This documentation is automatically generated by online-judge-tools/verification-helper
#include "ds/segtree/sortable_segtree.hpp"#include "ds/fastset.hpp"
#include "ds/segtree/segtree.hpp"
#include "ds/node_pool.hpp"
template <typename Monoid>
struct Sortable_SegTree {
using MX = Monoid;
using X = typename MX::value_type;
const int N, KEY_MAX;
struct Node {
X x, rev_x;
int size;
Node *l, *r;
};
Node_Pool<Node> pool;
using np = Node*;
FastSet ss; // 区間の左端全体を表す fastset
SegTree<MX> seg; // 区間を集約した値を区間の左端にのせた segtree
vector<np> root; // 区間の左端に、dynamic segtree の node を乗せる
vector<bool> rev;
Sortable_SegTree(int KEY_MAX, vector<int> key, vector<X> dat)
: N(key.size()), KEY_MAX(KEY_MAX), ss(key.size()), seg(dat) {
init(key, dat);
}
void set(int i, int key, const X& x) {
assert(key < KEY_MAX);
split_at(i), split_at(i + 1);
rev[i] = 0, root[i] = new_node();
set_rec(root[i], 0, KEY_MAX, key, x);
seg.set(i, x);
}
X prod_all() { return seg.prod_all(); }
X prod(int l, int r) {
split_at(l), split_at(r);
return seg.prod(l, r);
}
void sort_inc(int l, int r) {
split_at(l), split_at(r);
while (1) {
np c = root[l];
int i = ss.next(l + 1);
if (i == r) break;
root[l] = merge(c, root[i]);
ss.erase(i), seg.set(i, MX::id());
}
rev[l] = 0, seg.set(l, root[l]->x);
};
void sort_dec(int l, int r) {
sort_inc(l, r), rev[l] = 1;
seg.set(l, root[l]->rev_x);
};
pair<vc<int>, vc<X>> get_all() {
vector<int> key;
vector<X> dat;
key.reserve(N);
dat.reserve(N);
auto dfs = [&](auto& dfs, np n, int l, int r, bool rev) -> void {
if (!n) return;
if (r == l + 1) {
key.eb(l), dat.eb(n->x);
return;
}
int m = (l + r) / 2;
if (!rev) {
dfs(dfs, n->l, l, m, rev), dfs(dfs, n->r, m, r, rev);
}
if (rev) {
dfs(dfs, n->r, m, r, rev), dfs(dfs, n->l, l, m, rev);
}
};
for (int i = 0; i < N; ++i) {
if (ss[i]) dfs(dfs, root[i], 0, KEY_MAX, rev[i]);
}
return {key, dat};
}
private:
void init(vector<int>& key, vector<X>& dat) {
rev.assign(N, 0), root.clear(), root.reserve(N);
seg.build(N, [&](int i) -> X { return dat[i]; });
for (int i = 0; i < N; ++i) {
ss.insert(i);
root.eb(new_node(MX::id()));
assert(key[i] < KEY_MAX);
set_rec(root[i], 0, KEY_MAX, key[i], dat[i]);
}
}
// x が左端になるようにする
void split_at(int x) {
if (x == N || ss[x]) return;
int a = ss.prev(x), b = ss.next(a + 1);
ss.insert(x);
if (!rev[a]) {
auto [nl, nr] = split(root[a], x - a);
root[a] = nl, root[x] = nr;
rev[a] = rev[x] = 0;
seg.set(a, root[a]->x), seg.set(x, root[x]->x);
} else {
auto [nl, nr] = split(root[a], b - x);
root[a] = nr, root[x] = nl;
rev[a] = rev[x] = 1;
seg.set(a, root[a]->rev_x), seg.set(x, root[x]->rev_x);
}
}
void rebuild() {
auto [key, dat] = get_all();
pool.reset();
init(key, dat);
}
np new_node(X x = MX::id()) {
np c = pool.create();
c->x = c->rev_x = x;
c->l = c->r = nullptr;
c->size = 1;
return c;
}
pair<np, np> split(np n, int k) {
if (k == 0) {
return {nullptr, n};
}
if (k == n->size) {
return {n, nullptr};
}
int s = (n->l ? n->l->size : 0);
Node* b = new_node();
if (k <= s) {
auto [nl, nr] = split(n->l, k);
b->l = nr, b->r = n->r, n->l = nl, n->r = nullptr;
}
if (k > s) {
auto [nl, nr] = split(n->r, k - s);
n->l = n->l, n->r = nl, b->l = nullptr, b->r = nr;
}
update(n), update(b);
return {n, b};
}
np merge(np a, np b) {
if (!a) return b;
if (!b) return a;
a->l = merge(a->l, b->l), a->r = merge(a->r, b->r);
update(a);
return a;
}
void update(np n) {
if (!(n->l) && !(n->r)) {
return;
}
if (!(n->l)) {
n->x = n->r->x, n->rev_x = n->r->rev_x, n->size = n->r->size;
return;
}
if (!(n->r)) {
n->x = n->l->x, n->rev_x = n->l->rev_x, n->size = n->l->size;
return;
}
n->x = MX::op(n->l->x, n->r->x);
n->rev_x = MX::op(n->r->rev_x, n->l->rev_x);
n->size = n->l->size + n->r->size;
}
void set_rec(np n, int l, int r, int k, const X& x) {
if (r == l + 1) {
n->x = n->rev_x = x;
return;
}
int m = (l + r) / 2;
if (k < m) {
if (!(n->l)) n->l = new_node();
set_rec(n->l, l, m, k, x);
}
if (m <= k) {
if (!(n->r)) n->r = new_node();
set_rec(n->r, m, r, k, x);
}
update(n);
}
};#line 1 "other/bit.hpp"
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T kth_bit(int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
assert(0 <= k && k < int(8 * sizeof(T)));
return x >> k & 1;
}
template <typename UINT>
struct all_bit {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_bit(UINT s) : s(s) {}
struct iter {
UINT s;
int operator*() const { return lowbit(s); }
void operator++() { s &= s - 1; }
bool operator!=(nullptr_t) const { return s; }
};
iter begin() const { return {s}; }
nullptr_t end() const { return nullptr; }
};
template <typename UINT>
struct all_subset {
static_assert(is_unsigned<UINT>::value);
UINT s;
all_subset(UINT s) : s(s) {}
struct iter {
UINT s, t;
bool done = false;
UINT operator*() const { return t; }
void operator++() {
done = (t == 0);
t = (t - 1) & s;
}
bool operator!=(nullptr_t) const { return !done; }
};
iter begin() const { return {s, s}; }
nullptr_t end() const { return nullptr; }
};
constexpr u64 full_mask(int n) {
assert(0 <= n && n <= 64);
return n == 64 ? -1ULL : (1ULL << n) - 1;
}
u64 bit_reverse(u64 x) {
x = ((x & 0x5555555555555555ULL) << 1) | ((x >> 1) & 0x5555555555555555ULL);
x = ((x & 0x3333333333333333ULL) << 2) | ((x >> 2) & 0x3333333333333333ULL);
x = ((x & 0x0f0f0f0f0f0f0f0fULL) << 4) | ((x >> 4) & 0x0f0f0f0f0f0f0f0fULL);
x = ((x & 0x00ff00ff00ff00ffULL) << 8) | ((x >> 8) & 0x00ff00ff00ff00ffULL);
x = ((x & 0x0000ffff0000ffffULL) << 16) | ((x >> 16) & 0x0000ffff0000ffffULL);
x = (x << 32) | (x >> 32);
return x;
}
#line 2 "ds/fastset.hpp"
// 64-ary tree
// space: (N/63) * u64
struct FastSet {
static constexpr u32 B = 64;
int n = 0, log = 0;
vvc<u64> seg;
FastSet() {}
FastSet(int n) { build(n); }
int size() { return n; }
void fill_one() {
int cur = n;
for (auto& vs : seg) {
int p = cur / B, q = cur % B;
FOR(i, p) vs[i] = -1ull;
if (q) vs[p] = full_mask(q);
cur = (cur + B - 1) / B;
}
}
template <typename F>
FastSet(int n, F f) {
build(n, f);
}
void build(int m) {
seg.clear();
n = m;
do {
seg.push_back(vc<u64>((m + B - 1) / B));
m = (m + B - 1) / B;
} while (m > 1);
log = len(seg);
}
template <typename F>
void build(int n, F f) {
build(n);
FOR(i, n) { seg[0][i / B] |= u64(bool(f(i))) << (i % B); }
FOR(h, log - 1) {
FOR(i, len(seg[h])) {
seg[h + 1][i / B] |= u64(bool(seg[h][i])) << (i % B);
}
}
}
bool operator[](int i) const {
assert(0 <= i && i < n);
return seg[0][i / B] >> (i % B) & 1;
}
void insert(int i) {
assert(0 <= i && i < n);
for (int h = 0; h < log; h++) {
seg[h][i / B] |= u64(1) << (i % B), i /= B;
}
}
void add(int i) { insert(i); }
void erase(int i) {
assert(0 <= i && i < n);
u64 x = 0;
for (int h = 0; h < log; h++) {
seg[h][i / B] &= ~(u64(1) << (i % B));
seg[h][i / B] |= x << (i % B);
x = bool(seg[h][i / B]);
i /= B;
}
}
void remove(int i) { erase(i); }
// min[x,n) or n
int next(int i) {
assert(i <= n);
chmax(i, 0);
for (int h = 0; h < log; h++) {
if (i / B == seg[h].size()) break;
u64 d = seg[h][i / B] >> (i % B);
if (!d) {
i = i / B + 1;
continue;
}
i += lowbit(d);
for (int g = h - 1; g >= 0; g--) {
i *= B;
i += lowbit(seg[g][i / B]);
}
return i;
}
return n;
}
// max [0,x], or -1
int prev(int i) {
assert(i >= -1);
if (i >= n) i = n - 1;
for (int h = 0; h < log; h++) {
if (i == -1) break;
u64 d = seg[h][i / B] << (63 - i % B);
if (!d) {
i = i / B - 1;
continue;
}
i -= __builtin_clzll(d);
for (int g = h - 1; g >= 0; g--) {
i *= B;
i += topbit(seg[g][i / B]);
}
return i;
}
return -1;
}
bool any(int l, int r) {
assert(0 <= l && l <= r && r <= n);
return next(l) < r;
}
// [l, r)
template <typename F>
void enumerate(int l, int r, F f) {
assert(0 <= l && l <= r && r <= n);
for (int x = next(l); x < r; x = next(x + 1)) f(x);
}
void reset() {
enumerate(0, n, [&](int i) -> void { erase(i); });
}
string to_string() {
string s(n, '?');
for (int i = 0; i < n; ++i) s[i] = ((*this)[i] ? '1' : '0');
return s;
}
};
#line 1 "ds/segtree/segtree.hpp"
template <class Monoid>
struct SegTree {
using MX = Monoid;
using X = typename MX::value_type;
using value_type = X;
vc<X> dat;
int n, log, size;
SegTree() {}
SegTree(int n) { build(n); }
template <typename F>
SegTree(int n, F f) {
build(n, f);
}
SegTree(const vc<X>& v) { build(v); }
void build(int m) {
build(m, [](int i) -> X { return MX::id(); });
}
void build(const vc<X>& v) {
build(len(v), [&](int i) -> X { return v[i]; });
}
template <typename F>
void build(int m, F f) {
n = m, log = 1;
while ((1 << log) < n) ++log;
size = 1 << log;
dat.assign(size << 1, MX::id());
FOR(i, n) dat[size + i] = f(i);
FOR_R(i, 1, size) update(i);
}
X get(int i) const { return dat[size + i]; }
vc<X> get_all() const { return {dat.begin() + size, dat.begin() + size + n}; }
void update(int i) { dat[i] = Monoid::op(dat[2 * i], dat[2 * i + 1]); }
void set(int i, const X& x) {
assert(i < n);
dat[i += size] = x;
while (i >>= 1) update(i);
}
void multiply(int i, const X& x) {
assert(i < n);
i += size;
dat[i] = Monoid::op(dat[i], x);
while (i >>= 1) update(i);
}
X prod(int L, int R) const {
assert(0 <= L && L <= R && R <= n);
X vl = Monoid::id(), vr = Monoid::id();
L += size, R += size;
while (L < R) {
if (L & 1) vl = Monoid::op(vl, dat[L++]);
if (R & 1) vr = Monoid::op(dat[--R], vr);
L >>= 1, R >>= 1;
}
return Monoid::op(vl, vr);
}
vc<int> prod_ids(int L, int R) const {
assert(0 <= L && L <= R && R <= n);
vc<int> I, J;
L += size, R += size;
while (L < R) {
if (L & 1) I.eb(L++);
if (R & 1) J.eb(--R);
L >>= 1, R >>= 1;
}
reverse(all(J));
concat(I, J);
return I;
}
X prod_all() const { return dat[1]; }
template <class F>
int max_right(F check, int L) const {
assert(0 <= L && L <= n && check(Monoid::id()));
if (L == n) return n;
L += size;
X sm = Monoid::id();
do {
while (L % 2 == 0) L >>= 1;
if (!check(Monoid::op(sm, dat[L]))) {
while (L < size) {
L = 2 * L;
if (check(Monoid::op(sm, dat[L]))) {
sm = Monoid::op(sm, dat[L++]);
}
}
return L - size;
}
sm = Monoid::op(sm, dat[L++]);
} while ((L & -L) != L);
return n;
}
template <class F>
int min_left(F check, int R) const {
assert(0 <= R && R <= n && check(Monoid::id()));
if (R == 0) return 0;
R += size;
X sm = Monoid::id();
do {
--R;
while (R > 1 && (R % 2)) R >>= 1;
if (!check(Monoid::op(dat[R], sm))) {
while (R < size) {
R = 2 * R + 1;
if (check(Monoid::op(dat[R], sm))) {
sm = Monoid::op(dat[R--], sm);
}
}
return R + 1 - size;
}
sm = Monoid::op(dat[R], sm);
} while ((R & -R) != R);
return 0;
}
// prod_{l<=i<r} A[i xor x]
X xor_prod(int l, int r, int xor_val) const {
static_assert(Monoid::commute);
X x = Monoid::id();
for (int k = 0; k < log + 1; ++k) {
if (l >= r) break;
if (l & 1) {
x = Monoid::op(x, dat[(size >> k) + ((l++) ^ xor_val)]);
}
if (r & 1) {
x = Monoid::op(x, dat[(size >> k) + ((--r) ^ xor_val)]);
}
l /= 2, r /= 2, xor_val /= 2;
}
return x;
}
};
#line 1 "ds/node_pool.hpp"
// マルチテストケースでも確保済み chunk を再利用する
template <class Node>
struct Node_Pool {
union Slot {
Node node;
Slot* next;
Slot() {}
~Slot() {}
};
using np = Node*;
static constexpr int CHUNK_SIZE = 1 << 12;
vc<unique_ptr<Slot[]>> chunks;
int chunk_id = 0;
int pos = 0;
Slot* free_head = nullptr;
~Node_Pool() {
auto& cache = chunk_cache();
for (auto& p : chunks) cache.eb(std::move(p));
}
template <class... Args>
np create(Args&&... args) {
Slot* s = new_slot();
return ::new (&s->node) Node(forward<Args>(args)...);
}
np clone(const np x) {
assert(x);
Slot* s = new_slot();
return ::new (&s->node) Node(*x);
}
void destroy(np x) {
if (!x) return;
x->~Node();
Slot* s = reinterpret_cast<Slot*>(x);
s->next = free_head;
free_head = s;
}
// 全 node を無効化する。
// 確保済み chunk は解放せず、次回以降に再利用する。
void reset() {
free_head = nullptr;
chunk_id = 0;
pos = 0;
}
private:
static vc<unique_ptr<Slot[]>>& chunk_cache() {
// static Node_Pool の destructor より先に破棄されないようにする。
static auto* cache = new vc<unique_ptr<Slot[]>>();
return *cache;
}
void alloc_chunk() {
auto& cache = chunk_cache();
if (cache.empty()) {
chunks.eb(make_unique<Slot[]>(CHUNK_SIZE));
} else {
chunks.eb(std::move(cache.back()));
cache.pop_back();
}
}
Slot* new_slot() {
if (free_head) {
Slot* s = free_head;
free_head = free_head->next;
return s;
}
if (chunk_id == len(chunks)) alloc_chunk();
Slot* s = &chunks[chunk_id][pos++];
if (pos == CHUNK_SIZE) {
++chunk_id;
pos = 0;
}
return s;
}
};
#line 4 "ds/segtree/sortable_segtree.hpp"
template <typename Monoid>
struct Sortable_SegTree {
using MX = Monoid;
using X = typename MX::value_type;
const int N, KEY_MAX;
struct Node {
X x, rev_x;
int size;
Node *l, *r;
};
Node_Pool<Node> pool;
using np = Node*;
FastSet ss; // 区間の左端全体を表す fastset
SegTree<MX> seg; // 区間を集約した値を区間の左端にのせた segtree
vector<np> root; // 区間の左端に、dynamic segtree の node を乗せる
vector<bool> rev;
Sortable_SegTree(int KEY_MAX, vector<int> key, vector<X> dat)
: N(key.size()), KEY_MAX(KEY_MAX), ss(key.size()), seg(dat) {
init(key, dat);
}
void set(int i, int key, const X& x) {
assert(key < KEY_MAX);
split_at(i), split_at(i + 1);
rev[i] = 0, root[i] = new_node();
set_rec(root[i], 0, KEY_MAX, key, x);
seg.set(i, x);
}
X prod_all() { return seg.prod_all(); }
X prod(int l, int r) {
split_at(l), split_at(r);
return seg.prod(l, r);
}
void sort_inc(int l, int r) {
split_at(l), split_at(r);
while (1) {
np c = root[l];
int i = ss.next(l + 1);
if (i == r) break;
root[l] = merge(c, root[i]);
ss.erase(i), seg.set(i, MX::id());
}
rev[l] = 0, seg.set(l, root[l]->x);
};
void sort_dec(int l, int r) {
sort_inc(l, r), rev[l] = 1;
seg.set(l, root[l]->rev_x);
};
pair<vc<int>, vc<X>> get_all() {
vector<int> key;
vector<X> dat;
key.reserve(N);
dat.reserve(N);
auto dfs = [&](auto& dfs, np n, int l, int r, bool rev) -> void {
if (!n) return;
if (r == l + 1) {
key.eb(l), dat.eb(n->x);
return;
}
int m = (l + r) / 2;
if (!rev) {
dfs(dfs, n->l, l, m, rev), dfs(dfs, n->r, m, r, rev);
}
if (rev) {
dfs(dfs, n->r, m, r, rev), dfs(dfs, n->l, l, m, rev);
}
};
for (int i = 0; i < N; ++i) {
if (ss[i]) dfs(dfs, root[i], 0, KEY_MAX, rev[i]);
}
return {key, dat};
}
private:
void init(vector<int>& key, vector<X>& dat) {
rev.assign(N, 0), root.clear(), root.reserve(N);
seg.build(N, [&](int i) -> X { return dat[i]; });
for (int i = 0; i < N; ++i) {
ss.insert(i);
root.eb(new_node(MX::id()));
assert(key[i] < KEY_MAX);
set_rec(root[i], 0, KEY_MAX, key[i], dat[i]);
}
}
// x が左端になるようにする
void split_at(int x) {
if (x == N || ss[x]) return;
int a = ss.prev(x), b = ss.next(a + 1);
ss.insert(x);
if (!rev[a]) {
auto [nl, nr] = split(root[a], x - a);
root[a] = nl, root[x] = nr;
rev[a] = rev[x] = 0;
seg.set(a, root[a]->x), seg.set(x, root[x]->x);
} else {
auto [nl, nr] = split(root[a], b - x);
root[a] = nr, root[x] = nl;
rev[a] = rev[x] = 1;
seg.set(a, root[a]->rev_x), seg.set(x, root[x]->rev_x);
}
}
void rebuild() {
auto [key, dat] = get_all();
pool.reset();
init(key, dat);
}
np new_node(X x = MX::id()) {
np c = pool.create();
c->x = c->rev_x = x;
c->l = c->r = nullptr;
c->size = 1;
return c;
}
pair<np, np> split(np n, int k) {
if (k == 0) {
return {nullptr, n};
}
if (k == n->size) {
return {n, nullptr};
}
int s = (n->l ? n->l->size : 0);
Node* b = new_node();
if (k <= s) {
auto [nl, nr] = split(n->l, k);
b->l = nr, b->r = n->r, n->l = nl, n->r = nullptr;
}
if (k > s) {
auto [nl, nr] = split(n->r, k - s);
n->l = n->l, n->r = nl, b->l = nullptr, b->r = nr;
}
update(n), update(b);
return {n, b};
}
np merge(np a, np b) {
if (!a) return b;
if (!b) return a;
a->l = merge(a->l, b->l), a->r = merge(a->r, b->r);
update(a);
return a;
}
void update(np n) {
if (!(n->l) && !(n->r)) {
return;
}
if (!(n->l)) {
n->x = n->r->x, n->rev_x = n->r->rev_x, n->size = n->r->size;
return;
}
if (!(n->r)) {
n->x = n->l->x, n->rev_x = n->l->rev_x, n->size = n->l->size;
return;
}
n->x = MX::op(n->l->x, n->r->x);
n->rev_x = MX::op(n->r->rev_x, n->l->rev_x);
n->size = n->l->size + n->r->size;
}
void set_rec(np n, int l, int r, int k, const X& x) {
if (r == l + 1) {
n->x = n->rev_x = x;
return;
}
int m = (l + r) / 2;
if (k < m) {
if (!(n->l)) n->l = new_node();
set_rec(n->l, l, m, k, x);
}
if (m <= k) {
if (!(n->r)) n->r = new_node();
set_rec(n->r, m, r, k, x);
}
update(n);
}
};