Christmas Game POJ - 3710

1. 无向图缩环变树
2. 树删边博弈
   边连通分量缩成一个点

#include<iostream>
#include<cstdio>
#include<cctype>
#include<cstring>
#include<algorithm>
#include<vector>
#include<stack>
#include<map>
#include<queue>
#include<cmath>
#define mem(ar,num) memset(ar,num,sizeof(ar))
#define me(ar) memset(ar,0,sizeof(ar))
#define lowbit(x) (x&(-x))
#define Pb push_back
#define FI first
#define SE second
#define rep(i,a,n) for (int i=a;i<n;i++)
#define per(i,a,n) for (int i=n-1;i>=a;i--)
#define IOS ios::sync_with_stdio(false)
#define DEBUG cout<<endl<<"DEBUG"<<endl; 
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
const int    prime = 999983;
const int    INF = 0x7FFFFFFF;
const LL     INFF =0x7FFFFFFFFFFFFFFF;
const double pi = acos(-1.0);
const double inf = 1e18;
const double eps = 1e-6;
const LL     mod = 1e9 + 7;
LL qpow(LL a,LL b){LL s=1;while(b>0){if(b&1)s=s*a%mod;a=a*a%mod;b>>=1;}return s;}
LL gcd(LL a,LL b) {return b?gcd(b,a%b):a;}
int dr[2][4] = {1,-1,0,0,0,0,-1,1};
typedef pair<int,int> P;
// 边连通分量
vector<P> edges;
const int maxn = 1e6+100;
int pre[maxn];
int dfs_clock = 0;
vector<int> G[maxn];
vector<int> G2[maxn];
int low[maxn];


//
int father[maxn];
bool vis[maxn];
int  belong[maxn];
int  num[maxn];
void init(int m){
    dfs_clock = 0;
    rep(i,1,m+1) G[i].clear(),G2[i].clear();
    // me(low);
    memset(low,0,sizeof(low[0])*(m+1));
    // me(pre);
    memset(pre,0,sizeof(pre[0])*(m+1));
        // me(vis);
    memset(vis,0,sizeof(vis[0])*(m+1));
    // me(num);
    memset(num,0,sizeof(num[0])*(m+1));
    // me(belong);
    memset(belong,0,sizeof(belong[0])*(m+1));
}
int dfs1(int u,int fa){
    father[u] = fa;
    int lowu = pre[u] =  ++dfs_clock;
    // int child = 0;
    int tofa = 0;
    for(int i = 0;i < (int)G[u].size(); ++i){
        int v = G[u][i];
        if(!pre[v]){
            int lowv = dfs1(v,u);
            lowu = min(lowu,lowv);
        }
        else if( v != fa){
            lowu = min(lowu,pre[v]);
        }
        else if(v == fa)
            {
                if(tofa) 
                   lowu = min(lowu,pre[v]);
                tofa++;
            }
    }
    return low[u] = lowu;
}
// #define Debug

bool Is_bridge(int u,int v){
    if(father[v] != u&&father[u] != v) return 0;
    return (pre[v] == low[v]);
}
void dfs(int u,int be){
     belong[u] = be;
     for(int i = 0;i < (int)G[u].size(); ++i){
        int v = G[u][i];
        if(belong[v])   continue;
        if(Is_bridge(u,v)) continue;
        // cout<<u<<" "<<v<<endl;
        dfs(v,be);
     }
}

int SG(int u,int fa){
    vis[u] = 1;
    int t = 0;
    for(int i = 0;i < (int)G2[u].size(); ++i){
        int v = G2[u][i];
        if(vis[v]) continue;
        t ^= (SG(v,u)+1);
    }
    if(num[u]&1) t  ^= 1;
    return t;
}
int main(void)
{
    // freopen("input.txt","r",stdin);
    // freopen("out.txt","w+",stdout);
    int  n,m,k;
    // while(cin>>n){
    cin>>n;
        
        while(n--){
            int sum = 0;
            
            edges.clear();
            scanf("%d%d",&m,&k);
            init(m);
            // cout<<m<<" "<<k<<endl;
            rep(i,0,k){
                int u,v;
                scanf("%d%d",&u,&v);
                G[u].Pb(v);
                G[v].Pb(u);
                edges.Pb(P(u,v));
            }
            // DEBUG
            // cout<<endl;

            dfs1(1,-1);
            int tot = 0;
            rep(i,1,m+1)
                if(!belong[i])
                    dfs(i,++tot);
                // cout<<en
            // cout<<tot<<endl;
            // dfs(m+1,)
                // DEBUG;
            for(int i = 0;i < (int)edges.size(); i  ++){
                int x = belong[edges[i].first];
                int y = belong[edges[i].second];
                    if(x != y)
                          G2[x].Pb(y),G2[y].Pb(x);
                    else
                          num[x]++;
            }
            // DEBUG;
           sum ^= SG(1,-1);
           // cout<<sum<<endl;
          //
           if (sum) cout << "Alice\n"; else cout << "Bob\n"; 
        }
       
    // }
   return 0;
}