#pragma once
#include "../../../util/alias/others/lib.hpp"
namespace tifa_libs {
class persistent_segtree {
//! initial cnt = 1;
u32 n, cnt{0};
struct TIFA {
u32 w, ls, rs;
CEXP TIFA(u32 W = 0, u32 LS = 0, u32 RS = 0) NE : w(W), ls(LS), rs(RS) {}
};
vec<TIFA> t;
vecu root;
public:
CEXP persistent_segtree(spnu a, u32 N) NE : n{N}, t(a.size() * 24, TIFA()), root(a.size()) {
build(root[0], 0, n - 1, a[0]);
flt_ (u32, i, 1, (u32)a.size()) add_(root[i - 1], root[i], 0, n - 1, a[i]);
}
CEXP void add(u32 old_x, u32 x, u32 pos) NE { add_(root[old_x], root[x], 0, n - 1, pos); }
CEXP u32 kth_min(u32 x, u32 y, u32 k) NE { retif_((x), kth_min_(root[x - 1], root[y], 0, n - 1, k), kth_min_(root[y], 0, n - 1, k)); }
CEXP u32 kth_max(u32 x, u32 y, u32 k) NE { retif_((x), kth_max_(root[x - 1], root[y], 0, n - 1, k), kth_max_(root[y], 0, n - 1, k)); }
CEXP u32 frequency(u32 x, u32 y, u32 pos) NE { retif_((x), frequency_(root[x - 1], root[y], 0, n - 1, pos, pos), frequency_(root[y], 0, n - 1, pos, pos)); }
CEXP u32 frequency(u32 x, u32 y, u32 L, u32 R) NE { retif_((x), frequency_(root[x - 1], root[y], 0, n - 1, L, R), frequency_(root[y], 0, n - 1, L, R)); }
private:
CEXP void pushup(u32 x) NE {
if (t[x].w = 0; t[x].ls) t[x].w = t[t[x].ls].w;
if (t[x].rs) t[x].w += t[t[x].rs].w;
}
CEXP void build(u32& x, u32 l, u32 r, u32 pos) NE {
if (x = ++cnt; l == r) {
if (l == pos) ++t[x].w;
return;
}
cu32 mid = l + (r - l) / 2;
build(t[x].ls, l, mid, pos), build(t[x].rs, mid + 1, r, pos), pushup(x);
}
CEXP void add_(u32 old_x, u32& x, u32 l, u32 r, u32 pos) NE {
if (assert(pos >= l && pos <= r), t[x = (++cnt)] = t[old_x]; l == r) return void(++t[x].w);
if (cu32 mid = l + (r - l) / 2; pos <= mid) add_(t[old_x].ls, t[x].ls, l, mid, pos);
else add_(t[old_x].rs, t[x].rs, mid + 1, r, pos);
pushup(x);
}
CEXP u32 kth_min_(u32 x, u32 y, u32 l, u32 r, u32 k) NE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2, kk = t[t[y].ls].w - t[t[x].ls].w; k <= kk) return kth_min_(t[x].ls, t[y].ls, l, mid, k);
else return kth_min_(t[x].rs, t[y].rs, mid + 1, r, k - kk);
}
CEXP u32 kth_max_(u32 x, u32 y, u32 l, u32 r, u32 k) NE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2, kk = t[t[y].rs].w - t[t[x].rs].w; k <= kk) return kth_max_(t[x].rs, t[y].rs, mid + 1, r, k);
else return kth_max_(t[x].ls, t[y].ls, l, mid, k - kk);
}
CEXP u32 frequency_(u32 x, u32 y, u32 l, u32 r, u32 L, u32 R) NE {
if (assert(R >= l && L <= r); L <= l && R >= r) return t[y].w - t[x].w;
cu32 mid = l + (r - l) / 2;
u32 ret = 0_u32;
if (L <= mid) ret = frequency_(t[x].ls, t[y].rs, l, mid, L, R);
if (R > mid) ret += frequency_(t[x].rs, t[y].rs, mid + 1, r, L, R);
return ret;
}
CEXP u32 kth_min_(u32 y, u32 l, u32 r, u32 k) NE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2, kk = t[t[y].ls].w; k <= kk) return kth_min_(t[y].ls, l, mid, k);
else return kth_min_(t[y].rs, mid + 1, r, k - kk);
}
CEXP u32 kth_max_(u32 y, u32 l, u32 r, u32 k) NE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2, kk = t[t[y].rs].w; k <= kk) return kth_max_(t[y].rs, mid + 1, r, k);
else return kth_max_(t[y].ls, l, mid, k - kk);
}
CEXP u32 frequency_(u32 y, u32 l, u32 r, u32 L, u32 R) NE {
if (assert(R >= l && L <= r); L <= l && R >= r) return t[y].w;
cu32 mid = l + (r - l) / 2;
u32 ret = 0_u32;
if (L <= mid) ret = frequency_(t[y].rs, l, mid, L, R);
if (R > mid) ret += frequency_(t[y].rs, mid + 1, r, L, R);
return ret;
}
};
} // namespace tifa_libs
#line 2 "src/ds/segtree/persistent/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 4 "src/ds/segtree/persistent/lib.hpp"
namespace tifa_libs {
class persistent_segtree {
//! initial cnt = 1;
u32 n, cnt{0};
struct TIFA {
u32 w, ls, rs;
CEXP TIFA(u32 W = 0, u32 LS = 0, u32 RS = 0) NE : w(W), ls(LS), rs(RS) {}
};
vec<TIFA> t;
vecu root;
public:
CEXP persistent_segtree(spnu a, u32 N) NE : n{N}, t(a.size() * 24, TIFA()), root(a.size()) {
build(root[0], 0, n - 1, a[0]);
flt_ (u32, i, 1, (u32)a.size()) add_(root[i - 1], root[i], 0, n - 1, a[i]);
}
CEXP void add(u32 old_x, u32 x, u32 pos) NE { add_(root[old_x], root[x], 0, n - 1, pos); }
CEXP u32 kth_min(u32 x, u32 y, u32 k) NE { retif_((x), kth_min_(root[x - 1], root[y], 0, n - 1, k), kth_min_(root[y], 0, n - 1, k)); }
CEXP u32 kth_max(u32 x, u32 y, u32 k) NE { retif_((x), kth_max_(root[x - 1], root[y], 0, n - 1, k), kth_max_(root[y], 0, n - 1, k)); }
CEXP u32 frequency(u32 x, u32 y, u32 pos) NE { retif_((x), frequency_(root[x - 1], root[y], 0, n - 1, pos, pos), frequency_(root[y], 0, n - 1, pos, pos)); }
CEXP u32 frequency(u32 x, u32 y, u32 L, u32 R) NE { retif_((x), frequency_(root[x - 1], root[y], 0, n - 1, L, R), frequency_(root[y], 0, n - 1, L, R)); }
private:
CEXP void pushup(u32 x) NE {
if (t[x].w = 0; t[x].ls) t[x].w = t[t[x].ls].w;
if (t[x].rs) t[x].w += t[t[x].rs].w;
}
CEXP void build(u32& x, u32 l, u32 r, u32 pos) NE {
if (x = ++cnt; l == r) {
if (l == pos) ++t[x].w;
return;
}
cu32 mid = l + (r - l) / 2;
build(t[x].ls, l, mid, pos), build(t[x].rs, mid + 1, r, pos), pushup(x);
}
CEXP void add_(u32 old_x, u32& x, u32 l, u32 r, u32 pos) NE {
if (assert(pos >= l && pos <= r), t[x = (++cnt)] = t[old_x]; l == r) return void(++t[x].w);
if (cu32 mid = l + (r - l) / 2; pos <= mid) add_(t[old_x].ls, t[x].ls, l, mid, pos);
else add_(t[old_x].rs, t[x].rs, mid + 1, r, pos);
pushup(x);
}
CEXP u32 kth_min_(u32 x, u32 y, u32 l, u32 r, u32 k) NE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2, kk = t[t[y].ls].w - t[t[x].ls].w; k <= kk) return kth_min_(t[x].ls, t[y].ls, l, mid, k);
else return kth_min_(t[x].rs, t[y].rs, mid + 1, r, k - kk);
}
CEXP u32 kth_max_(u32 x, u32 y, u32 l, u32 r, u32 k) NE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2, kk = t[t[y].rs].w - t[t[x].rs].w; k <= kk) return kth_max_(t[x].rs, t[y].rs, mid + 1, r, k);
else return kth_max_(t[x].ls, t[y].ls, l, mid, k - kk);
}
CEXP u32 frequency_(u32 x, u32 y, u32 l, u32 r, u32 L, u32 R) NE {
if (assert(R >= l && L <= r); L <= l && R >= r) return t[y].w - t[x].w;
cu32 mid = l + (r - l) / 2;
u32 ret = 0_u32;
if (L <= mid) ret = frequency_(t[x].ls, t[y].rs, l, mid, L, R);
if (R > mid) ret += frequency_(t[x].rs, t[y].rs, mid + 1, r, L, R);
return ret;
}
CEXP u32 kth_min_(u32 y, u32 l, u32 r, u32 k) NE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2, kk = t[t[y].ls].w; k <= kk) return kth_min_(t[y].ls, l, mid, k);
else return kth_min_(t[y].rs, mid + 1, r, k - kk);
}
CEXP u32 kth_max_(u32 y, u32 l, u32 r, u32 k) NE {
if (l == r) return l;
if (cu32 mid = l + (r - l) / 2, kk = t[t[y].rs].w; k <= kk) return kth_max_(t[y].rs, mid + 1, r, k);
else return kth_max_(t[y].ls, l, mid, k - kk);
}
CEXP u32 frequency_(u32 y, u32 l, u32 r, u32 L, u32 R) NE {
if (assert(R >= l && L <= r); L <= l && R >= r) return t[y].w;
cu32 mid = l + (r - l) / 2;
u32 ret = 0_u32;
if (L <= mid) ret = frequency_(t[y].rs, l, mid, L, R);
if (R > mid) ret += frequency_(t[y].rs, mid + 1, r, L, R);
return ret;
}
};
} // namespace tifa_libs
src/ds/segtree/persistent/lib.hpp