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// GRUNDY GRAPH
// Official Solution by Jacob Plachta
#define DEBUG 0
#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;
#define LL long long
#define LD long double
#define PR pair<int,int>
#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second
template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x*x); }
string plural(string s) { return(Sz(s) && s[Sz(s)-1]=='x' ? s+"en" : s+"s"); }
const int INF = (int)1e9;
const LD EPS = 1e-9;
const LD PI = acos(-1.0);
//#if DEBUG
#define GETCHAR getchar
/*#else
#define GETCHAR getchar_unlocked
#endif*/
bool Read(int &x)
{
char c,r=0,n=0;
x=0;
for(;;)
{
c=GETCHAR();
if ((c<0) && (!r))
return(0);
if ((c=='-') && (!r))
n=1;
else
if ((c>='0') && (c<='9'))
x=x*10+c-'0',r=1;
else
if (r)
break;
}
if (n)
x=-x;
return(1);
}
#define LIM 2000002
struct edge{int e, nxt;};
int V, E;
edge e[LIM], er[LIM];
int sp[LIM], spr[LIM];
int group_cnt, comp[LIM];
bool v[LIM];
int stk[LIM];
void fill_forward(int x)
{
int i;
v[x]=true;
for(i=sp[x];i;i=e[i].nxt) if(!v[e[i].e]) fill_forward(e[i].e);
stk[++stk[0]]=x;
}
void fill_backward(int x)
{
int i;
v[x]=false;
comp[x]=group_cnt;
for(i=spr[x];i;i=er[i].nxt) if(v[er[i].e]) fill_backward(er[i].e);
}
void add_edge(int v1, int v2) //add edge v1->v2
{
e [++E].e=v2; e [E].nxt=sp [v1]; sp [v1]=E;
er[ E].e=v1; er[E].nxt=spr[v2]; spr[v2]=E;
}
void SCC()
{
int i;
stk[0]=0;
memset(v, false, sizeof(v));
for(i=1;i<=V;i++) if(!v[i]) fill_forward(i);
group_cnt=0;
for(i=stk[0];i>=1;i--) if(v[stk[i]]){group_cnt++; fill_backward(stk[i]);}
}
int val[LIM];
bool visA[LIM],visB[LIM];
vector<int> con[LIM];
bool rec(int s,int i)
{
if ((i!=s) && ((i-1)/2%2))
return(1);
if (visB[i])
return(0);
visB[i]=1;
int j;
Fox(j,Sz(con[i]))
if (rec(s,con[i][j]))
return(1);
return(0);
}
int main()
{
if (DEBUG)
freopen("in.txt","r",stdin);
int T,t;
int N,M;
int i,j,a,b;
Read(T);
Fox1(t,T)
{
printf("Case #%d: ",t);
Read(N),Read(M);
N<<=1;
Fox1(i,N)
con[i].clear();
V=N;
E=0;
Fill(sp,0);
Fill(spr,0);
while (M--)
{
Read(i),Read(j);
con[i].pb(j);
add_edge(i,j);
if (j%2)
j++;
else
j--;
if (i%2)
i++;
else
i--;
con[j].pb(i);
add_edge(j,i);
}
SCC();
Fill(visA,0);
Fill(visB,0);
Fox1(i,N)
{
//Alice
a=comp[i],b=comp[i+1];
if (a==b)
goto Bad;
visA[a]=visA[b]=1;
i+=2;
//Bob
a=comp[i],b=comp[i+1];
if ((visA[a]) || (visA[b]) || (rec(i,i)) || (rec(i+1,i+1)))
goto Bad;
i++;
}
printf("Alice\n");
continue;
Bad:;
printf("Bob\n");
}
return(0);
} |