#pragma once
#include "../ost/lib.hpp"
namespace tifa_libs {
namespace rbt_impl_ {
using namespace ost_impl_;
struct rbt_op_leaf : bst_op_leaf {
template <tp2_ds_c pointer>
static CEXP bool is_red(pointer p) NE { retif_((p), p->red, false); }
template <tp2_ds_c pointer>
static CEXP void insert_leaf(pointer& root, pointer p, pointer n, bool dir) NE {
n->red = p, bst_op_leaf::insert_leaf(root, p, n, dir);
while (is_red(p = n->fa)) {
bool p_dir = p->child_dir();
auto g = p->fa, u = g->ch[!p_dir];
if (is_red(u)) {
p->red = u->red = false, g->red = true, n = g;
continue;
}
if (n->child_dir() != p_dir) rotate(root, p, p_dir), swap(n, p);
p->red = false, g->red = true, rotate(root, g, !p_dir);
}
root->red = false;
}
template <tp2_ds_c pointer>
static CEXP void erase_branch_leaf(pointer& root, pointer n) NE {
bool n_dir = n == root ? false : n->child_dir();
bst_op_leaf::erase_branch_leaf(root, n);
auto p = n->fa;
if (!p) {
if (root) root->red = false;
return;
} else if (auto s = p->ch[n_dir]; s) return void(s->red = false);
while (p && !n->red) {
auto s = p->ch[!n_dir];
if (is_red(s)) {
s->red = false, p->red = true;
rotate(root, p, n_dir), s = p->ch[!n_dir];
}
auto c = s->ch[n_dir], d = s->ch[!n_dir];
if (!is_red(c) && !is_red(d)) {
if (s->red = true, n = p, p = n->fa; !p) break;
n_dir = n->child_dir();
continue;
}
if (!is_red(d)) {
c->red = false, s->red = true;
rotate(root, s, !n_dir);
s = p->ch[!n_dir], c = s->ch[n_dir], d = s->ch[!n_dir];
}
s->red = p->red, p->red = d->red = false, rotate(root, p, n_dir), n = root;
break;
}
n->red = false;
}
};
using rbt_tag = bst_op<rbt_op_leaf>;
} // namespace rbt_impl_
namespace ostnode_impl_ {
template <class K>
struct ostree_node_t<rbt_impl_::rbt_tag, K> {
// NOLINTNEXTLINE(modernize-avoid-c-arrays)
ostree_node_t *fa, *ch[2];
K data;
u32 sz;
bool red;
// @return child direction of this non-root point
ND CEXP bool child_dir() CNE { return this == fa->ch[1]; }
};
} // namespace ostnode_impl_
template <class K, class Comp = std::less<K>>
using rbtree = ost_impl_::ostree<K, rbt_impl_::rbt_tag, Comp>;
} // namespace tifa_libs
#line 2 "src/ds/bst/rbt/lib.hpp"
#line 2 "src/ds/bst/ost/lib.hpp"
#line 2 "src/util/alias/others/lib.hpp"
#line 2 "src/util/consts/lib.hpp"
#line 2 "src/util/alias/num/lib.hpp"
#line 2 "src/util/util/lib.hpp"
// https://github.com/Tiphereth-A/CP-lib
#include <bits/extc++.h>
// clang-format off
namespace tifa_libs {
#define CEXP constexpr
#define CEXPE constexpr explicit
#define CR const&
#define CP const*
#define PC *const
#define CPC const*const
#define TPN typename
#define NE noexcept
#define CNE const noexcept
#define ND [[nodiscard]]
#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t) * 2, __VA_ARGS__, __VA_ARGS__ CR>
// NOLINTNEXTLINE(misc-const-correctness)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)
#define retif_(cond, if_true, ...) if cond return if_true __VA_OPT__(; else return __VA_ARGS__)
#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif
using namespace std::ranges;
using namespace std::literals;
template <class T>
CEXP T abs(T x) NE { retif_((x < 0), -x, x); }
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/num/lib.hpp"
// clang-format off
namespace tifa_libs {
#define mk0_(w, t) using w = t; using c##w = const t
#define mk_(w, t) mk0_(w, t); CEXP w operator""_##w(unsigned long long x) NE { return (w)x; }
mk_(i8, int8_t) mk_(u8, uint8_t) mk_(i16, int16_t) mk_(u16, uint16_t) mk_(i32, int32_t) mk_(u32, uint32_t) mk_(i64, int64_t) mk_(u64, uint64_t) mk_(isz, ssize_t) mk_(usz, size_t) mk_(chr, char) mk_(schr, signed char) mk_(uchr, unsigned char) mk_(sint, signed) mk_(uint, unsigned);
mk0_(i128, __int128_t); mk0_(u128, __uint128_t); mk0_(f32, float); mk0_(f64, double); mk0_(f128, long double);
#undef mk0_
#undef mk_
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/consts/lib.hpp"
// clang-format off
namespace tifa_libs {
using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) NE { eps_v<FP> = v; }
CEXP u32 TIME = ((__TIME__[0] & 15) << 20) | ((__TIME__[1] & 15) << 16) | ((__TIME__[3] & 15) << 12) | ((__TIME__[4] & 15) << 8) | ((__TIME__[6] & 15) << 4) | (__TIME__[7] & 15);
CEXP auto STR2U16 = [] { std::array<u32, 65536> table{}; table.fill(-1_u32); flt_ (u32, i, 48, 58) flt_ (u32, j, 48, 58) table[i << 8 | j] = (j & 15) * 10 + (i & 15); return table; }();
inline const auto fn_0 = [](auto&&...) NE {};
inline const auto fn_is0 = [](auto x) NE { return x == 0; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/util/alias/others/lib.hpp"
namespace tifa_libs {
template <class T>
struct chash {
CEXP static u64 C = u64(pi_v<f128> * 2e18) | 71;
CEXP u64 operator()(T x) CNE { return __builtin_bswap64(((u64)x ^ TIME) * C); }
};
// clang-format off
#define mk_(w, t) using w = t; using c##w = const t;
mk_(strn, std::string) mk_(strnv, std::string_view)
#undef mk_
template <class T> struct edge_t { T w; u32 u, v; CEXP auto operator<=>(edge_t CR) const = default; }; template <class T> using cedge_t = const edge_t<T>;
template <class T> struct pt3 { T _0, _1, _2; CEXP auto operator<=>(pt3 CR) const = default; }; template <class T> using cpt3 = const pt3<T>;
template <class T> struct pt4 { T _0, _1, _2, _3; CEXP auto operator<=>(pt4 CR) const = default; }; template <class T> using cpt4 = const pt4<T>;
#define mkT_(w, t, ...) template <class T> using w = t __VA_OPT__(, ) __VA_ARGS__; template <class T> using c##w = const t __VA_OPT__(, ) __VA_ARGS__;
mkT_(ptt, std::pair<T, T>) mkT_(alc, std::pmr::polymorphic_allocator<T>) mkT_(vec, std::vector<T>) mkT_(vvec, vec<vec<T>>) mkT_(v3ec, vvec<vec<T>>) mkT_(vecpt, vec<ptt<T>>) mkT_(vvecpt, vvec<ptt<T>>) mkT_(ptvec, ptt<vec<T>>) mkT_(ptvvec, ptt<vvec<T>>)
#undef mkT_
template <class T> using itl = std ::initializer_list<T>;
template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>; template <class T, usz N> using carr = std::array<const T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>; template <class U, class T> using vvecp = vvec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>; template <class U, class T> using vvvecp = vvec<vvec<std::pair<U, T>>>;
#ifdef PB_DS_ASSOC_CNTNR_HPP
template <class T, class C = std::less<T>> using set = __gnu_pbds::tree<T, __gnu_pbds::null_type, C>;
template <class K, class V, class C = std::less<K>> using map = __gnu_pbds::tree<K, V, C>;
// hset<u64> s({}, {}, {}, {}, {1<<16});
template <class T, class HF = chash<T>> using hset = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, HF>;
// hmap<u64, int> s({}, {}, {}, {}, {1<<16});
template <class K, class V, class HF = chash<K>> using hmap = __gnu_pbds::gp_hash_table<K, V, HF>;
#else
using std::set, std::map;
template <class T, class HF = chash<T>> using hset = std::unordered_set<T, HF>;
template <class K, class V, class HF = chash<K>> using hmap = std::unordered_map<K, V, HF>;
#endif
#ifdef PB_DS_PRIORITY_QUEUE_HPP
template <class T, class C = std::less<T>> using pq = __gnu_pbds::priority_queue<T, C>;
#else
template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
#endif
template <class T> using pqg = pq<T, std::greater<T>>;
// clang-format on
#define mk1_(V, A, T) using V##A = V<T>;
#define mk_(V, A, T) mk1_(V, A, T) mk1_(c##V, A, T)
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk1_(spn, A, T) mk1_(itl, A, T)
mk(b, bool) mk(c, chr) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64) mk(t, isz) mk(z, usz) mk(f, f32) mk(d, f64) mk(s, strn);
#undef mk
#undef mk_
#undef mk1_
} // namespace tifa_libs
#line 2 "src/ds/bt_trv/lib.hpp"
#line 2 "src/util/traits/ds/lib.hpp"
// clang-format off
#line 4 "src/util/traits/ds/lib.hpp"
namespace tifa_libs {
// tree pointer (for DS)
template <class P> concept tp_ds_c = requires(P p) { p->ch; std::is_array_v<decltype(p->ch)>; std::rank_v<decltype(p->ch)> == 1; };
// binary tree pointer (for DS)
template <class P> concept tp2_ds_c = tp_ds_c<P> && std::extent_v<decltype(std::declval<P>()->ch)> == 2;
template <class T> concept dsu_c = requires(T dsu, u32 x, u32 y) { {dsu.find(x)} -> std::same_as<i32>; {dsu.size()} -> std::same_as<u32>; {dsu.size(x)} -> std::same_as<u32>; {dsu.same(x, y)} -> std::same_as<bool>; {dsu.merge(x, y)} -> std::same_as<bool>; };
} // namespace tifa_libs
// clang-format on
#line 4 "src/ds/bt_trv/lib.hpp"
namespace tifa_libs {
template <tp2_ds_c pointer, class F>
requires requires(pointer p, F&& f) { f(p); }
CEXP void pre_order(pointer p, F&& f) NE {
if (p) f(p), pre_order(p->ch[0], std::forward<F>(f)), pre_order(p->ch[1], std::forward<F>(f));
}
template <tp2_ds_c pointer, class F>
requires requires(pointer p, F f) { f(p); }
CEXP void in_order(pointer p, F&& f) NE {
if (p) in_order(p->ch[0], std::forward<F>(f)), f(p), in_order(p->ch[1], std::forward<F>(f));
}
template <tp2_ds_c pointer, class F>
requires requires(pointer p, F f) { f(p); }
CEXP void post_order(pointer p, F&& f) NE {
if (p) post_order(p->ch[0], std::forward<F>(f)), post_order(p->ch[1], std::forward<F>(f)), f(p);
}
template <tp_ds_c pointer, class F>
requires requires(pointer p, u32 level, F f) { f(p, level); }
CEXP void level_order(pointer p, F&& f) NE {
if (!p) return;
u32 level = 0;
std::queue<pointer> q({p});
while (!q.empty()) {
flt_ (u32, i, 0, (u32)q.size()) {
auto now = q.front();
q.pop(), f(now, level);
for (auto&& s : now->ch) q.push(s);
}
++level;
}
}
template <tp_ds_c pointer, class Alloc>
CEXP void dealloc_subtree(pointer p, Alloc& alloc) NE {
if (!p) return;
for (auto&& s : p->ch) dealloc_subtree(s, alloc);
alloc.deallocate(p, 1);
}
template <tp_ds_c pointer>
CEXP pointer most(pointer p, bool dir) NE {
if (!p) return nullptr;
while (p->ch[dir]) p = p->ch[dir];
return p;
}
template <tp2_ds_c pointer>
CEXP auto leftmost(pointer p) NE { return most(p, 0); }
template <tp2_ds_c pointer>
CEXP auto rightmost(pointer p) NE { return most(p, 1); }
} // namespace tifa_libs
#line 5 "src/ds/bst/ost/lib.hpp"
namespace tifa_libs {
namespace ostnode_impl_ {
template <class T, class K>
struct ostree_node_t {};
} // namespace ostnode_impl_
namespace ost_impl_ {
struct ostree_tag_base {
template <tp2_ds_c pointer>
static CEXP u32 size(pointer p) NE { retif_((p), p->sz, 0); }
template <tp2_ds_c pointer>
static CEXP u32 count(pointer p) NE { retif_((p), p->sz - size(p->ch[0]) - size(p->ch[1]), 0); }
// [size(begin), size(begin->fa), ..., size(end)) += v
template <tp2_ds_c pointer>
static CEXP void modify_size(pointer begin, i32 v, pointer end = nullptr) NE {
while (begin != end) begin->sz += (u32)v, begin = begin->fa;
}
template <tp2_ds_c pointer>
static CEXP pointer neighbour(pointer p, bool dir) NE {
if (!p) return nullptr;
if (p->ch[dir]) return most(p->ch[dir], !dir);
while (p && p->fa && p->child_dir() == dir) p = p->fa;
retif_((p), p->fa, nullptr);
}
template <tp2_ds_c pointer>
static CEXP auto prev(pointer p) NE { return neighbour(p, 0); }
template <tp2_ds_c pointer>
static CEXP auto next(pointer p) NE { return neighbour(p, 1); }
template <tp2_ds_c pointer>
static CEXP pointer rotate(pointer& root, pointer p, bool dir) NE {
auto g = p->fa, s = p->ch[!dir];
u32 psz = p->sz, ssz = s->sz;
s->sz = psz, p->sz += size(s->ch[dir]) - ssz;
auto c = s->ch[dir];
if (c) c->fa = p;
p->ch[!dir] = c, s->ch[dir] = p, p->fa = s, s->fa = g;
(g ? g->ch[p == g->ch[1]] : root) = s;
return s;
}
};
//! will NOT change sz
struct bst_op_leaf : ostree_tag_base {
template <tp2_ds_c pointer>
static CEXP void insert_leaf(pointer& root, pointer p, pointer n, bool dir) NE {
if (!p) return void(root = n);
p->ch[dir] = n, n->fa = p;
}
template <tp2_ds_c pointer>
static CEXP void erase_branch_leaf(pointer& root, pointer n) NE {
auto p = n->fa, s = n->ch[0] ? n->ch[0] : n->ch[1];
if (s) s->fa = p;
if (!p) return void(root = s);
p->ch[n->child_dir()] = s;
}
};
template <class leaf>
struct bst_op : leaf {
using tag_t = ostree_tag_base;
template <tp2_ds_c pointer, class K, class Alloc, class Comp>
CEXP pointer insert(pointer& root, const K& data, Alloc& alloc, Comp compare) NE {
pointer now = root, p = nullptr;
bool dir = false;
while (now)
if (dir = compare((p = now)->data, data), now = now->ch[dir]; !dir && !compare(data, p->data)) {
tag_t::modify_size(p, 1);
return p;
}
pointer n = alloc.allocate(1);
n->fa = n->ch[0] = n->ch[1] = nullptr, n->data = data, n->sz = 1;
tag_t::modify_size(p, 1), leaf::insert_leaf(root, p, n, dir);
return n;
}
template <tp2_ds_c pointer, class Alloc>
CEXP pointer erase(pointer& root, pointer p, Alloc& alloc) NE {
if (!p) return nullptr;
pointer result;
if (p->ch[0] && p->ch[1]) {
auto s = leftmost(p->ch[1]);
std::swap(s->data, p->data);
tag_t::modify_size(s, (i32)tag_t::count(p) - (i32)tag_t::count(s), p);
result = p, p = s;
} else result = tag_t::next(p);
tag_t::modify_size(p, -(i32)tag_t::count(p));
leaf::erase_branch_leaf(root, p), alloc.deallocate(p, 1);
return result;
}
};
using bst_tag = bst_op<bst_op_leaf>;
} // namespace ost_impl_
namespace ostnode_impl_ {
template <class K>
struct ostree_node_t<ost_impl_::bst_tag, K> {
ostree_node_t *fa, *ch[2]; // NOLINT(modernize-avoid-c-arrays)
K data;
u32 sz;
// @return child direction of this non-root point
ND CEXP bool child_dir() CNE { return this == fa->ch[1]; }
};
} // namespace ostnode_impl_
namespace ost_impl_ {
using namespace ostnode_impl_;
template <class K, std::derived_from<ostree_tag_base> tag_t, class Comp = std::less<K>>
requires requires(ostree_node_t<tag_t, K>*& root, ostree_node_t<tag_t, K> n, tag_t tag, bool dir, K key, alc<ostree_node_t<tag_t, K>> alloc, Comp comp) {
n.fa->ch[0]->ch[1]->data;
n.sz;
{ comp(key, key) } -> std::same_as<bool>;
{ n.child_dir() } -> std::same_as<bool>;
{ tag.size(&n) } -> std::same_as<u32>;
tag.insert(root, key, alloc, comp);
tag.erase(root, &n, alloc);
}
struct ostree : tag_t {
using node_t = ostree_node_t<tag_t, K>;
using pointer = node_t*;
using const_pointer = node_t CP;
using pointer_const = node_t PC;
static CEXP Comp compare{};
pointer root{nullptr};
CEXP ostree() NE = default;
ostree(ostree CR) = delete;
ostree& operator=(ostree CR) = delete;
CEXP ~ostree() NE { dealloc_subtree(root, alloc); }
ND CEXP u32 size() CNE { return tag_t::size(root); }
CEXP pointer lower_bound(const K& key) CNE {
const_pointer now = root, ans = nullptr;
while (now) {
if (!compare(now->data, key)) ans = now, now = now->ch[0];
else now = now->ch[1];
}
return (pointer)ans;
}
CEXP pointer upper_bound(const K& key) CNE {
const_pointer now = root, ans = nullptr;
while (now) {
if (compare(key, now->data)) ans = now, now = now->ch[0];
else now = now->ch[1];
}
return (pointer)ans;
}
CEXP pointer find(const K& key) CNE {
auto p = lower_bound(key);
retif_(((!p || compare(p->data, key) || compare(key, p->data))), nullptr, p);
}
// Order start from 0
CEXP u32 order_of_key(const K& key) CNE {
u32 ans = 0;
auto now = root;
while (now) {
if (!compare(now->data, key)) now = now->ch[0];
else ans += tag_t::size(now->ch[0]) + tag_t::count(now), now = now->ch[1];
}
return ans;
}
// Order start from 0
CEXP const_pointer find_by_order(u32 order) CNE {
const_pointer now = root, ans = nullptr;
while (now && now->sz >= order)
if (auto lsz = tag_t::size(now->ch[0]), cnt = tag_t::count(now); order < lsz) now = now->ch[0];
else {
if (ans = now; order < lsz + cnt) break;
now = now->ch[1], order -= lsz + cnt;
}
return ans;
}
CEXP const_pointer insert(const K& data) NE { return tag_t::insert(root, data, alloc, compare); }
//! count -= 1
CEXP bool erase(const K& key) NE {
if (auto p = find(key); !p) return false;
else if (tag_t::count(p) > 1) {
tag_t::modify_size(p, -1);
return true;
} else {
erase(p);
return true;
}
}
CEXP const_pointer erase(pointer p) NE { return tag_t::erase(root, p, alloc); }
private:
alc<node_t> alloc;
};
} // namespace ost_impl_
template <class K, class Comp = std::less<K>>
using bstree = ost_impl_::ostree<K, ost_impl_::bst_tag, Comp>;
} // namespace tifa_libs
#line 4 "src/ds/bst/rbt/lib.hpp"
namespace tifa_libs {
namespace rbt_impl_ {
using namespace ost_impl_;
struct rbt_op_leaf : bst_op_leaf {
template <tp2_ds_c pointer>
static CEXP bool is_red(pointer p) NE { retif_((p), p->red, false); }
template <tp2_ds_c pointer>
static CEXP void insert_leaf(pointer& root, pointer p, pointer n, bool dir) NE {
n->red = p, bst_op_leaf::insert_leaf(root, p, n, dir);
while (is_red(p = n->fa)) {
bool p_dir = p->child_dir();
auto g = p->fa, u = g->ch[!p_dir];
if (is_red(u)) {
p->red = u->red = false, g->red = true, n = g;
continue;
}
if (n->child_dir() != p_dir) rotate(root, p, p_dir), swap(n, p);
p->red = false, g->red = true, rotate(root, g, !p_dir);
}
root->red = false;
}
template <tp2_ds_c pointer>
static CEXP void erase_branch_leaf(pointer& root, pointer n) NE {
bool n_dir = n == root ? false : n->child_dir();
bst_op_leaf::erase_branch_leaf(root, n);
auto p = n->fa;
if (!p) {
if (root) root->red = false;
return;
} else if (auto s = p->ch[n_dir]; s) return void(s->red = false);
while (p && !n->red) {
auto s = p->ch[!n_dir];
if (is_red(s)) {
s->red = false, p->red = true;
rotate(root, p, n_dir), s = p->ch[!n_dir];
}
auto c = s->ch[n_dir], d = s->ch[!n_dir];
if (!is_red(c) && !is_red(d)) {
if (s->red = true, n = p, p = n->fa; !p) break;
n_dir = n->child_dir();
continue;
}
if (!is_red(d)) {
c->red = false, s->red = true;
rotate(root, s, !n_dir);
s = p->ch[!n_dir], c = s->ch[n_dir], d = s->ch[!n_dir];
}
s->red = p->red, p->red = d->red = false, rotate(root, p, n_dir), n = root;
break;
}
n->red = false;
}
};
using rbt_tag = bst_op<rbt_op_leaf>;
} // namespace rbt_impl_
namespace ostnode_impl_ {
template <class K>
struct ostree_node_t<rbt_impl_::rbt_tag, K> {
// NOLINTNEXTLINE(modernize-avoid-c-arrays)
ostree_node_t *fa, *ch[2];
K data;
u32 sz;
bool red;
// @return child direction of this non-root point
ND CEXP bool child_dir() CNE { return this == fa->ch[1]; }
};
} // namespace ostnode_impl_
template <class K, class Comp = std::less<K>>
using rbtree = ost_impl_::ostree<K, rbt_impl_::rbt_tag, Comp>;
} // namespace tifa_libs
src/ds/bst/rbt/lib.hpp