Popular Cows poj 2186 tarjan

最新推荐文章于 2020-08-15 10:29:27 发布

原创最新推荐文章于 2020-08-15 10:29:27 发布 · 148 阅读

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本文介绍了一种使用Tarjan算法解决奶牛人气排名的问题。在一个包含N头奶牛的群体中，通过M对奶牛之间的评价关系，计算出被所有其他奶牛认为最受欢迎的奶牛数量。文章详细阐述了算法流程及其实现代码。

题意/Description:

Every cow's dream is to become the most popular cow in the herd. In a herd of N (1 <= N <= 10,000) cows, you are given up to M (1 <= M <= 50,000) ordered pairs of the form (A, B) that tell you that cow A thinks that cow B is popular. Since popularity is transitive, if A thinks B is popular and B thinks C is popular, then A will also think that C is popular, even if this is not explicitly specified by an ordered pair in the input. Your task is to compute the number of cows that are considered popular by every other cow.

读入/Input：

Line 1: Two space-separated integers, N and M

Lines 2..1+M: Two space-separated numbers A and B, meaning that A thinks B is popular.

输出/Output：

Line 1: A single integer that is the number of cows who are considered popular by every other cow.

题解/solution：

先跑一遍taijian算法。那么出度为0的强连通分量代表的就是受其他奶牛欢迎的，但是如果出度为0的强连通分量的个数大于1.那么则无解。因为将至少有两个分量里的奶牛互相不喜欢。所以我们的算法就是如果出度为0的强连通分量的个数是1.那么我们算出这里面点的个数就是最后的答案。

代码/Code：

const
  maxE=500001;
  maxV=50001;

type
  arr=record
        x,y,w,next:longint;
      end;
Var
  n,m,t,ans,t1:longint;
  tu:array [0..maxE] of arr;
  v:array [0..maxV] of Boolean;
  ls,a,ru,cu,low,dfn,f:array [0..maxV] of longint;
procedure dfs(o:longint);
Var
  i,j,k:longint;
begin
  inc(t);
  f[t]:=o;
  v[o]:=true;
  inc(t1);
  low[o]:=t1;
  dfn[o]:=t1;
  i:=ls[o];
  while i<>0 do
    with tu[i] do
      begin
        if dfn[y]=0 then
          begin
            dfs(y);
            if low[o]>low[y] then low[o]:=low[y];
          end else
            if (low[o]>dfn[y]) and (v[y]) then low[o]:=dfn[y];
        i:=next;
      end;
  if low[o]=dfn[o]then
    begin
      ans:=ans+1;
      repeat
        j:=f[t];
        t:=t-1;
        a[j]:=ans;
        v[j]:=false;
      until j=o;
    end;
end;

procedure init;
var
  i,k:longint;
begin
  readln(n,m);
  k:=0;
  ans:=0;
  for i:=1 to m do
    with tu[i] do
      begin
        readln(x,y);
        next:=ls[x];
        ls[x]:=i;
      end;
  for i:=1 to n do
    if a[i]=0 then dfs(i);
end;

procedure main;
var
  i,j:longint;
begin
  for i:=1 to n do
    begin
      j:=ls[i];
      while j<>0 do
        with tu[j] do
          begin
            if a[x]<>a[y]
              then
                begin
                  cu[a[x]]:=cu[a[x]]+1;
                  ru[a[y]]:=ru[a[y]]+1;
                end;
            j:=next;
          end;
    end;
end;

procedure print;
var
  i,o,k:longint;
begin
  k:=0;
  for i:=1 to ans do
    if cu[i]=0 then k:=k+1;
  if k<>1 then
    begin
      write(0);
      halt;
    end;
  k:=0;
  for i:=1 to ans do
    if cu[i]=0 then k:=i;
  o:=0;
  for i:=1 to n do
    if a[i]=k then o:=o+1;
  write(o);
end;

begin
  init;
  main;
  print;
end.