1009 - Back to Underworld（二分图染色）

最新推荐文章于 2025-07-26 12:35:25 发布

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最新推荐文章于 2025-07-26 12:35:25 发布

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分类专栏： lightoj

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本文探讨了一种方法，通过分析不同种族之间的战斗记录，来预测最终存活的最大种族成员数量。通过输入战斗数量及参与者的具体对战信息，算法能够高效计算出可能的种族规模。

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http://www.lightoj.com/volume_showproblem.php?problem=1009

1009 - Back to Underworld

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Time Limit: 4 second(s)

Memory Limit: 32 MB

The Vampires and Lykans are fighting each other to death. The war has become so fierce that, none knows who will win. The humans want to know who will survive finally. But humans are afraid of going to the battlefield.

So, they made a plan. They collected the information from the newspapers of Vampires and Lykans. They found the information about all the dual fights. Dual fight means a fight between a Lykan and a Vampire. They know the name of the dual fighters, but don't know which one of them is a Vampire or a Lykan.

So, the humans listed all the rivals. They want to find the maximum possible number of Vampires or Lykans.

Input

Input starts with an integer T (≤ 10), denoting the number of test cases.

Each case contains an integer n (1 ≤ n ≤ 10⁵), denoting the number of dual fights. Each of the next n lines will contain two different integers u v (1 ≤ u, v ≤ 20000) denoting there was a fight between u and v. No rival will be reported more than once.

Output

For each case, print the case number and the maximum possible members of any race.

Sample Input

Output for Sample Input

1 2

2 3

1 2

2 3

4 2

Case 1: 2

Case 2: 3

Note

Dataset is huge, use faster I/O methods.

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <map>
#include <set>
#include <stack>
#include <string>
#define SI(T)int T;scanf("%d",&T)
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define LL long long
using namespace std;
const int SIZE=2e4+10;
const int maxn=1<<30;
int vis[SIZE];
int node[SIZE];
int sum_tot[SIZE][2];
vector<vector<int> >G;
void bfs(int s,int tot){
    queue<int> q;
    q.push(s);
    vis[s]=1;
    while(!q.empty()){
        int u=q.front();
        q.pop();
        sum_tot[tot][vis[u]]++;
        for(int i=0;i<G[u].size();i++){
            int v=G[u][i];
            if(vis[v]!=-1)continue;//匹配过了return false;
            q.push(v);
            vis[v]=vis[u]^1;
        }
    }
    return;
}
int main()
{
    SI(T);
    for(int cas=1;cas<=T;cas++){
        G.clear();
        G.resize(SIZE);
        memset(vis,0,sizeof(vis));
        int n,u,v,cnt=0;
        scanf("%d",&n);
        while(n--){
            scanf("%d%d",&u,&v);
            if(!vis[u]){
                node[cnt++]=u;
                vis[u]=1;
            }
            if(!vis[v]){
                node[cnt++]=v;
                vis[v]=1;
            }
            G[u].push_back(v);
            G[v].push_back(u);
        }
        int tot=0;
        memset(vis,-1,sizeof(vis));
        memset(sum_tot,0,sizeof(sum_tot));
        for(int i=0;i<cnt;i++){
            int x=node[i];
            if(vis[x]==-1){
                bfs(x,tot++);
            }
        }
        int ans=0;
        for(int i=0;i<tot;i++){
            ans+=max(sum_tot[i][0],sum_tot[i][1]);
        }
        printf("Case %d: %d\n",cas,ans);
    }
    return 0;
}