#include #include #include #include #include #include #include using namespace std; // HL 分解 // 頂点 v を根とする部分木: [ in[v], out[v] ) // 頂点 v から見た heavy edge chain の頭: head[v] struct HLD { vector< vector > G; vector sub, par, depth, in, out, rev, head; void dfs_sub(int cur) { for(auto& to : G[cur]) { if(par[cur] == to) continue; par[to] = cur; depth[to] = depth[cur] + 1; dfs_sub(to); sub[cur] += sub[to]; if(sub[to] > sub[ G[cur][0] ]) swap(to, G[cur][0]); } } void dfs_hld(int cur, int& ptr) { in[cur] = ptr; rev[ptr++] = cur; for(auto to : G[cur]) { if(par[cur] == to) continue; head[to] = (to == G[cur][0] ? head[cur] : to); dfs_hld(to, ptr); } out[cur] = ptr; } HLD(int N) : G(N), sub(N, 1), par(N, -1), depth(N), in(N), out(N), rev(N), head(N) {} void add_edge(int u, int v) { G[u].emplace_back(v); G[v].emplace_back(u); } void build(int root=0) { int ptr = 0; dfs_sub(root); dfs_hld(root, ptr); } int lca(int u, int v) { while(1) { if(in[u] > in[v]) swap(u, v); if(head[u] == head[v]) return u; v = par[ head[v] ]; } } int distance(int u, int v) { return depth[u] + depth[v] - 2 * depth[lca(u, v)]; } template void preceed(int u, int v, const F& f, bool b) { for(; head[u] != head[v]; v = par[ head[v] ]) { if(in[u] > in[v]) swap(u, v); f(in[ head[v] ], in[v] + 1); } if(in[u] > in[v]) swap(u, v); f(in[u] + b, in[v] + 1); } // u - v パス上に存在する「頂点」or「辺」全体に f(l, r) を作用 template void query_vertices(int u, int v, const F& f) { preceed(u, v, f, false); } template void query_edges(int u, int v, const F& f) { preceed(u, v, f, true); } template T preceed(int u, int v, T E, const F& f, const M& m, bool b) { T vl(E), vr(E); for(; head[u] != head[v]; v = par[ head[v] ]) { if(in[u] > in[v]) swap(u, v), swap(vl, vr); vr = m(f(in[ head[v] ], in[v] + 1), vr); } if(in[u] > in[v]) swap(u, v), swap(vl, vr); vr = m(f(in[u] + b, in[v] + 1), vr); return m(vl, vr); } // u - v パス上に存在する「頂点」or「辺」全体に割り当てられた値を // 各 chunk に対して f(u, v) で得て // それらを m(l, r) で merge したものを得る // 単位元 E も渡そう template T query_vertices(int u, int v, T E, const F& f, const M& m) { return preceed(u, v, E, f, m, false); } template T query_edges(int u, int v, T E, const F& f, const M& m) { return preceed(u, v, E, f, m, true); } }; template struct LazySegmentTree { using MMtoM = function< MonoidType(MonoidType, MonoidType) >; using OOtoO = function< OperatorType(OperatorType, OperatorType) >; using MOtoM = function< MonoidType(MonoidType, OperatorType) >; using OItoO = function< OperatorType(OperatorType, int) >; // node, lazy, update flag (for lazy), identity element int n; vector node; vector lazy; vector need_update; MonoidType E0; OperatorType E1; // update / combine / lazy / accumulate function MOtoM upd_f; MMtoM cmb_f; OOtoO lzy_f; OItoO acc_f; void build(int m, vector v = vector()) { if(v != vector()) m = v.size(); n = 1; while(n < m) n *= 2; node = vector(2*n-1, E0); lazy = vector(2*n-1, E1); need_update = vector(2*n-1, false); if(v != vector()) { for(int i=0; i=0; i--) { node[i] = cmb_f(node[2*i+1], node[2*i+2]); } } } // initialize LazySegmentTree() {} LazySegmentTree(int n_, MonoidType E0_, OperatorType E1_, MOtoM upd_f_, MMtoM cmb_f_, OOtoO lzy_f_, OItoO acc_f_, vector v = vector()) : E0(E0_), E1(E1_), upd_f(upd_f_), cmb_f(cmb_f_), lzy_f(lzy_f_), acc_f(acc_f_) { build(n_, v); } void eval(int k, int l, int r) { if(!need_update[k]) return; node[k] = upd_f(node[k], acc_f(lazy[k], r - l)); if(r - l > 1) { lazy[2*k+1] = lzy_f(lazy[2*k+1], lazy[k]); lazy[2*k+2] = lzy_f(lazy[2*k+2], lazy[k]); need_update[2*k+1] = need_update[2*k+2] = true; } lazy[k] = E1; need_update[k] = false; } void update(int a, int b, OperatorType x, int l, int r, int k) { eval(k, l, r); if(b <= l or r <= a) return; if(a <= l and r <= b) { lazy[k] = lzy_f(lazy[k], x); need_update[k] = true; eval(k, l, r); } else { int mid = (l + r) / 2; update(a, b, x, l, mid, 2*k+1); update(a, b, x, mid, r, 2*k+2); node[k] = cmb_f(node[2*k+1], node[2*k+2]); } } MonoidType query(int a, int b, int l, int r, int k) { if(b <= l or r <= a) return E0; eval(k, l, r); if(a <= l and r <= b) return node[k]; int mid = (l + r) / 2; MonoidType vl = query(a, b, l, mid, 2*k+1); MonoidType vr = query(a, b, mid, r, 2*k+2); return cmb_f(vl, vr); } // update [a, b)-th element (applied value, x) void update(int a, int b, OperatorType x) { update(a, b, x, 0, n, 0); } // range query for [a, b) MonoidType query(int a, int b) { return query(a, b, 0, n, 0); } void dump() { fprintf(stderr, "[lazy]\n"); for(int i=0; i<2*n-1; i++) { if(i == n-1) fprintf(stderr, "xxx "); if(lazy[i] == E1) fprintf(stderr, " E "); else fprintf(stderr, "%3d ", lazy[i]); } fprintf(stderr, "\n"); fprintf(stderr, "[node]\n"); for(int i=0; i<2*n-1; i++) { if(i == n-1) fprintf(stderr, "xxx "); if(node[i] == E0) fprintf(stderr, " E "); else fprintf(stderr, "%3d ", node[i]); } fprintf(stderr, "\n"); } }; /* void GRL_5_C() { int N; cin >> N; HLD hl(N); for(int i=0; i> c; for(int j=0; j> v; hl.add_edge(u, v); } } hl.build(); int Q; cin >> Q; for(int i=0; i> u >> v; cout << hl.lca(u, v) << endl; } } void ABC014_D() { int N; cin >> N; HLD hl(N); for(int i=0; i> u >> v; u--; v--; hl.add_edge(u, v); } hl.build(); int Q; cin >> Q; for(int i=0; i> u >> v; u--; v--; cout << hl.distance(u, v) + 1 << endl; } } void AOJ2871() { int N, Q; cin >> N >> Q; HLD hl(N); for(int i=1; i> v; v--; hl.add_edge(u, v); } hl.build(); vector color(N); auto &in = hl.in, &out = hl.out; for(int i=0; i> c; color[ in[i] ] = (c == 'G' ? 1 : -1); } LazySegmentTree seg(N, 0, 1, [](int a, int b) { return a * b; }, [](int a, int b) { return a + b; }, [](int a, int b) { return a * b; }, [](int a, int x) { return a; }, color); // seg.dump(); for(int i=0; i> v; v--; seg.update(in[v], out[v], -1); int res = seg.query(in[0], out[0]); if(res < 0) cout << "cauliflower" << endl; else cout << "broccoli" << endl; // seg.dump(); } } void yuki_650() { using mint = ModInt<1000000007>; int N; cin >> N; HLD hl(N); vector u(N), v(N); for(int i=0; i> u[i] >> v[i]; hl.add_edge(u[i], v[i]); } hl.build(); auto &ord = hl.in; using Mat = Matrix; Mat I = eigen(2); LazySegmentTree seg(N, I, I, [](Mat a, Mat b) { return b; }, [](Mat a, Mat b) { return a * b; }, [](Mat a, Mat b) { return b; }, [](Mat a, int x) { return a; }); auto f = [&](int l, int r) { return seg.query(l, r); }; auto m = [&](Mat a, Mat b) { return a * b; }; int Q; cin >> Q; for(int i=0; i> q; if(q == 'x') { int e; mint ul, ur, dl, dr; cin >> e >> ul >> ur >> dl >> dr; Mat mat(2, 2); mat[0] = {ul, ur}; mat[1] = {dl, dr}; hl.query_edges(u[e], v[e], [&mat, &seg](int l, int r) { seg.update(l, r, mat); }); } if(q == 'g') { int x, y; cin >> x >> y; Mat res = hl.query_edges(x, y, I, f, m); cout << res[0][0] << " " << res[0][1] << " " << res[1][0] << " " << res[1][1] << endl; } } } */ void yuki_399() { int N; cin >> N; HLD hl(N); for(int i=0; i> u >> v; u--; v--; hl.add_edge(u, v); } hl.build(); using int64 = long long int; LazySegmentTree seg(N, 0, 0, [](int64 a, int64 b) { return a + b; }, [](int64 a, int64 b) { return a + b; }, [](int64 a, int64 b) { return a + b; }, [](int64 a, int x) { return a * x; }); auto f = [&](int l, int r) { return seg.query(l, r); }; auto g = [&](int l, int r) { seg.update(l, r, 1); }; auto m = [&](int64 a, int64 b) { return a + b; }; int Q; cin >> Q; int64 ans = 0; for(int i=0; i> u >> v; u--; v--; ans += hl.distance(u, v) + 1; ans += hl.query_vertices(u, v, 0LL, f, m); hl.query_vertices(u, v, g); } cout << ans << endl; } int main() { // GRL_5_C(); // LCA // ABC014_D(); // distance // AOJ2871(); // query (subtree) // yuki_650(); // query (edges) yuki_399(); }