【UOJ #266】【清华集训2016】Alice和Bob又在玩游戏（SG函数+01Trie）

传送门

和$Combat on a tree$没有区别
选了一条链之后各个子树互相独立
对于一个点子树内所有点都可以选

可以用$01Trie$维护选每个子孙的$SG$函数值
往上可以直接$01Trie$合并，然后打上其他子树的异或和的标记
每次查询$mex$即可

#include<bits/stdc++.h>
using namespace std;
#define cs const
#define pb push_back
#define pii pair<int,int>
#define fi first
#define se second
#define ll long long
cs int RLEN=1<<20|1;
inline char gc(){
	static char ibuf[RLEN],*ib,*ob;
	(ib==ob)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin));
	return (ib==ob)?EOF:*ib++;
}
inline int read(){
	char ch=gc();
	int res=0;bool f=1;
	while(!isdigit(ch))f^=ch=='-',ch=gc();
	while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc();
	return f?res:-res;
}
cs int N=100005;
namespace Trie{
	cs int M=N*18;
	int vt[M],son[M][2],tag[M],tot;
	#define lc(u) son[u][0]
	#define rc(u) son[u][1]
	inline void clear(){
		while(tot)lc(tot)=rc(tot)=0,tag[tot]=0,vt[tot--]=0;
	}
	inline void pushnow(int u,int k,int dep){
		if(k&(1<<dep))swap(lc(u),rc(u));
		tag[u]^=k;
	}
	inline void pushdown(int u,int dep){
		if(!tag[u]||dep==0)return;
		if(lc(u))pushnow(lc(u),tag[u],dep-1);
		if(rc(u))pushnow(rc(u),tag[u],dep-1);
		tag[u]=0;
	}
	void merge(int &u,int r1,int r2,int dep){
		if(!r1||!r2){u=r1+r2;return;}
		pushdown(r1,dep),pushdown(r2,dep);
		u=r1,vt[u]=vt[r1]|vt[r2];
		merge(lc(u),lc(r1),lc(r2),dep-1),merge(rc(u),rc(r1),rc(r2),dep-1);
		vt[u]|=vt[lc(u)]&vt[rc(u)];
	}
	void insert(int &u,int k,int dep){
		if(!u)u=++tot;
		if(dep==-1){vt[u]=1;return;}		
		pushdown(u,dep);
		if(k&(1<<dep))insert(rc(u),k,dep-1);
		else insert(lc(u),k,dep-1);
		vt[u]=vt[lc(u)]&vt[rc(u)];
	}
	int mex(int u,int dep){
		if(dep<0)return 0;
		pushdown(u,dep);
		if(vt[lc(u)])return (1<<dep)+mex(rc(u),dep-1);
		else return mex(lc(u),dep-1);
	}
}
vector<int> e[N];
int n,m;
int vis[N],rt[N],sg[N];
void dfs(int u,int fa){
	int s=0;vis[u]=1;
	for(int &v:e[u]){
		if(v==fa)continue;
		dfs(v,u);
		s^=sg[v];
	}
	Trie::insert(rt[u],s,16);
	for(int &v:e[u]){
		if(v==fa)continue;
		Trie::pushnow(rt[v],s^sg[v],16);
		Trie::merge(rt[u],rt[u],rt[v],16);
	}
	sg[u]=Trie::mex(rt[u],16);
}
inline void solve(){
	n=read(),m=read();
	for(int i=1;i<=m;i++){
		int u=read(),v=read();
		e[u].pb(v),e[v].pb(u);
	}
	int ret=0;
	for(int i=1;i<=n;i++)if(!vis[i])dfs(i,0),ret^=sg[i];
	if(ret>0)puts("Alice");
	else puts("Bob");
	for(int i=1;i<=n;i++)e[i].clear(),rt[i]=vis[i]=sg[i]=0;
	Trie::clear();
}
int main(){
	#ifdef Stargazer
	freopen("lx.in","r",stdin);
	#endif
	int T=read();
	while(T--)solve();
}