#pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include #include #include #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; using Int = long long; template ostream &operator<<(ostream &os, const pair &a) { return os << "(" << a.first << ", " << a.second << ")"; }; template ostream &operator<<(ostream &os, const vector &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; } template void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; } template bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; } template bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; } #define COLOR(s) ("\x1b[" s "m") struct Hld { int n, rt; // needs to be tree // vertex lists // modified in build(rt) (parent removed, heavy child first) vector> graph; vector sz, par, dep; int zeit; vector dis, fin, sid; // head vertex (minimum depth) in heavy path vector head; Hld() : n(0), rt(-1), zeit(0) {} explicit Hld(int n_) : n(n_), rt(-1), graph(n), zeit(0) {} void ae(int u, int v) { assert(0 <= u); assert(u < n); assert(0 <= v); assert(v < n); graph[u].push_back(v); graph[v].push_back(u); } void dfsSz(int u) { sz[u] = 1; for (const int v : graph[u]) { auto it = std::find(graph[v].begin(), graph[v].end(), u); if (it != graph[v].end()) graph[v].erase(it); par[v] = u; dep[v] = dep[u] + 1; dfsSz(v); sz[u] += sz[v]; } } void dfsHld(int u) { dis[u] = zeit++; const int deg = graph[u].size(); if (deg > 0) { int vm = graph[u][0]; int jm = 0; for (int j = 1; j < deg; ++j) { const int v = graph[u][j]; if (sz[vm] < sz[v]) { vm = v; jm = j; } } swap(graph[u][0], graph[u][jm]); head[vm] = head[u]; dfsHld(vm); for (int j = 1; j < deg; ++j) { const int v = graph[u][j]; head[v] = v; dfsHld(v); } } fin[u] = zeit; } void build(int rt_) { assert(0 <= rt_); assert(rt_ < n); rt = rt_; sz.assign(n, 0); par.assign(n, -1); dep.assign(n, -1); dep[rt] = 0; dfsSz(rt); zeit = 0; dis.assign(n, -1); fin.assign(n, -1); head.assign(n, -1); head[rt] = rt; dfsHld(rt); assert(zeit == n); sid.assign(n, -1); for (int u = 0; u < n; ++u) sid[dis[u]] = u; } friend ostream &operator<<(ostream &os, const Hld &hld) { const int maxDep = *max_element(hld.dep.begin(), hld.dep.end()); vector ss(2 * maxDep + 1); int pos = 0, maxPos = 0; for (int j = 0; j < hld.n; ++j) { const int u = hld.sid[j]; const int d = hld.dep[u]; if (hld.head[u] == u) { if (j != 0) { pos = maxPos + 1; ss[2 * d - 1].resize(pos, '-'); ss[2 * d - 1] += '+'; } } else { ss[2 * d - 1].resize(pos, ' '); ss[2 * d - 1] += '|'; } ss[2 * d].resize(pos, ' '); ss[2 * d] += std::to_string(u); if (maxPos < static_cast(ss[2 * d].size())) { maxPos = ss[2 * d].size(); } } for (int d = 0; d <= 2 * maxDep; ++d) os << ss[d] << '\n'; return os; } bool contains(int u, int v) const { return (dis[u] <= dis[v] && dis[v] < fin[u]); } int lca(int u, int v) const { assert(0 <= u); assert(u < n); assert(0 <= v); assert(v < n); for (; head[u] != head[v]; ) (dis[u] > dis[v]) ? (u = par[head[u]]) : (v = par[head[v]]); return (dis[u] > dis[v]) ? v : u; } int jumpUp(int u, int d) const { assert(0 <= u); assert(u < n); assert(d >= 0); if (dep[u] < d) return -1; const int tar = dep[u] - d; for (u = head[u]; ; u = head[par[u]]) { if (dep[u] <= tar) return sid[dis[u] + (tar - dep[u])]; } } int jump(int u, int v, int d) const { assert(0 <= u); assert(u < n); assert(0 <= v); assert(v < n); assert(d >= 0); const int l = lca(u, v); const int du = dep[u] - dep[l], dv = dep[v] - dep[l]; if (d <= du) { return jumpUp(u, d); } else if (d <= du + dv) { return jumpUp(v, du + dv - d); } else { return -1; } } // [u, v) or [u, v] template void doPathUp(int u, int v, bool inclusive, F f) const { assert(contains(v, u)); for (; head[u] != head[v]; u = par[head[u]]) f(dis[head[u]], dis[u] + 1); if (inclusive) { f(dis[v], dis[u] + 1); } else { if (v != u) f(dis[v] + 1, dis[u] + 1); } } // not path order, include lca(u, v) or not template void doPath(int u, int v, bool inclusive, F f) const { const int l = lca(u, v); doPathUp(u, l, false, f); doPathUp(v, l, inclusive, f); } // (vs, ps): compressed tree // vs: DFS order (sorted by dis) // vs[ps[x]]: the parent of vs[x] // ids[vs[x]] = x, not set for non-tree vertex vector ids; pair, vector> compress(vector us) { // O(n) first time ids.resize(n, -1); std::sort(us.begin(), us.end(), [&](int u, int v) -> bool { return (dis[u] < dis[v]); }); us.erase(std::unique(us.begin(), us.end()), us.end()); int usLen = us.size(); assert(usLen >= 1); for (int x = 1; x < usLen; ++x) us.push_back(lca(us[x - 1], us[x])); std::sort(us.begin(), us.end(), [&](int u, int v) -> bool { return (dis[u] < dis[v]); }); us.erase(std::unique(us.begin(), us.end()), us.end()); usLen = us.size(); for (int x = 0; x < usLen; ++x) ids[us[x]] = x; vector ps(usLen, -1); for (int x = 1; x < usLen; ++x) ps[x] = ids[lca(us[x - 1], us[x])]; return make_pair(us, ps); } }; //////////////////////////////////////////////////////////////////////////////// // build: O(n log(n)) time/space // operator(): O(1) time struct Lca { int n, rt; vector> graph; vector par, dep, su; int usLen; vector us; vector buffer; vector mn; Lca() : n(0), rt(-1), usLen(0) {} explicit Lca(int n_) : n(n_), rt(-1), graph(n), usLen(0) {} void ae(int u, int v) { assert(0 <= u); assert(u < n); assert(0 <= v); assert(v < n); graph[u].push_back(v); graph[v].push_back(u); } void dfs(int u, int p) { us[su[u] = usLen++] = u; for (const int v : graph[u]) if (p != v) { par[v] = u; dep[v] = dep[u] + 1; dfs(v, u); us[usLen++] = u; } } void build(int rt_) { assert(0 <= rt_); assert(rt_ < n); rt = rt_; par.assign(n, -1); dep.assign(n, -1); su.assign(n, -1); usLen = 0; us.assign(2 * n - 1, -1); dep[rt] = 0; dfs(rt, -1); assert(usLen == 2 * n - 1); const int l = (31 - __builtin_clz(usLen)) + 1; buffer.resize(l * usLen); mn.resize(l); for (int e = 0; e < l; ++e) mn[e] = buffer.data() + e * usLen; for (int j = 0; j < usLen; ++j) mn[0][j] = us[j]; for (int e = 0; e < l - 1; ++e) for (int i = 0; i + (1 << (e + 1)) <= usLen; ++i) { mn[e + 1][i] = shallower(mn[e][i], mn[e][i + (1 << e)]); } } int shallower(int u, int v) const { return (dep[u] <= dep[v]) ? u : v; } int operator()(int u, int v) const { int j0 = su[u], j1 = su[v]; if (j0 > j1) swap(j0, j1); ++j1; const int e = 31 - __builtin_clz(j1 - j0); return shallower(mn[e][j0], mn[e][j1 - (1 << e)]); } int dist(int u, int v) const { return dep[u] + dep[v] - 2 * dep[operator()(u, v)]; } }; //////////////////////////////////////////////////////////////////////////////// struct Tree { int n; // vector>> graph; vector>> edges; // explicit Tree(int n_) : n(n_), graph(n) {} explicit Tree(int n_) : n(n_), edges() { edges.reserve(n - 1); } void ae(int u, int v, int c) { // graph[u].emplace_back(c, v); // graph[v].emplace_back(c, u); edges.emplace_back(c, make_pair(u, v)); } vector pt; vector> zu; void build() { pt.assign(n + 1, 0); for (int i = 0; i < n - 1; ++i) { const int u = edges[i].second.first; const int v = edges[i].second.second; ++pt[u]; ++pt[v]; } for (int u = 0; u < n; ++u) pt[u + 1] += pt[u]; zu.resize(2 * (n - 1)); for (int i = n - 1; --i >= 0; ) { const int c = edges[i].first; const int u = edges[i].second.first; const int v = edges[i].second.second; zu[--pt[u]] = make_pair(c, v); zu[--pt[v]] = make_pair(c, u); } } template void decomp(F f) { sz.assign(n, 0); dfsSz(0, -1); del.assign(n, 0); solveRec(0, f); } vector sz, del; void dfsSz(int u, int p) { sz[u] = 1; // for (const auto &e : graph[u]) { const int v = e.second; if (p != v) { for (int j = pt[u]; j < pt[u + 1]; ++j) { const auto &e = zu[j]; const int v = e.second; if (p != v) { dfsSz(v, u); sz[u] += sz[v]; }} } template void solveRec(int u, F f) { for (; ; ) { int vm = -1; // for (const auto &e : graph[u]) { const int v = e.second; if (!del[v]) { for (int j = pt[u]; j < pt[u + 1]; ++j) { const auto &e = zu[j]; const int v = e.second; if (!del[v]) { if (!~vm || sz[vm] < sz[v]) { vm = v; } }} if (!~vm || 2 * sz[vm] <= sz[u]) { solveSubtree(u, f); del[u] = 1; // for (const auto &e : graph[u]) { const int v = e.second; if (!del[v]) { for (int j = pt[u]; j < pt[u + 1]; ++j) { const auto &e = zu[j]; const int v = e.second; if (!del[v]) { solveRec(v, f); }} break; } else { sz[u] -= sz[vm]; sz[vm] += sz[u]; u = vm; } } } template void solveSubtree(int r, F f) { int allLen = 0; vector> all(sz[r]); all[allLen++] = make_pair(0, r); // for (const auto &e1 : graph[r]) { const int r1 = e1.second; if (!del[r1]) { for (int j1 = pt[r]; j1 < pt[r + 1]; ++j1) { const auto &e1 = zu[j1]; const int r1 = e1.second; if (!del[r1]) { int queLen = 0; // vector> que(sz[r1]); auto *que = all.data() + allLen; que[queLen++] = e1; for (int k = 0; k < sz[r1]; ++k) { const int d = que[k].first; const int u = que[k].second; // for (const auto &e : graph[u]) { const int v = e.second; if (!del[v] && sz[u] > sz[v]) { for (int j = pt[u]; j < pt[u + 1]; ++j) { const auto &e = zu[j]; const int v = e.second; if (!del[v] && sz[u] > sz[v]) { que[queLen++] = make_pair(d + e.first, v); }} } // f(-1, que); f(-1, que, que + queLen); // for (int k = 0; k < sz[r1]; ++k) all[allLen++] = que[k]; allLen += queLen; }} // f(+1, all); f(+1, all.data(), all.data() + allLen); } }; int N; vector A[2], B[2]; int main() { for (; ~scanf("%d", &N); ) { for (int h = 0; h < 2; ++h) { A[h].resize(N - 1); B[h].resize(N - 1); for (int i = 0; i < N - 1; ++i) { scanf("%d%d", &A[h][i], &B[h][i]); --A[h][i]; --B[h][i]; } } Hld hld[2]; for (int h = 0; h < 2; ++h) { hld[h] = Hld(N); for (int i = 0; i < N - 1; ++i) hld[h].ae(A[h][i], B[h][i]); hld[h].build(0); // cerr< ds(N, -1); Tree T0(N); for (int i = 0; i < N - 1; ++i) T0.ae(A[0][i], B[0][i], 1); T0.build(); // T0.decomp([&](int s0, const vector> &fs) -> void { T0.decomp([&](int s0, const pair *fL, const pair *fR) -> void { const vector> fs(fL, fR); // cerr<<"s0 = "<