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#include "graph/ds/tree_wavelet_matrix.hpp"
#include "ds/wavelet_matrix/wavelet_matrix.hpp" #include "graph/tree.hpp" // https://atcoder.jp/contests/pakencamp-2022-day1/tasks/pakencamp_2022_day1_j // https://atcoder.jp/contests/utpc2011/tasks/utpc2011_12 template <typename TREE, bool edge, typename T, bool COMPRESS, typename Monoid = Monoid_Add<T>> struct Tree_Wavelet_Matrix { TREE& tree; int N; using WM = Wavelet_Matrix<T, COMPRESS, Monoid_Add<T>>; using X = typename Monoid::value_type; WM wm; Tree_Wavelet_Matrix(TREE& tree, vc<T> A, vc<X> SUM_data = {}, int log = -1) : tree(tree), N(tree.N) { vc<X>& S = SUM_data; vc<T> A1; vc<X> S1; A1.resize(N); if (!S.empty()) S1.resize(N); if (!edge) { assert(len(A) == N && (len(S) == 0 || len(S) == N)); FOR(v, N) A1[tree.LID[v]] = A[v]; if (len(S) == N) { FOR(v, N) S1[tree.LID[v]] = S[v]; } wm.build(A1, S1, log); } else { assert(len(A) == N - 1 && (len(S) == 0 || len(S) == N - 1)); if (!S.empty()) { FOR(e, N - 1) { S1[tree.LID[tree.e_to_v(e)]] = S[e]; } } FOR(e, N - 1) { A1[tree.LID[tree.e_to_v(e)]] = A[e]; } wm.build(A1, S1, log); } } // xor した結果で [a, b) に収まるものを数える int count_path(int s, int t, T a, T b, T xor_val = 0) { return wm.count(get_segments(s, t), a, b, xor_val); } // xor した結果で [a, b) に収まるものを数える int count_subtree(int u, T a, T b, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.count(l + edge, r, a, b, xor_val); } // xor した結果で、[L, R) の中で k>=0 番目と prefix sum pair<T, X> kth_value_and_sum_path(int s, int t, int k, T xor_val = 0) { return wm.kth_value_and_sum(get_segments(s, t), k, xor_val); } // xor した結果で、[L, R) の中で k>=0 番目と prefix sum pair<T, X> kth_value_and_sum_subtree(int u, int k, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.kth_value_and_sum(l + edge, r, k, xor_val); } // xor した結果で、[L, R) の中で k>=0 番目 T kth_path(int s, int t, int k, T xor_val = 0) { return wm.kth(get_segments(s, t), k, xor_val); } // xor した結果で、[L, R) の中で k>=0 番目 T kth_subtree(int u, int k, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.kth(l + edge, r, k, xor_val); } // xor した結果で、[L, R) の中で中央値。 // LOWER = true:下側中央値、false:上側中央値 T median_path(bool UPPER, int s, int t, T xor_val = 0) { return wm.median(UPPER, get_segments(s, t), xor_val); } T median_subtree(bool UPPER, int u, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.median(UPPER, l + edge, r, xor_val); } // xor した結果で [k1, k2) 番目であるところの SUM_data の和 X sum_path(int s, int t, int k1, int k2, T xor_val = 0) { return wm.sum(get_segments(s, t), k1, k2, xor_val); } // xor した結果で [k1, k2) 番目であるところの SUM_data の和 X sum_subtree(int u, int k1, int k2, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.sum(l + edge, r, k1, k2, xor_val); } X sum_all_path(int s, int t) { return wm.sum_all(get_segments(s, t)); } X sum_all_subtree(int u) { int l = tree.LID[u], r = tree.RID[u]; return wm.sum_all(l + edge, r); } private: vc<pair<int, int>> get_segments(int s, int t) { vc<pair<int, int>> segments = tree.get_path_decomposition(s, t, edge); for (auto&& [a, b]: segments) { if (a >= b) swap(a, b); ++b; } return segments; } };
#line 1 "graph/ds/tree_wavelet_matrix.hpp" #line 1 "ds/bit_vector.hpp" struct Bit_Vector { vc<pair<u32, u32>> dat; Bit_Vector(int n) { dat.assign((n + 63) >> 5, {0, 0}); } void set(int i) { dat[i >> 5].fi |= u32(1) << (i & 31); } void build() { FOR(i, len(dat) - 1) dat[i + 1].se = dat[i].se + popcnt(dat[i].fi); } // [0, k) 内の 1 の個数 int rank(int k, bool f = 1) { auto [a, b] = dat[k >> 5]; int ret = b + popcnt(a & ((u32(1) << (k & 31)) - 1)); return (f ? ret : k - ret); } }; #line 2 "ds/wavelet_matrix/wavelet_matrix.hpp" // 座圧するかどうかを COMPRESS で指定する // xor 的な使い方をする場合には、コンストラクタで log を渡すこと template <typename T, bool COMPRESS, bool USE_SUM> struct Wavelet_Matrix { static_assert(is_same_v<T, int> || is_same_v<T, ll>); int N, lg; vector<int> mid; vector<Bit_Vector> bv; vc<T> key; bool set_log; vvc<T> cumsum; Wavelet_Matrix() {} // 和を使わないなら、SUM_data は空でよい Wavelet_Matrix(vc<T> A, vc<T> SUM_data = {}, int log = -1) { build(A, SUM_data, log); } void build(vc<T> A, vc<T> SUM_data = {}, int log = -1) { if constexpr (USE_SUM) { assert(len(SUM_data) == len(A)); } N = len(A), lg = log, set_log = (log != -1); if (N == 0) { lg = 0; cumsum.resize(1); cumsum[0] = {0}; return; } vc<T>& S = SUM_data; if (COMPRESS) { assert(!set_log); key.reserve(N); vc<int> I = argsort(A); for (auto&& i: I) { if (key.empty() || key.back() != A[i]) key.eb(A[i]); A[i] = len(key) - 1; } key.shrink_to_fit(); } if (lg == -1) lg = __lg(max<ll>(MAX(A), 1)) + 1; mid.resize(lg), bv.assign(lg, Bit_Vector(N)); if constexpr (USE_SUM) cumsum.assign(1 + lg, vc<T>(N + 1, 0)); S.resize(N); vc<T> A0(N), A1(N); vc<T> S0(N), S1(N); FOR_R(d, -1, lg) { int p0 = 0, p1 = 0; if constexpr (USE_SUM) { FOR(i, N) { cumsum[d + 1][i + 1] = cumsum[d + 1][i] + S[i]; } } if (d == -1) break; FOR(i, N) { bool f = (A[i] >> d & 1); if (!f) { if constexpr (USE_SUM) S0[p0] = S[i]; A0[p0++] = A[i]; } else { if constexpr (USE_SUM) S1[p1] = S[i]; bv[d].set(i), A1[p1++] = A[i]; } } mid[d] = p0; bv[d].build(); swap(A, A0), swap(S, S0); FOR(i, p1) A[p0 + i] = A1[i], S[p0 + i] = S1[i]; } } // [L,R) x [a,b), (cnt, monoid value) pair<int, T> range_cnt_sum(int L, int R, T a, T b, T xor_val = 0) { if (xor_val != 0) assert(set_log); if (a == b) return {0, 0}; if (COMPRESS) a = LB(key, a), b = LB(key, b); int cnt = 0; T sm = 0; auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void { if (rx <= a || b <= lx) return; if (a <= lx && rx <= b) { cnt += R - L, sm += get(d, L, R); return; } --d; T mx = (lx + rx) / 2; int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1); dfs(dfs, d, l0, r0, lx, mx), dfs(dfs, d, l1, r1, mx, rx); }; dfs(dfs, lg, L, R, 0, T(1) << lg); return {cnt, sm}; } // smallest k, sum of [0,k) pair<T, T> kth_value_sum(int L, int R, int k, T xor_val = 0) { assert(0 <= k && k <= R - L); if (k == R - L) { return {infty<T>, sum_all(L, R)}; } if (L == R) return {infty<T>, 0}; if (xor_val != 0) assert(set_log); T sm = 0, val = 0; for (int d = lg - 1; d >= 0; --d) { // いま幅 d+1 の trie node に居て, 幅 d のところに行く int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1); if (k < r0 - l0) { L = l0, R = r0; } else { k -= r0 - l0, val |= T(1) << d, L = l1, R = r1; if constexpr (USE_SUM) sm += get(d, l0, r0); } } if constexpr (USE_SUM) sm += get(0, L, L + k); if (COMPRESS) val = key[val]; return {val, sm}; } int count(int L, int R, T a, T b, T xor_val = 0) { return range_cnt_sum(L, R, a, b, xor_val).fi; } T sum(int L, int R, T a, T b, T xor_val = 0) { static_assert(USE_SUM); return range_cnt_sum(L, R, a, b, xor_val).se; } T sum_index_range(int L, int R, int k1, int k2, T xor_val = 0) { static_assert(USE_SUM); return kth_value_sum(L, R, k2, xor_val).se - kth_value_sum(L, R, k1, xor_val).se; } T kth(int L, int R, int k, T xor_val = 0) { assert(0 <= k && k < R - L); return kth_value_sum(L, R, k, xor_val).fi; } // x 以上最小 OR infty<T> T next(int L, int R, T x, T xor_val = 0) { if (xor_val != 0) assert(set_log); if (L == R) return infty<T>; if (COMPRESS) x = LB(key, x); T ans = infty<T>; auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void { if (ans <= lx || L == R || rx <= x) return; if (d == 0) { chmin(ans, lx); return; } --d; T mx = (lx + rx) / 2; int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1); dfs(dfs, d, l0, r0, lx, mx), dfs(dfs, d, l1, r1, mx, rx); }; dfs(dfs, lg, L, R, 0, T(1) << lg); if (COMPRESS && ans < infty<T>) ans = key[ans]; return ans; } // x 以下最大 OR -infty<T> T prev(int L, int R, T x, T xor_val = 0) { if (xor_val != 0) assert(set_log); if (L == R) return -infty<T>; T ans = -infty<int>; ++x; if (COMPRESS) x = LB(key, x); auto dfs = [&](auto& dfs, int d, int L, int R, T lx, T rx) -> void { if ((rx - 1) <= ans || L == R || x <= lx) return; if (d == 0) { chmax(ans, lx); return; } --d; T mx = (lx + rx) / 2; int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1); dfs(dfs, d, l1, r1, mx, rx), dfs(dfs, d, l0, r0, lx, mx); }; dfs(dfs, lg, L, R, 0, T(1) << lg); if (COMPRESS && ans != -infty<T>) ans = key[ans]; return ans; } // xor した結果で、[L, R) の中で中央値。 // LOWER = true:下側中央値、false:上側中央値 T median(bool UPPER, int L, int R, T xor_val = 0) { int n = R - L; int k = (UPPER ? n / 2 : (n - 1) / 2); return kth(L, R, k, xor_val); } T sum_all(int L, int R) { return get(lg, L, R); } // check(cnt, prefix sum) が true となるような最大の (cnt, sum) template <typename F> pair<int, T> max_right(F check, int L, int R, T xor_val = 0) { assert(check(0, 0)); if (xor_val != 0) assert(set_log); if (L == R) return {0, 0}; if (check(R - L, get(lg, L, R))) return {R - L, get(lg, L, R)}; int cnt = 0; T sm = 0; for (int d = lg - 1; d >= 0; --d) { int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0); int l1 = L + mid[d] - l0, r1 = R + mid[d] - r0; if (xor_val >> d & 1) swap(l0, l1), swap(r0, r1); if (check(cnt + r0 - l0, sm + get(d, l0, r0))) { cnt += r0 - l0, sm += get(d, l0, r0); L = l1, R = r1; } else { L = l0, R = r0; } } int k = binary_search( [&](int k) -> bool { return check(cnt + k, sm + get(0, L, L + k)); }, 0, R - L); cnt += k, sm += get(0, L, L + k); return {cnt, sm}; } private: inline T get(int d, int L, int R) { if constexpr (USE_SUM) return cumsum[d][R] - cumsum[d][L]; return 0; } }; #line 2 "graph/tree.hpp" #line 2 "graph/base.hpp" template <typename T> struct Edge { int frm, to; T cost; int id; }; template <typename T = int, bool directed = false> struct Graph { static constexpr bool is_directed = directed; int N, M; using cost_type = T; using edge_type = Edge<T>; vector<edge_type> edges; vector<int> indptr; vector<edge_type> csr_edges; vc<int> vc_deg, vc_indeg, vc_outdeg; bool prepared; class OutgoingEdges { public: OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {} const edge_type* begin() const { if (l == r) { return 0; } return &G->csr_edges[l]; } const edge_type* end() const { if (l == r) { return 0; } return &G->csr_edges[r]; } private: const Graph* G; int l, r; }; bool is_prepared() { return prepared; } Graph() : N(0), M(0), prepared(0) {} Graph(int N) : N(N), M(0), prepared(0) {} void build(int n) { N = n, M = 0; prepared = 0; edges.clear(); indptr.clear(); csr_edges.clear(); vc_deg.clear(); vc_indeg.clear(); vc_outdeg.clear(); } void add(int frm, int to, T cost = 1, int i = -1) { assert(!prepared); assert(0 <= frm && 0 <= to && to < N); if (i == -1) i = M; auto e = edge_type({frm, to, cost, i}); edges.eb(e); ++M; } #ifdef FASTIO // wt, off void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); } void read_graph(int M, bool wt = false, int off = 1) { for (int m = 0; m < M; ++m) { INT(a, b); a -= off, b -= off; if (!wt) { add(a, b); } else { T c; read(c); add(a, b, c); } } build(); } #endif void build() { assert(!prepared); prepared = true; indptr.assign(N + 1, 0); for (auto&& e: edges) { indptr[e.frm + 1]++; if (!directed) indptr[e.to + 1]++; } for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; } auto counter = indptr; csr_edges.resize(indptr.back() + 1); for (auto&& e: edges) { csr_edges[counter[e.frm]++] = e; if (!directed) csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id}); } } OutgoingEdges operator[](int v) const { assert(prepared); return {this, indptr[v], indptr[v + 1]}; } vc<int> deg_array() { if (vc_deg.empty()) calc_deg(); return vc_deg; } pair<vc<int>, vc<int>> deg_array_inout() { if (vc_indeg.empty()) calc_deg_inout(); return {vc_indeg, vc_outdeg}; } int deg(int v) { if (vc_deg.empty()) calc_deg(); return vc_deg[v]; } int in_deg(int v) { if (vc_indeg.empty()) calc_deg_inout(); return vc_indeg[v]; } int out_deg(int v) { if (vc_outdeg.empty()) calc_deg_inout(); return vc_outdeg[v]; } #ifdef FASTIO void debug() { print("Graph"); if (!prepared) { print("frm to cost id"); for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id); } else { print("indptr", indptr); print("frm to cost id"); FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id); } } #endif vc<int> new_idx; vc<bool> used_e; // G における頂点 V[i] が、新しいグラフで i になるようにする // {G, es} Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) { if (len(new_idx) != N) new_idx.assign(N, -1); int n = len(V); FOR(i, n) new_idx[V[i]] = i; Graph<T, directed> G(n); vc<int> history; FOR(i, n) { for (auto&& e: (*this)[V[i]]) { if (len(used_e) <= e.id) used_e.resize(e.id + 1); if (used_e[e.id]) continue; int a = e.frm, b = e.to; if (new_idx[a] != -1 && new_idx[b] != -1) { history.eb(e.id); used_e[e.id] = 1; int eid = (keep_eid ? e.id : -1); G.add(new_idx[a], new_idx[b], e.cost, eid); } } } FOR(i, n) new_idx[V[i]] = -1; for (auto&& eid: history) used_e[eid] = 0; G.build(); return G; } private: void calc_deg() { assert(vc_deg.empty()); vc_deg.resize(N); for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++; } void calc_deg_inout() { assert(vc_indeg.empty()); vc_indeg.resize(N); vc_outdeg.resize(N); for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; } } }; #line 4 "graph/tree.hpp" // HLD euler tour をとっていろいろ。 template <typename GT> struct Tree { using Graph_type = GT; GT &G; using WT = typename GT::cost_type; int N; vector<int> LID, RID, head, V, parent, VtoE; vc<int> depth; vc<WT> depth_weighted; Tree(GT &G, int r = 0, bool hld = 1) : G(G) { build(r, hld); } void build(int r = 0, bool hld = 1) { if (r == -1) return; // build を遅延したいとき N = G.N; LID.assign(N, -1), RID.assign(N, -1), head.assign(N, r); V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1); depth.assign(N, -1), depth_weighted.assign(N, 0); assert(G.is_prepared()); int t1 = 0; dfs_sz(r, -1, hld); dfs_hld(r, t1); } void dfs_sz(int v, int p, bool hld) { auto &sz = RID; parent[v] = p; depth[v] = (p == -1 ? 0 : depth[p] + 1); sz[v] = 1; int l = G.indptr[v], r = G.indptr[v + 1]; auto &csr = G.csr_edges; // 使う辺があれば先頭にする for (int i = r - 2; i >= l; --i) { if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]); } int hld_sz = 0; for (int i = l; i < r; ++i) { auto e = csr[i]; if (depth[e.to] != -1) continue; depth_weighted[e.to] = depth_weighted[v] + e.cost; VtoE[e.to] = e.id; dfs_sz(e.to, v, hld); sz[v] += sz[e.to]; if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); } } } void dfs_hld(int v, int ×) { LID[v] = times++; RID[v] += LID[v]; V[LID[v]] = v; bool heavy = true; for (auto &&e: G[v]) { if (depth[e.to] <= depth[v]) continue; head[e.to] = (heavy ? head[v] : e.to); heavy = false; dfs_hld(e.to, times); } } vc<int> heavy_path_at(int v) { vc<int> P = {v}; while (1) { int a = P.back(); for (auto &&e: G[a]) { if (e.to != parent[a] && head[e.to] == v) { P.eb(e.to); break; } } if (P.back() == a) break; } return P; } int heavy_child(int v) { int k = LID[v] + 1; if (k == N) return -1; int w = V[k]; return (parent[w] == v ? w : -1); } int e_to_v(int eid) { auto e = G.edges[eid]; return (parent[e.frm] == e.to ? e.frm : e.to); } int v_to_e(int v) { return VtoE[v]; } int ELID(int v) { return 2 * LID[v] - depth[v]; } int ERID(int v) { return 2 * RID[v] - depth[v] - 1; } // 目標地点へ進む個数が k int LA(int v, int k) { assert(k <= depth[v]); while (1) { int u = head[v]; if (LID[v] - k >= LID[u]) return V[LID[v] - k]; k -= LID[v] - LID[u] + 1; v = parent[u]; } } int la(int u, int v) { return LA(u, v); } int LCA(int u, int v) { for (;; v = parent[head[v]]) { if (LID[u] > LID[v]) swap(u, v); if (head[u] == head[v]) return u; } } int meet(int a, int b, int c) { return LCA(a, b) ^ LCA(a, c) ^ LCA(b, c); } int lca(int u, int v) { return LCA(u, v); } int subtree_size(int v, int root = -1) { if (root == -1) return RID[v] - LID[v]; if (v == root) return N; int x = jump(v, root, 1); if (in_subtree(v, x)) return RID[v] - LID[v]; return N - RID[x] + LID[x]; } int dist(int a, int b) { int c = LCA(a, b); return depth[a] + depth[b] - 2 * depth[c]; } WT dist_weighted(int a, int b) { int c = LCA(a, b); return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c]; } // a is in b bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; } int jump(int a, int b, ll k) { if (k == 1) { if (a == b) return -1; return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]); } int c = LCA(a, b); int d_ac = depth[a] - depth[c]; int d_bc = depth[b] - depth[c]; if (k > d_ac + d_bc) return -1; if (k <= d_ac) return LA(a, k); return LA(b, d_ac + d_bc - k); } vc<int> collect_child(int v) { vc<int> res; for (auto &&e: G[v]) if (e.to != parent[v]) res.eb(e.to); return res; } vc<int> collect_light(int v) { vc<int> res; bool skip = true; for (auto &&e: G[v]) if (e.to != parent[v]) { if (!skip) res.eb(e.to); skip = false; } return res; } vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) { // [始点, 終点] の"閉"区間列。 vc<pair<int, int>> up, down; while (1) { if (head[u] == head[v]) break; if (LID[u] < LID[v]) { down.eb(LID[head[v]], LID[v]); v = parent[head[v]]; } else { up.eb(LID[u], LID[head[u]]); u = parent[head[u]]; } } if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]); elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge); reverse(all(down)); up.insert(up.end(), all(down)); return up; } vc<int> restore_path(int u, int v) { vc<int> P; for (auto &&[a, b]: get_path_decomposition(u, v, 0)) { if (a <= b) { FOR(i, a, b + 1) P.eb(V[i]); } else { FOR_R(i, b, a + 1) P.eb(V[i]); } } return P; } // path [a,b] と [c,d] の交わり. 空ならば {-1,-1}. // https://codeforces.com/problemset/problem/500/G pair<int, int> path_intersection(int a, int b, int c, int d) { int ab = lca(a, b), ac = lca(a, c), ad = lca(a, d); int bc = lca(b, c), bd = lca(b, d), cd = lca(c, d); int x = ab ^ ac ^ bc, y = ab ^ ad ^ bd; // meet(a,b,c), meet(a,b,d) if (x != y) return {x, y}; int z = ac ^ ad ^ cd; if (x != z) x = -1; return {x, x}; } }; #line 4 "graph/ds/tree_wavelet_matrix.hpp" // https://atcoder.jp/contests/pakencamp-2022-day1/tasks/pakencamp_2022_day1_j // https://atcoder.jp/contests/utpc2011/tasks/utpc2011_12 template <typename TREE, bool edge, typename T, bool COMPRESS, typename Monoid = Monoid_Add<T>> struct Tree_Wavelet_Matrix { TREE& tree; int N; using WM = Wavelet_Matrix<T, COMPRESS, Monoid_Add<T>>; using X = typename Monoid::value_type; WM wm; Tree_Wavelet_Matrix(TREE& tree, vc<T> A, vc<X> SUM_data = {}, int log = -1) : tree(tree), N(tree.N) { vc<X>& S = SUM_data; vc<T> A1; vc<X> S1; A1.resize(N); if (!S.empty()) S1.resize(N); if (!edge) { assert(len(A) == N && (len(S) == 0 || len(S) == N)); FOR(v, N) A1[tree.LID[v]] = A[v]; if (len(S) == N) { FOR(v, N) S1[tree.LID[v]] = S[v]; } wm.build(A1, S1, log); } else { assert(len(A) == N - 1 && (len(S) == 0 || len(S) == N - 1)); if (!S.empty()) { FOR(e, N - 1) { S1[tree.LID[tree.e_to_v(e)]] = S[e]; } } FOR(e, N - 1) { A1[tree.LID[tree.e_to_v(e)]] = A[e]; } wm.build(A1, S1, log); } } // xor した結果で [a, b) に収まるものを数える int count_path(int s, int t, T a, T b, T xor_val = 0) { return wm.count(get_segments(s, t), a, b, xor_val); } // xor した結果で [a, b) に収まるものを数える int count_subtree(int u, T a, T b, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.count(l + edge, r, a, b, xor_val); } // xor した結果で、[L, R) の中で k>=0 番目と prefix sum pair<T, X> kth_value_and_sum_path(int s, int t, int k, T xor_val = 0) { return wm.kth_value_and_sum(get_segments(s, t), k, xor_val); } // xor した結果で、[L, R) の中で k>=0 番目と prefix sum pair<T, X> kth_value_and_sum_subtree(int u, int k, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.kth_value_and_sum(l + edge, r, k, xor_val); } // xor した結果で、[L, R) の中で k>=0 番目 T kth_path(int s, int t, int k, T xor_val = 0) { return wm.kth(get_segments(s, t), k, xor_val); } // xor した結果で、[L, R) の中で k>=0 番目 T kth_subtree(int u, int k, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.kth(l + edge, r, k, xor_val); } // xor した結果で、[L, R) の中で中央値。 // LOWER = true:下側中央値、false:上側中央値 T median_path(bool UPPER, int s, int t, T xor_val = 0) { return wm.median(UPPER, get_segments(s, t), xor_val); } T median_subtree(bool UPPER, int u, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.median(UPPER, l + edge, r, xor_val); } // xor した結果で [k1, k2) 番目であるところの SUM_data の和 X sum_path(int s, int t, int k1, int k2, T xor_val = 0) { return wm.sum(get_segments(s, t), k1, k2, xor_val); } // xor した結果で [k1, k2) 番目であるところの SUM_data の和 X sum_subtree(int u, int k1, int k2, T xor_val = 0) { int l = tree.LID[u], r = tree.RID[u]; return wm.sum(l + edge, r, k1, k2, xor_val); } X sum_all_path(int s, int t) { return wm.sum_all(get_segments(s, t)); } X sum_all_subtree(int u) { int l = tree.LID[u], r = tree.RID[u]; return wm.sum_all(l + edge, r); } private: vc<pair<int, int>> get_segments(int s, int t) { vc<pair<int, int>> segments = tree.get_path_decomposition(s, t, edge); for (auto&& [a, b]: segments) { if (a >= b) swap(a, b); ++b; } return segments; } };