Tifa's CP Library

:heavy_check_mark: cantor_inv (src/code/edh/cantor_inv.hpp)

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Code

#ifndef TIFALIBS_EDH_CANTOR_INV
#define TIFALIBS_EDH_CANTOR_INV

#include "../ds/weighted_segtree.hpp"

namespace tifa_libs {

//! [0, n)
//! p \in [1, n], a_i == a_j \iff i == j
constexpr vecu cantor_inv_seq(vecu const &s) {
  u32 n = (u32)s.size();
  ds::weighted_segtree tr(n + 1);
  for (u32 i = 1; i <= n; ++i) tr.ins(i);
  vecu p(n);
  for (u32 i = 0; i < n; ++i) tr.del(p[i] = (u32)tr.kth_min(s[i] + 1));
  return p;
}

}  // namespace tifa_libs

#endif
#line 1 "src/code/edh/cantor_inv.hpp"



#line 1 "src/code/ds/weighted_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&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };


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

namespace tifa_libs::ds {

class weighted_segtree {
  const u32 n;
  vecu t;

 public:
  explicit constexpr weighted_segtree(u32 N) : n(N), t(N * 4) {}

  constexpr void ins(u32 pos) { ins_(1, 0, n - 1, pos); }
  constexpr void del(u32 pos) { del_(1, 0, n - 1, pos); }
  constexpr u32 kth_min(u32 k) { return kth_min_(1, 0, n - 1, k); }
  constexpr u32 kth_max(u32 k) { return kth_max_(1, 0, n - 1, k); }
  constexpr u32 frequency(u32 k) { return frequency_(1, 0, n - 1, k, k); }
  constexpr u32 frequency(u32 l, u32 r) { return frequency_(1, 0, n - 1, l, r); }

 private:
  constexpr void ins_(u32 x, u32 l, u32 r, u32 pos) {
    if (l == r) return void(++t[x]);
    u32 mid = l + (r - l) / 2;
    if (pos <= mid) ins_(x << 1, l, mid, pos);
    else ins_(x << 1 | 1, mid + 1, r, pos);
    t[x] = t[x << 1] + t[x << 1 | 1];
  }
  constexpr void del_(u32 x, u32 l, u32 r, u32 pos) {
    if (l == r) return void(--t[x]);
    u32 mid = l + (r - l) / 2;
    if (pos <= mid) del_(x << 1, l, mid, pos);
    else del_(x << 1 | 1, mid + 1, r, pos);
    t[x] = t[x << 1] + t[x << 1 | 1];
  }
  constexpr u32 kth_min_(u32 x, u32 l, u32 r, u32 k) const {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2;
    if (k <= t[x << 1]) return kth_min_(x << 1, l, mid, k);
    return kth_min_(x << 1 | 1, mid + 1, r, k - t[x << 1]);
  }
  constexpr u32 kth_max_(u32 x, u32 l, u32 r, u32 k) const {
    if (l == r) return l;
    u32 mid = l + (r - l) / 2;
    if (k <= t[x << 1 | 1]) return kth_max_(x << 1 | 1, mid + 1, r, k);
    return kth_max_(x << 1, l, mid, k - t[x << 1 | 1]);
  }
  constexpr u32 frequency_(u32 x, u32 l, u32 r, u32 L, u32 R) const {
    if (L <= l && R >= r) return t[x];
    u32 mid = l + (r - l) / 2, ret = u32(0);
    if (L <= mid) ret = frequency_(x << 1, l, mid, L, R);
    if (R > mid) ret += frequency_(x << 1 | 1, mid + 1, r, L, R);
    return ret;
  }
};

}  // namespace tifa_libs::ds


#line 5 "src/code/edh/cantor_inv.hpp"

namespace tifa_libs {

//! [0, n)
//! p \in [1, n], a_i == a_j \iff i == j
constexpr vecu cantor_inv_seq(vecu const &s) {
  u32 n = (u32)s.size();
  ds::weighted_segtree tr(n + 1);
  for (u32 i = 1; i <= n; ++i) tr.ins(i);
  vecu p(n);
  for (u32 i = 0; i < n; ++i) tr.del(p[i] = (u32)tr.kth_min(s[i] + 1));
  return p;
}

}  // namespace tifa_libs


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