#include <bits/stdc++.h>
using namespace std;
#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 pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
typedef vector<int> VI;
typedef long long ll;
typedef pair<int,int> PII;
typedef double db;
//mt19937 mrand(random_device{}());
const ll mod=1000000007;
//int rnd(int x) { return mrand() % x;}
ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;}
int gcd(int a,int b) { return b?gcd(b,a%b):a;}
// head
const int N=1e3+5;
#define INF 0x3f3f3f3f
template<class T> inline void read(T &x) {
x=0; int c=getchar(),f=1;
for (;!isdigit(c);c=getchar()) if (c==45) f=-1;
for (;isdigit(c);c=getchar()) (x*=10)+=f*(c-'0');
}
int n,par[N],deg[N],q[N],dep[N],subtree_size[N],nd_label[N],trial[N];
VI e[N],e_label[N];
bool vis[N],is_inner_node[N],used[N];
int prufer(VI &best,VI &seq) {
rep(i,1,n+1) {
e_label[i].clear();
deg[i]=0;
}
rep(u,1,n+1) for (const auto &v:e[u]) if (u<v) {
int a=nd_label[u],b=nd_label[v];
e_label[a].pb(b);
e_label[b].pb(a);
deg[a]++;
deg[b]++;
}
int res=0,ptr=1;
while (ptr<=n&°[ptr]!=1) ptr++;
int leaf=ptr;
rep(i,0,n-2) {
int par_label=-1;
for (const auto &x:e_label[leaf]) if (deg[x]>0) {
par_label=x;
break;
}
seq.pb(par_label);
deg[leaf]=0;
deg[par_label]--;
if (res==0&&!best.empty()&&i<SZ(best)) {
if (par_label<best[i]) res=1;
else if (par_label>best[i]) return -1;
}
if (deg[par_label]==1&&par_label<ptr) leaf=par_label;
else {
ptr++;
while (ptr<=n&°[ptr]!=1) ptr++;
leaf=ptr;
}
}
return best.empty()?1:res;
}
void solve() {
scanf("%d",&n);
rep(i,1,n+1) e[i].clear();
rep(i,0,n-1) {
int a,b;
scanf("%d%d",&a,&b);
e[a].pb(b);
e[b].pb(a);
}
if (n<=2) {
puts("");
return;
}
int max_leaves=0;
rep(u,1,n+1) {
int n_leaves=0;
for (const auto &v:e[u]) if (SZ(e[v])==1) n_leaves++;
max_leaves=max(max_leaves,n_leaves);
}
VI ans;
rep(root,1,n+1) {
int n_leaves=0;
for (const auto &v:e[root]) if (SZ(e[v])==1) n_leaves++;
if (n_leaves<max_leaves) continue;
memset(par,-1,(n+1)*sizeof(int));
memset(vis,false,(n+1)*sizeof(bool));
memset(is_inner_node,false,(n+1)*sizeof(bool));
VI bfs;
int t_1=0,t_2=0;
q[t_1++]=root;
vis[root]=true;
while (t_2<t_1) {
int u=q[t_2++];
bfs.pb(u);
for (const auto &v:e[u]) if (!vis[v]) {
par[v]=u;
q[t_1++]=v;
vis[v]=true;
}
}
for (const auto &u:bfs) for (const auto &v:e[u]) if (par[v]==u) {
is_inner_node[u]=true;
break;
}
VI inner_nodes;
for (const auto &u:bfs) subtree_size[u]=1;
int bfs_sz=SZ(bfs);
per(i,0,bfs_sz) {
int u=bfs[i];
if (par[u]!=-1) subtree_size[par[u]]+=subtree_size[u];
}
dep[root]=0;
for (const auto &u:bfs) if (par[u]!=-1) dep[u]=dep[par[u]]+1;
for (const auto &u:bfs) if (is_inner_node[u]) inner_nodes.pb(u);
int k=SZ(inner_nodes);
VI inner_nodes_sorted = inner_nodes;
sort(all(inner_nodes_sorted),[&](int u,int v) {
if (dep[u]!=dep[v]) return dep[u]<dep[v];
return subtree_size[u]>subtree_size[v];
});
VI order={root};
memset(used,false,(n+1)*sizeof(bool));
used[root]=true;
rep(j,2,k+1) {
int best_u=-1;
VI best_seq;
for (const auto &u:inner_nodes_sorted) {
if (used[u]) continue;
int next_label=0;
for (const auto &x:order) trial[next_label++]=x;
trial[next_label++]=u;
for (const auto &v:inner_nodes_sorted) if (!used[v]&&u!=v) trial[next_label++]=v;
memset(nd_label,0,(n+1)*sizeof(int));
rep(i,1,k+1) nd_label[trial[i-1]]=i;
int curr=k+1;
rep(i,1,k+1) {
int u_=trial[i-1];
for (const auto &v:e[u_]) if (par[v]==u_&&!is_inner_node[v]) nd_label[v]=curr++;
}
VI seq;
int cmp=prufer(best_seq,seq);
if (cmp==1) {
best_u=u;
best_seq=seq;
}
}
order.pb(best_u);
used[best_u]=true;
}
memset(nd_label,0,(n+1)*sizeof(int));
rep(i,1,k+1) nd_label[order[i-1]]=i;
int curr=k+1;
rep(j,1,k+1) {
int u=order[j-1];
for (const auto &v:e[u]) if (par[v]==u&&!is_inner_node[v]) nd_label[v]=curr++;
}
VI seq;
prufer(ans,seq);
if (ans.empty()||seq<ans) ans=seq;
}
int ans_size=SZ(ans);
rep(i,0,ans_size) printf("%d%c",ans[i]," \n"[i==ans_size-1]);
}
int main() {
int t;
scanf("%d",&t);
while (t--) solve();
}
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 | #include <bits/stdc++.h> using namespace std; #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 pb push_back #define mp make_pair #define all(x) (x).begin(),(x).end() #define fi first #define se second #define SZ(x) ((int)(x).size()) typedef vector<int> VI; typedef long long ll; typedef pair<int,int> PII; typedef double db; //mt19937 mrand(random_device{}()); const ll mod=1000000007; //int rnd(int x) { return mrand() % x;} ll powmod(ll a,ll b) {ll res=1;a%=mod; assert(b>=0); for(;b;b>>=1){if(b&1)res=res*a%mod;a=a*a%mod;}return res;} int gcd(int a,int b) { return b?gcd(b,a%b):a;} // head const int N=1e3+5; #define INF 0x3f3f3f3f template<class T> inline void read(T &x) { x=0; int c=getchar(),f=1; for (;!isdigit(c);c=getchar()) if (c==45) f=-1; for (;isdigit(c);c=getchar()) (x*=10)+=f*(c-'0'); } int n,par[N],deg[N],q[N],dep[N],subtree_size[N],nd_label[N],trial[N]; VI e[N],e_label[N]; bool vis[N],is_inner_node[N],used[N]; int prufer(VI &best,VI &seq) { rep(i,1,n+1) { e_label[i].clear(); deg[i]=0; } rep(u,1,n+1) for (const auto &v:e[u]) if (u<v) { int a=nd_label[u],b=nd_label[v]; e_label[a].pb(b); e_label[b].pb(a); deg[a]++; deg[b]++; } int res=0,ptr=1; while (ptr<=n&°[ptr]!=1) ptr++; int leaf=ptr; rep(i,0,n-2) { int par_label=-1; for (const auto &x:e_label[leaf]) if (deg[x]>0) { par_label=x; break; } seq.pb(par_label); deg[leaf]=0; deg[par_label]--; if (res==0&&!best.empty()&&i<SZ(best)) { if (par_label<best[i]) res=1; else if (par_label>best[i]) return -1; } if (deg[par_label]==1&&par_label<ptr) leaf=par_label; else { ptr++; while (ptr<=n&°[ptr]!=1) ptr++; leaf=ptr; } } return best.empty()?1:res; } void solve() { scanf("%d",&n); rep(i,1,n+1) e[i].clear(); rep(i,0,n-1) { int a,b; scanf("%d%d",&a,&b); e[a].pb(b); e[b].pb(a); } if (n<=2) { puts(""); return; } int max_leaves=0; rep(u,1,n+1) { int n_leaves=0; for (const auto &v:e[u]) if (SZ(e[v])==1) n_leaves++; max_leaves=max(max_leaves,n_leaves); } VI ans; rep(root,1,n+1) { int n_leaves=0; for (const auto &v:e[root]) if (SZ(e[v])==1) n_leaves++; if (n_leaves<max_leaves) continue; memset(par,-1,(n+1)*sizeof(int)); memset(vis,false,(n+1)*sizeof(bool)); memset(is_inner_node,false,(n+1)*sizeof(bool)); VI bfs; int t_1=0,t_2=0; q[t_1++]=root; vis[root]=true; while (t_2<t_1) { int u=q[t_2++]; bfs.pb(u); for (const auto &v:e[u]) if (!vis[v]) { par[v]=u; q[t_1++]=v; vis[v]=true; } } for (const auto &u:bfs) for (const auto &v:e[u]) if (par[v]==u) { is_inner_node[u]=true; break; } VI inner_nodes; for (const auto &u:bfs) subtree_size[u]=1; int bfs_sz=SZ(bfs); per(i,0,bfs_sz) { int u=bfs[i]; if (par[u]!=-1) subtree_size[par[u]]+=subtree_size[u]; } dep[root]=0; for (const auto &u:bfs) if (par[u]!=-1) dep[u]=dep[par[u]]+1; for (const auto &u:bfs) if (is_inner_node[u]) inner_nodes.pb(u); int k=SZ(inner_nodes); VI inner_nodes_sorted = inner_nodes; sort(all(inner_nodes_sorted),[&](int u,int v) { if (dep[u]!=dep[v]) return dep[u]<dep[v]; return subtree_size[u]>subtree_size[v]; }); VI order={root}; memset(used,false,(n+1)*sizeof(bool)); used[root]=true; rep(j,2,k+1) { int best_u=-1; VI best_seq; for (const auto &u:inner_nodes_sorted) { if (used[u]) continue; int next_label=0; for (const auto &x:order) trial[next_label++]=x; trial[next_label++]=u; for (const auto &v:inner_nodes_sorted) if (!used[v]&&u!=v) trial[next_label++]=v; memset(nd_label,0,(n+1)*sizeof(int)); rep(i,1,k+1) nd_label[trial[i-1]]=i; int curr=k+1; rep(i,1,k+1) { int u_=trial[i-1]; for (const auto &v:e[u_]) if (par[v]==u_&&!is_inner_node[v]) nd_label[v]=curr++; } VI seq; int cmp=prufer(best_seq,seq); if (cmp==1) { best_u=u; best_seq=seq; } } order.pb(best_u); used[best_u]=true; } memset(nd_label,0,(n+1)*sizeof(int)); rep(i,1,k+1) nd_label[order[i-1]]=i; int curr=k+1; rep(j,1,k+1) { int u=order[j-1]; for (const auto &v:e[u]) if (par[v]==u&&!is_inner_node[v]) nd_label[v]=curr++; } VI seq; prufer(ans,seq); if (ans.empty()||seq<ans) ans=seq; } int ans_size=SZ(ans); rep(i,0,ans_size) printf("%d%c",ans[i]," \n"[i==ans_size-1]); } int main() { int t; scanf("%d",&t); while (t--) solve(); } |
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