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graph/ds/tree_wavelet_matrix.hpp
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- Last update: 2023-11-30 16:31:51+09:00
- Include:
#include "graph/ds/tree_wavelet_matrix.hpp" - Link: https://atcoder.jp/contests/pakencamp-2022-day1/tasks/pakencamp_2022_day1_j
- Link: https://atcoder.jp/contests/utpc2011/tasks/utpc2011_12
Depends on
alg/monoid/add.hpp
Code
#include "ds/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 "alg/monoid/add.hpp"
template <typename X>
struct Monoid_Add {
using value_type = X;
static constexpr X op(const X &x, const X &y) noexcept { return x + y; }
static constexpr X inverse(const X &x) noexcept { return -x; }
static constexpr X power(const X &x, ll n) noexcept { return X(n) * x; }
static constexpr X unit() { return X(0); }
static constexpr bool commute = true;
};
#line 3 "ds/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, typename Monoid = Monoid_Add<T>>
struct Wavelet_Matrix {
using MX = Monoid;
using X = typename MX::value_type;
static_assert(MX::commute);
int N, lg;
vector<int> mid;
vector<Bit_Vector> bv;
vc<T> key;
bool set_log;
vvc<X> cumsum;
Wavelet_Matrix() {}
// 和を使わないなら、SUM_data は空でよい
Wavelet_Matrix(vc<T> A, vc<X> SUM_data = {}, int log = -1) {
build(A, SUM_data, log);
}
void build(vc<T> A, vc<X> SUM_data = {}, int log = -1) {
N = len(A), lg = log, set_log = (log != -1);
bool MAKE_SUM = !(SUM_data.empty());
vc<X>& 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 (MAKE_SUM) cumsum.assign(1 + lg, vc<X>(N + 1, MX::unit()));
S.resize(N);
vc<T> A0(N), A1(N);
vc<X> S0(N), S1(N);
FOR_R(d, -1, lg) {
int p0 = 0, p1 = 0;
if (MAKE_SUM) {
FOR(i, N) { cumsum[d + 1][i + 1] = MX::op(cumsum[d + 1][i], S[i]); }
}
if (d == -1) break;
FOR(i, N) {
bool f = (A[i] >> d & 1);
if (!f) {
if (MAKE_SUM) S0[p0] = S[i];
A0[p0++] = A[i];
}
if (f) {
if (MAKE_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];
}
}
// xor した結果で [a, b) に収まるものを数える
int count(int L, int R, T a, T b, T xor_val = 0) {
return prefix_count(L, R, b, xor_val) - prefix_count(L, R, a, xor_val);
}
int count(vc<pair<int, int>> segments, T a, T b, T xor_val = 0) {
int res = 0;
for (auto&& [L, R]: segments) res += count(L, R, a, b, xor_val);
return res;
}
// 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(int L, int R, int k, T xor_val = 0) {
assert(!cumsum.empty());
if (xor_val != 0) assert(set_log);
assert(0 <= k && k <= R - L);
if (k == R - L) { return {infty<T>, sum_all(L, R)}; }
int cnt = 0;
X sm = MX::unit();
T ret = 0;
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
if (cnt + c > k) {
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
} else {
X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
cnt += c, ret |= T(1) << d, sm = MX::op(sm, s);
if (!f) L += mid[d] - l0, R += mid[d] - r0;
if (f) L = l0, R = r0;
}
}
sm = MX::op(sm, get(0, L, L + k - cnt));
if (COMPRESS) ret = key[ret];
return {ret, sm};
}
// 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(vc<pair<int, int>> segments, int k,
T xor_val = 0) {
assert(!cumsum.empty());
if (xor_val != 0) assert(set_log);
int total_len = 0;
for (auto&& [L, R]: segments) total_len += R - L;
assert(0 <= k && k <= total_len);
if (k == total_len) { return {infty<T>, sum_all(segments)}; }
int cnt = 0;
X sm = MX::unit();
T ret = 0;
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int c = 0;
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
c += (f ? (R - L) - (r0 - l0) : (r0 - l0));
}
if (cnt + c > k) {
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
}
} else {
cnt += c, ret |= T(1) << d;
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
sm = MX::op(sm, s);
if (!f) L += mid[d] - l0, R += mid[d] - r0;
if (f) L = l0, R = r0;
}
}
}
for (auto&& [L, R]: segments) {
int t = min(R - L, k - cnt);
sm = MX::op(sm, get(0, L, L + t));
cnt += t;
}
if (COMPRESS) ret = key[ret];
return {ret, sm};
}
// xor した結果で、[L, R) の中で k>=0 番目
T kth(int L, int R, int k, T xor_val = 0) {
if (xor_val != 0) assert(set_log);
assert(0 <= k && k < R - L);
int cnt = 0;
T ret = 0;
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
if (cnt + c > k) {
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
} else {
cnt += c, ret |= T(1) << d;
if (!f) L += mid[d] - l0, R += mid[d] - r0;
if (f) L = l0, R = r0;
}
}
if (COMPRESS) ret = key[ret];
return ret;
}
T kth(vc<pair<int, int>> segments, int k, T xor_val = 0) {
int total_len = 0;
for (auto&& [L, R]: segments) total_len += R - L;
assert(0 <= k && k < total_len);
int cnt = 0;
T ret = 0;
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int c = 0;
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
c += (f ? (R - L) - (r0 - l0) : (r0 - l0));
}
if (cnt + c > k) {
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
}
} else {
cnt += c, ret |= T(1) << d;
for (auto&& [L, R]: segments) {
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
if (!f) L += mid[d] - l0, R += mid[d] - r0;
if (f) L = l0, R = r0;
}
}
}
if (COMPRESS) ret = key[ret];
return ret;
}
// 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 median(bool UPPER, vc<pair<int, int>> segments, T xor_val = 0) {
int n = 0;
for (auto&& [L, R]: segments) n += R - L;
int k = (UPPER ? n / 2 : (n - 1) / 2);
return kth(segments, k, 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(int L, int R, int k1, int k2, T xor_val = 0) {
X add = prefix_sum(L, R, k2, xor_val);
X sub = prefix_sum(L, R, k1, xor_val);
return MX::op(add, MX::inverse(sub));
}
X sum_all(int L, int R) { return get(lg, L, R); }
X sum_all(vc<pair<int, int>> segments) {
X sm = MX::unit();
for (auto&& [L, R]: segments) { sm = MX::op(sm, get(lg, L, R)); }
return sm;
}
// check(cnt, prefix sum) が true となるような最大の (cnt, sum)
template <typename F>
pair<int, X> max_right(F check, int L, int R, T xor_val = 0) {
assert(check(0, MX::unit()));
if (xor_val != 0) assert(set_log);
if (check(R - L, get(lg, L, R))) return {R - L, get(lg, L, R)};
int cnt = 0;
X sm = MX::unit();
for (int d = lg - 1; d >= 0; --d) {
bool f = (xor_val >> d) & 1;
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
int c = (f ? (R - L) - (r0 - l0) : (r0 - l0));
X s = (f ? get(d, L + mid[d] - l0, R + mid[d] - r0) : get(d, l0, r0));
if (check(cnt + c, MX::op(sm, s))) {
cnt += c, sm = MX::op(sm, s);
if (f) L = l0, R = r0;
if (!f) L += mid[d] - l0, R += mid[d] - r0;
} else {
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
}
}
int k = binary_search(
[&](int k) -> bool {
return check(cnt + k, MX::op(sm, get(0, L, L + k)));
},
0, R - L);
cnt += k;
sm = MX::op(sm, get(0, L, L + k));
return {cnt, sm};
}
private:
inline X get(int d, int L, int R) {
assert(!cumsum.empty());
return MX::op(MX::inverse(cumsum[d][L]), cumsum[d][R]);
}
// xor した結果で [0, x) に収まるものを数える
int prefix_count(int L, int R, T x, T xor_val = 0) {
if (xor_val != 0) assert(set_log);
x = (COMPRESS ? LB(key, x) : x);
if (x == 0) return 0;
if (x >= (1 << lg)) return R - L;
int cnt = 0;
FOR_R(d, lg) {
bool add = (x >> d) & 1;
bool f = ((xor_val) >> d) & 1;
int l0 = bv[d].rank(L, 0), r0 = bv[d].rank(R, 0);
int kf = (f ? (R - L) - (r0 - l0) : (r0 - l0));
if (add) {
cnt += kf;
if (f) { L = l0, R = r0; }
if (!f) { L += mid[d] - l0, R += mid[d] - r0; }
} else {
if (!f) L = l0, R = r0;
if (f) L += mid[d] - l0, R += mid[d] - r0;
}
}
return cnt;
}
// xor した結果で [0, k) 番目のものの和
X prefix_sum(int L, int R, int k, T xor_val = 0) {
return kth_value_and_sum(L, R, k, xor_val).se;
}
// xor した結果で [0, k) 番目のものの和
X prefix_sum(vc<pair<int, int>> segments, int k, T xor_val = 0) {
return kth_value_and_sum(segments, k, xor_val).se;
}
};
#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);
if (len(used_e) != M) used_e.assign(M, 0);
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 (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;
}
}
// root を根とした場合の lca
int LCA_root(int u, int v, int root) {
return LCA(u, v) ^ LCA(u, root) ^ LCA(v, root);
}
int lca(int u, int v) { return LCA(u, v); }
int lca_root(int u, int v, int root) { return LCA_root(u, v, root); }
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;
}
};
#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;
}
};