// Trees as a Service // Solution by Jacob Plachta #define DEBUG 0 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define LL long long #define LD long double #define PR pair #define Fox(i,n) for (i=0; 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 T Abs(T x) { return(x<0 ? -x : x); } template 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 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 con[MAXN]; set badp; vector > 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 subtree; queue 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 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); }