚走去，就可以搜集到很多糖果．事实上这是一种有点欺骗意味的手段，来节约他的糖果．  第i只奶牛从牛棚i开始她的旅程．请你计算，每一只奶牛可以采集到多少糖果．

Input

    第1行输入N，之后一行一个整数表示牛棚i的后继牛棚Xi，共N行．

Output

 

    共N行，一行一个整数表示一只奶牛可以采集的糖果数量．

Sample Input

4 //有四个点
1 //1有一条边指向1
3 //2有一条边指向3
2 //3有一条边指向2
3

INPUT DETAILS:

Four stalls.
* Stall 1 directs the cow back to stall 1.
* Stall 2 directs the cow to stall 3
* Stall 3 directs the cow to stall 2
* Stall 4 directs the cow to stall 3

Sample Output

1
2
2
3

HINT

Cow 1: Start at 1, next is 1. Total stalls visited: 1. Cow 2: Start at 2, next is 3, next is 2. Total stalls visited: 2. Cow 3: Start at 3, next is 2, next is 3. Total stalls visited: 2. Cow 4: Start at 4, next is 3, next is 2, next is 3. Total stalls visited: 3.

Source

Gold

题解：N个月前刚刚开BZOJ权限的时候，看了这道题，毫无思路，甚至想过暴搜（实际上此题求的就是各点所能到达的点的个数），但是要是 \( N \leq 1000 \) 的话倒还说的过去，\( O({N}^{2} ) \) 的复杂度毕竟。。。

实际上现在做起来也不难，就是个tarjan算法，将复杂图缩点转化为拓扑图，然后慢慢递推即可A掉。。。

 /**************************************************************
     Problem:
     User: HansBug
     Language: Pascal
     Result: Accepted
     Time: ms
     Memory: kb
 ****************************************************************/

 type
     point=^node;
     node=record
                g:longint;
                next:point;
     end;
     map=array[..] of point;
 var
    i,j,k,l,m,n,h,t,ans:longint;
    low,dfn,f,b,d,e:array[..] of longint;
    a,c:map;p:point;
    ss,s:array[..] of boolean;
 function min(x,y:longint):longint;
          begin
               if x<y then min:=x else min:=y;
          end;
 procedure add(x,y:longint;var a:map);
           var p:point;
           begin
                new(p);p^.g:=y;
                p^.next:=a[x];a[x]:=p;
           end;
 procedure tarjan(x:longint);
           var p:point;
           begin
                inc(h);low[x]:=h;dfn[x]:=h;
                inc(t);f[t]:=x;
                ss[x]:=true;s[x]:=true;
                p:=a[x];
                while p<>nil do
                      begin
                           if not(s[p^.g]) then
                              begin
                                   tarjan(p^.g);
                                   low[x]:=min(low[x],low[p^.g]);
                              end
                           else if ss[p^.g] then low[x]:=min(low[x],dfn[p^.g]);
                           p:=p^.next;
                      end;
                if low[x]=dfn[x] then
                   begin
                        inc(ans);
                        while f[t+]<>x do
                              begin
                                   ss[f[t]]:=false;
                                   b[f[t]]:=ans;
                                   dec(t);
                              end;
                   end;
           end;
 procedure dfs(x:longint);
           var p:point;
           begin
                p:=c[x];
                e[x]:=d[x];
                while p<>nil do
                      begin
                           if e[p^.g]= then dfs(p^.g);
                           e[x]:=e[x]+e[p^.g];
                           p:=p^.next;
                      end;
           end;
 begin
      readln(n);
      for i:= to n do a[i]:=nil;
      for i:= to n do
          begin
               readln(j);
               add(i,j,a);
          end;
      fillchar(s,sizeof(s),false);
      fillchar(ss,sizeof(ss),false);
      fillchar(low,sizeof(low),);
      fillchar(dfn,sizeof(dfn),);
      fillchar(f,sizeof(f),);
      h:=;t:=;ans:=;
      for i:= to n do
          if b[i]= then tarjan(i);
      fillchar(d,sizeof(d),);
      for i:= to n do inc(d[b[i]]);
      for i:= to ans do c[i]:=nil;
      for i:= to n do
          begin
               p:=a[i];
               while p<>nil do
                     begin
                          if b[i]<>b[p^.g] then add(b[i],b[p^.g],c);
                          p:=p^.next;
                     end;
          end;
      fillchar(e,sizeof(e),);
      for i:= to ans do
          if e[i]= then dfs(i);
      for i:= to n do
          writeln(e[b[i]]);
      readln;
 end.