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// Trees as a Service
// 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-12;
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 MAXN 60
#define MAXM 120
int N,M;
int X[MAXM],Y[MAXM],Z[MAXM],P[MAXN];
bool BuildTree(int par,vector<int> nodes)
{
int s=Sz(nodes);
int i,j,k,a,b,c;
bool here[MAXN]={0};
bool good;
Fox(i,s)
here[nodes[i]]=1;
// consider each possible root
Fox(i,s)
{
// compute nodes which must or must not be in the same subtree
int r=nodes[i];
vector<int> con[MAXN];
set<PR> badp;
vector<vector<int> > subtrees;
bool used[MAXN]={0};
Fox(j,M)
if (here[a=X[j]] && here[b=Y[j]] && here[c=Z[j]])
if (a==r || b==r)
{
// LCA of pair including root must be equal to root
if (c!=r)
goto Bad;
}
else
if (c==r)
{
// pair with LCA equal to root must be in different subtrees
badp.insert(mp(a,b));
badp.insert(mp(b,a));
}
else
{
// otherwise, triple must be in the same subtree
con[a].pb(b);
con[b].pb(a);
con[a].pb(c);
con[c].pb(a);
}
// floodfill to compute subtrees
Fox(j,s)
if (j!=i && !used[k=nodes[j]])
{
vector<int> subtree;
queue<int> Q;
Q.push(k),used[k]=1;
while (!Q.empty())
{
k=Q.front(),Q.pop();
subtree.pb(k);
Fox(a,Sz(con[k]))
if (!used[b=con[k][a]])
Q.push(b),used[b]=1;
}
Fox(a,Sz(subtree))
Fox(b,a)
if (badp.count(mp(subtree[a],subtree[b])))
goto Bad;
subtrees.pb(subtree);
}
// recursively attempt to build each subtree
P[r]=par;
Fox(j,Sz(subtrees))
if (!BuildTree(r,subtrees[j]))
return(0);
return(1);
Bad:;
}
return(0);
}
int main()
{
if (DEBUG)
freopen("in.txt","r",stdin);
// vars
int T,t;
int i;
// testcase loop
Read(T);
Fox1(t,T)
{
// input
Read(N),Read(M);
Fox(i,M)
Read(X[i]),Read(Y[i]),Read(Z[i]),X[i]--,Y[i]--,Z[i]--;
// recursively build tree, and output
Fill(P,-1);
vector<int> nodes;
Fox(i,N)
nodes.pb(i);
printf("Case #%d: ",t);
if (!BuildTree(-1,nodes))
printf("Impossible\n");
else
{
Fox(i,N)
printf("%d%c",P[i]+1,(i==N-1)?'\n':' ');
}
}
return(0);
} |