#pragma once
#include "../../../util/alias/others/lib.hpp"
#include "../../../util/rand/lib.hpp"
namespace tifa_libs {
template <class T, bool recovery = false, class Comp = std::less<T>>
struct fhq_treap {
static CEXP Comp compare{};
struct TIFA {
T val;
// NOLINTNEXTLINE(modernize-avoid-c-arrays)
u32 r, sz, son[2];
};
rand_gen<u32> rnd;
vec<TIFA> data{1};
vecu stk;
u32 root{};
private:
CEXP u32 new_node(cT_(T) val) NE {
u32 ret;
if CEXP (recovery) {
if (stk.size()) data[ret = stk.back()] = {val, rnd(), 1, {0, 0}}, stk.pop_back();
else ret = (u32)data.size(), data.push_back(TIFA{val, rnd(), 1, {0, 0}});
} else ret = (u32)data.size(), data.push_back(TIFA{val, rnd(), 1, {0, 0}});
return ret;
}
CEXP void pushup(u32 pos) NE { data[pos].sz = data[data[pos].son[0]].sz + 1 + data[data[pos].son[1]].sz; }
template <bool strict = false>
CEXP pttu split_root(u32 pos, cT_(T) key) NE {
if (!pos) return {};
bool f;
if CEXP (strict) f = compare(data[pos].val, key);
else f = !compare(key, data[pos].val);
if (f) {
auto [l, r] = split_root<strict>(data[pos].son[1], key);
data[pos].son[1] = l, pushup(pos);
return {pos, r};
}
auto [l, r] = split_root<strict>(data[pos].son[0], key);
data[pos].son[0] = r, pushup(pos);
return {l, pos};
}
CEXP u32 merge_root(u32 l, u32 r) NE {
if (!l | !r) return l | r;
if (data[l].r < data[r].r) {
data[l].son[1] = merge_root(data[l].son[1], r), pushup(l);
return l;
}
data[r].son[0] = merge_root(l, data[r].son[0]), pushup(r);
return r;
}
public:
CEXP fhq_treap() : rnd{}, stk{} { data[0].sz = {}; }
CEXP void insert(cT_(T) val) NE {
u32 tar = new_node(val);
auto dfs = [&](auto&& f, u32& pos) NE -> void {
if (!pos) return void(pos = tar);
if (data[tar].r < data[pos].r) {
auto [l, r] = split_root<true>(pos, val);
data[tar].son[0] = l, data[tar].son[1] = r;
pos = tar;
} else f(f, compare(data[pos].val, val) ? data[pos].son[1] : data[pos].son[0]);
pushup(pos);
};
dfs(dfs, root);
}
CEXP bool erase(cT_(T) val) NE {
auto dfs = [&](auto&& f, u32& pos) NE -> bool {
if (!pos) return false;
if (data[pos].val == val) {
if CEXP (recovery) stk.push_back(pos);
pos = merge_root(data[pos].son[0], data[pos].son[1]);
return true;
}
if (!f(f, compare(data[pos].val, val) ? data[pos].son[1] : data[pos].son[0])) return false;
pushup(pos);
return true;
};
return dfs(dfs, root);
}
ND CEXP auto find(cT_(T) val) CNE {
u32 pos = root;
while (pos)
if (val == data[pos].val) return data.cbegin() + pos;
else pos = data[pos].son[!compare(val, data[pos].val)];
return data.cend();
}
ND CEXP u32 rank(cT_(T) val) CNE {
u32 pos = root, res = 0;
while (pos)
if (compare(data[pos].val, val)) res += data[data[pos].son[0]].sz + 1, pos = data[pos].son[1];
else pos = data[pos].son[0];
return res + 1;
}
ND CEXP u32 count(cT_(T) val) CNE {
u32 rk = rank(val);
if (auto res = next(val); !res) return data[root].sz - rk + 1;
else return rank(res.value()) - rk;
}
ND CEXP auto kth(u32 k) CNE {
std::optional<T> ret;
if (k < 1 || k > data[root].sz) return ret;
u32 pos = root;
while (true)
if (auto _ = data[pos].sz - data[data[pos].son[1]].sz; _ == k) {
ret.emplace(data[pos].val);
return ret;
} else if (_ < k) k -= _, pos = data[pos].son[1];
else pos = data[pos].son[0];
}
ND CEXP auto prev(cT_(T) val) CNE {
u32 pos = root;
std::optional<T> ret;
while (pos)
if (!compare(data[pos].val, val)) pos = data[pos].son[0];
else ret.emplace(data[pos].val), pos = data[pos].son[1];
return ret;
}
ND CEXP auto next(cT_(T) val) CNE {
u32 pos = root;
std::optional<T> ret;
while (pos)
if (!compare(val, data[pos].val)) pos = data[pos].son[1];
else ret.emplace(data[pos].val), pos = data[pos].son[0];
return ret;
}
};
} // namespace tifa_libs
#line 2 "src/ds/bst/fhq/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/util/rand/lib.hpp"
#line 5 "src/util/rand/lib.hpp"
namespace tifa_libs {
template <class T>
requires std::is_arithmetic_v<T>
class rand_gen {
using res_t = std::conditional_t<sizeof(T) <= 4, u32, u64>;
using res_wt = std::conditional_t<sizeof(T) <= 4, u64, u128>;
// clang-format off
struct mt19937_param { static CEXP u32 w = 32, n = 624, m = 397, r = 31, a = 0x9908b0df, u = 11, d = 0xffffffff, s = 7, b = 0x9d2c5680, t = 15, c = 0xefc60000, l = 18, f = 1812433253; };
struct mt19937_64_param { static CEXP u64 w = 64, n = 312, m = 156, r = 31, a = 0xb5026f5aa96619e9, u = 29, d = 0x5555555555555555, s = 17, b = 0x71d67fffeda60000, t = 37, c = 0xfff7eee000000000, l = 43, f = 6364136223846793005; };
using pm = std::conditional_t<std::is_same_v<res_t, u32>, mt19937_param, mt19937_64_param>;
// clang-format on
T a_, b_;
arr<res_t, pm::n> x_;
u32 p_;
CEXP void gen_() NE {
CEXP res_t um = (~res_t()) << pm::r, lm = ~um;
res_t _;
flt_ (res_t, i, p_ = 0, pm::n - pm::m) _ = ((x_[i] & um) | (x_[i + 1] & lm)), x_[i] = (x_[i + pm::m] ^ (_ >> 1) ^ ((_ & 1) ? pm::a : 0));
flt_ (res_t, i, pm::n - pm::m, pm::n - 1) _ = ((x_[i] & um) | (x_[i + 1] & lm)), x_[i] = (x_[i + (pm::m - pm::n)] ^ (_ >> 1) ^ ((_ & 1) ? pm::a : 0));
_ = ((x_[pm::n - 1] & um) | (x_[0] & lm)), x_[pm::n - 1] = (x_[pm::m - 1] ^ (_ >> 1) ^ ((_ & 1) ? pm::a : 0));
}
public:
CEXPE rand_gen(T a = std::numeric_limits<T>::min(), T b = std::numeric_limits<T>::max(), res_t sd = (res_t)TIME) NE : a_(a), b_(b) { assert(a < b || (std::is_integral_v<T> && a == b)), seed(sd); }
CEXP void range(T min, T max) NE { assert(min < max || (std::is_integral_v<T> && min == max)), a_ = min, b_ = max; }
void seed() NE { seed((res_t)std::chrono::duration_cast<std::chrono::nanoseconds>(std::chrono::high_resolution_clock::now().time_since_epoch()).count()); }
CEXP void seed(res_t sd) NE {
x_[0] = sd & gen_max();
flt_ (res_t, i, 1, p_ = pm::n) x_[i] = ((x_[i - 1] ^ (x_[i - 1] >> (pm::w - 2))) * pm::f + i % pm::n) & gen_max();
}
ND CEXP res_t gen_min() CNE { return 0; }
ND CEXP res_t gen_max() CNE {
if CEXP (sizeof(res_t) * 8 == pm::w) return ~res_t();
else return ((res_t)1 << pm::w) - 1;
}
CEXP res_t next() NE {
if (p_ >= pm::n) gen_();
res_t _ = x_[p_++];
_ ^= (_ >> pm::u) & pm::d, _ ^= (_ << pm::s) & pm::b, _ ^= (_ << pm::t) & pm::c, _ ^= (_ >> pm::l);
return _;
}
CEXP T operator()() NE {
if CEXP (std::integral<T>) {
const res_wt r = (res_wt)b_ - (res_wt)a_ + 1;
res_wt p = r * next();
if (auto l = (res_t)p, _ = res_t(res_wt(-(res_t)r) % r); l < r)
while (l < _) l = res_t(p = r * next());
return T((res_t)(p >> pm::w) + (res_t)a_);
} else return T(next() / (f128)((u128)gen_max() + 1) * (b_ - a_) + a_);
}
};
} // namespace tifa_libs
#line 5 "src/ds/bst/fhq/lib.hpp"
namespace tifa_libs {
template <class T, bool recovery = false, class Comp = std::less<T>>
struct fhq_treap {
static CEXP Comp compare{};
struct TIFA {
T val;
// NOLINTNEXTLINE(modernize-avoid-c-arrays)
u32 r, sz, son[2];
};
rand_gen<u32> rnd;
vec<TIFA> data{1};
vecu stk;
u32 root{};
private:
CEXP u32 new_node(cT_(T) val) NE {
u32 ret;
if CEXP (recovery) {
if (stk.size()) data[ret = stk.back()] = {val, rnd(), 1, {0, 0}}, stk.pop_back();
else ret = (u32)data.size(), data.push_back(TIFA{val, rnd(), 1, {0, 0}});
} else ret = (u32)data.size(), data.push_back(TIFA{val, rnd(), 1, {0, 0}});
return ret;
}
CEXP void pushup(u32 pos) NE { data[pos].sz = data[data[pos].son[0]].sz + 1 + data[data[pos].son[1]].sz; }
template <bool strict = false>
CEXP pttu split_root(u32 pos, cT_(T) key) NE {
if (!pos) return {};
bool f;
if CEXP (strict) f = compare(data[pos].val, key);
else f = !compare(key, data[pos].val);
if (f) {
auto [l, r] = split_root<strict>(data[pos].son[1], key);
data[pos].son[1] = l, pushup(pos);
return {pos, r};
}
auto [l, r] = split_root<strict>(data[pos].son[0], key);
data[pos].son[0] = r, pushup(pos);
return {l, pos};
}
CEXP u32 merge_root(u32 l, u32 r) NE {
if (!l | !r) return l | r;
if (data[l].r < data[r].r) {
data[l].son[1] = merge_root(data[l].son[1], r), pushup(l);
return l;
}
data[r].son[0] = merge_root(l, data[r].son[0]), pushup(r);
return r;
}
public:
CEXP fhq_treap() : rnd{}, stk{} { data[0].sz = {}; }
CEXP void insert(cT_(T) val) NE {
u32 tar = new_node(val);
auto dfs = [&](auto&& f, u32& pos) NE -> void {
if (!pos) return void(pos = tar);
if (data[tar].r < data[pos].r) {
auto [l, r] = split_root<true>(pos, val);
data[tar].son[0] = l, data[tar].son[1] = r;
pos = tar;
} else f(f, compare(data[pos].val, val) ? data[pos].son[1] : data[pos].son[0]);
pushup(pos);
};
dfs(dfs, root);
}
CEXP bool erase(cT_(T) val) NE {
auto dfs = [&](auto&& f, u32& pos) NE -> bool {
if (!pos) return false;
if (data[pos].val == val) {
if CEXP (recovery) stk.push_back(pos);
pos = merge_root(data[pos].son[0], data[pos].son[1]);
return true;
}
if (!f(f, compare(data[pos].val, val) ? data[pos].son[1] : data[pos].son[0])) return false;
pushup(pos);
return true;
};
return dfs(dfs, root);
}
ND CEXP auto find(cT_(T) val) CNE {
u32 pos = root;
while (pos)
if (val == data[pos].val) return data.cbegin() + pos;
else pos = data[pos].son[!compare(val, data[pos].val)];
return data.cend();
}
ND CEXP u32 rank(cT_(T) val) CNE {
u32 pos = root, res = 0;
while (pos)
if (compare(data[pos].val, val)) res += data[data[pos].son[0]].sz + 1, pos = data[pos].son[1];
else pos = data[pos].son[0];
return res + 1;
}
ND CEXP u32 count(cT_(T) val) CNE {
u32 rk = rank(val);
if (auto res = next(val); !res) return data[root].sz - rk + 1;
else return rank(res.value()) - rk;
}
ND CEXP auto kth(u32 k) CNE {
std::optional<T> ret;
if (k < 1 || k > data[root].sz) return ret;
u32 pos = root;
while (true)
if (auto _ = data[pos].sz - data[data[pos].son[1]].sz; _ == k) {
ret.emplace(data[pos].val);
return ret;
} else if (_ < k) k -= _, pos = data[pos].son[1];
else pos = data[pos].son[0];
}
ND CEXP auto prev(cT_(T) val) CNE {
u32 pos = root;
std::optional<T> ret;
while (pos)
if (!compare(data[pos].val, val)) pos = data[pos].son[0];
else ret.emplace(data[pos].val), pos = data[pos].son[1];
return ret;
}
ND CEXP auto next(cT_(T) val) CNE {
u32 pos = root;
std::optional<T> ret;
while (pos)
if (!compare(val, data[pos].val)) pos = data[pos].son[1];
else ret.emplace(data[pos].val), pos = data[pos].son[0];
return ret;
}
};
} // namespace tifa_libs
src/ds/bst/fhq/lib.hpp