Tifa's CP Library

:heavy_check_mark: persistent_segtree (src/code/ds/persistent_segtree.hpp)

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#ifndef TIFALIBS_DS_PERSISTENT_SEGTREE
#define TIFALIBS_DS_PERSISTENT_SEGTREE

#include "../util/util.hpp"

namespace tifa_libs::ds {

class persistent_segtree {
  //! initial cnt = 1;
  u32 n, cnt;
  struct YYZ {
    u32 w, ls, rs;
    constexpr YYZ(u32 W = 0, u32 LS = 0, u32 RS = 0) : w(W), ls(LS), rs(RS) {}
  };
  vec<YYZ> t;
  vecu root;

 public:
  constexpr persistent_segtree(vecu const& a, u32 N) : n(N), cnt(0), t(a.size() * 24, YYZ()), root(a.size()) {
    build(root[0], 0, n - 1, a[0]);
    for (u32 i = 1; i < a.size(); ++i) add_(root[i - 1], root[i], 0, n - 1, a[i]);
  }
  constexpr void add(u32 old_x, u32 x, u32 pos) { add_(root[old_x], root[x], 0, n - 1, pos); }
  constexpr u32 kth_min(u32 x, u32 y, u32 k) { return x ? kth_min_(root[x - 1], root[y], 0, n - 1, k) : kth_min_(root[y], 0, n - 1, k); }
  constexpr u32 kth_max(u32 x, u32 y, u32 k) { return x ? kth_max_(root[x - 1], root[y], 0, n - 1, k) : kth_max_(root[y], 0, n - 1, k); }
  constexpr u32 frequency(u32 x, u32 y, u32 pos) { return x ? frequency_(root[x - 1], root[y], 0, n - 1, pos, pos) : frequency_(root[y], 0, n - 1, pos, pos); }
  constexpr u32 frequency(u32 x, u32 y, u32 L, u32 R) { return x ? frequency_(root[x - 1], root[y], 0, n - 1, L, R) : frequency_(root[y], 0, n - 1, L, R); }

 private:
  constexpr void pushup(u32 x) {
    t[x].w = 0;
    if (t[x].ls) t[x].w = t[t[x].ls].w;
    if (t[x].rs) t[x].w += t[t[x].rs].w;
  }
  constexpr void build(u32& x, u32 l, u32 r, u32 pos) {
    x = (++cnt);
    if (l == r) {
      if (l == pos) ++t[x].w;
      return;
    }
    u32 mid = l + (r - l) / 2;
    build(t[x].ls, l, mid, pos), build(t[x].rs, mid + 1, r, pos);
    pushup(x);
  }
  constexpr void add_(u32 old_x, u32& x, u32 l, u32 r, u32 pos) {
    assert(pos >= l && pos <= r);
    t[x = (++cnt)] = t[old_x];
    if (l == r) return void(++t[x].w);
    u32 mid = l + (r - l) / 2;
    if (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);
  }
  constexpr u32 kth_min_(u32 x, u32 y, u32 l, u32 r, u32 k) {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2, kk = t[t[y].ls].w - t[t[x].ls].w;
    if (k <= kk) return kth_min_(t[x].ls, t[y].ls, l, mid, k);
    return kth_min_(t[x].rs, t[y].rs, mid + 1, r, k - kk);
  }
  constexpr u32 kth_max_(u32 x, u32 y, u32 l, u32 r, u32 k) {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2, kk = t[t[y].rs].w - t[t[x].rs].w;
    if (k <= kk) return kth_max_(t[x].rs, t[y].rs, mid + 1, r, k);
    return kth_max_(t[x].ls, t[y].ls, l, mid, k - kk);
  }
  constexpr u32 frequency_(u32 x, u32 y, u32 l, u32 r, u32 L, u32 R) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return t[y].w - t[x].w;
    u32 mid = l + (r - l) / 2, ret = u32(0);
    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;
  }
  constexpr u32 kth_min_(u32 y, u32 l, u32 r, u32 k) {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2, kk = t[t[y].ls].w;
    if (k <= kk) return kth_min_(t[y].ls, l, mid, k);
    return kth_min_(t[y].rs, mid + 1, r, k - kk);
  }
  constexpr u32 kth_max_(u32 y, u32 l, u32 r, u32 k) {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2, kk = t[t[y].rs].w;
    if (k <= kk) return kth_max_(t[y].rs, mid + 1, r, k);
    return kth_max_(t[y].ls, l, mid, k - kk);
  }
  constexpr u32 frequency_(u32 y, u32 l, u32 r, u32 L, u32 R) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return t[y].w;
    u32 mid = l + (r - l) / 2, ret = u32(0);
    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::ds

#endif
#line 1 "src/code/ds/persistent_segtree.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
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 T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/ds/persistent_segtree.hpp"

namespace tifa_libs::ds {

class persistent_segtree {
  //! initial cnt = 1;
  u32 n, cnt;
  struct YYZ {
    u32 w, ls, rs;
    constexpr YYZ(u32 W = 0, u32 LS = 0, u32 RS = 0) : w(W), ls(LS), rs(RS) {}
  };
  vec<YYZ> t;
  vecu root;

 public:
  constexpr persistent_segtree(vecu const& a, u32 N) : n(N), cnt(0), t(a.size() * 24, YYZ()), root(a.size()) {
    build(root[0], 0, n - 1, a[0]);
    for (u32 i = 1; i < a.size(); ++i) add_(root[i - 1], root[i], 0, n - 1, a[i]);
  }
  constexpr void add(u32 old_x, u32 x, u32 pos) { add_(root[old_x], root[x], 0, n - 1, pos); }
  constexpr u32 kth_min(u32 x, u32 y, u32 k) { return x ? kth_min_(root[x - 1], root[y], 0, n - 1, k) : kth_min_(root[y], 0, n - 1, k); }
  constexpr u32 kth_max(u32 x, u32 y, u32 k) { return x ? kth_max_(root[x - 1], root[y], 0, n - 1, k) : kth_max_(root[y], 0, n - 1, k); }
  constexpr u32 frequency(u32 x, u32 y, u32 pos) { return x ? frequency_(root[x - 1], root[y], 0, n - 1, pos, pos) : frequency_(root[y], 0, n - 1, pos, pos); }
  constexpr u32 frequency(u32 x, u32 y, u32 L, u32 R) { return x ? frequency_(root[x - 1], root[y], 0, n - 1, L, R) : frequency_(root[y], 0, n - 1, L, R); }

 private:
  constexpr void pushup(u32 x) {
    t[x].w = 0;
    if (t[x].ls) t[x].w = t[t[x].ls].w;
    if (t[x].rs) t[x].w += t[t[x].rs].w;
  }
  constexpr void build(u32& x, u32 l, u32 r, u32 pos) {
    x = (++cnt);
    if (l == r) {
      if (l == pos) ++t[x].w;
      return;
    }
    u32 mid = l + (r - l) / 2;
    build(t[x].ls, l, mid, pos), build(t[x].rs, mid + 1, r, pos);
    pushup(x);
  }
  constexpr void add_(u32 old_x, u32& x, u32 l, u32 r, u32 pos) {
    assert(pos >= l && pos <= r);
    t[x = (++cnt)] = t[old_x];
    if (l == r) return void(++t[x].w);
    u32 mid = l + (r - l) / 2;
    if (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);
  }
  constexpr u32 kth_min_(u32 x, u32 y, u32 l, u32 r, u32 k) {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2, kk = t[t[y].ls].w - t[t[x].ls].w;
    if (k <= kk) return kth_min_(t[x].ls, t[y].ls, l, mid, k);
    return kth_min_(t[x].rs, t[y].rs, mid + 1, r, k - kk);
  }
  constexpr u32 kth_max_(u32 x, u32 y, u32 l, u32 r, u32 k) {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2, kk = t[t[y].rs].w - t[t[x].rs].w;
    if (k <= kk) return kth_max_(t[x].rs, t[y].rs, mid + 1, r, k);
    return kth_max_(t[x].ls, t[y].ls, l, mid, k - kk);
  }
  constexpr u32 frequency_(u32 x, u32 y, u32 l, u32 r, u32 L, u32 R) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return t[y].w - t[x].w;
    u32 mid = l + (r - l) / 2, ret = u32(0);
    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;
  }
  constexpr u32 kth_min_(u32 y, u32 l, u32 r, u32 k) {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2, kk = t[t[y].ls].w;
    if (k <= kk) return kth_min_(t[y].ls, l, mid, k);
    return kth_min_(t[y].rs, mid + 1, r, k - kk);
  }
  constexpr u32 kth_max_(u32 y, u32 l, u32 r, u32 k) {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2, kk = t[t[y].rs].w;
    if (k <= kk) return kth_max_(t[y].rs, mid + 1, r, k);
    return kth_max_(t[y].ls, l, mid, k - kk);
  }
  constexpr u32 frequency_(u32 y, u32 l, u32 r, u32 L, u32 R) {
    assert(R >= l && L <= r);
    if (L <= l && R >= r) return t[y].w;
    u32 mid = l + (r - l) / 2, ret = u32(0);
    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::ds


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