Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/aizu/itp2_5_c.test.cpp

Depends on

Code

#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/8/ITP2/all/ITP2_5_C"

#include "../../code/edh/cantor.hpp"
#include "../../code/edh/cantor_inv.hpp"
#include "../../code/edh/cantor_seq2val.hpp"
#include "../../code/edh/cantor_val2seq.hpp"
#include "../../code/io/ios_container.hpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n;
  std::cin >> n;
  vecu p(n);
  std::cin >> p;
  auto s = tifa_libs::cantor_seq(p);
  auto fact = tifa_libs::math::gen_fact((u32)s.size(), -1_u64);
  u64 v = tifa_libs::cantor_seq2val(s, fact);
  if (v > 1) std::cout << tifa_libs::cantor_inv_seq(tifa_libs::cantor_val2seq(v - 1, fact)) << '\n';
  std::cout << p << '\n';
  if (v < fact.back() * n) std::cout << tifa_libs::cantor_inv_seq(tifa_libs::cantor_val2seq(v + 1, fact)) << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/aizu/itp2_5_c.test.cpp"
#define PROBLEM "https://onlinejudge.u-aizu.ac.jp/courses/lesson/8/ITP2/all/ITP2_5_C"

#line 1 "src/code/edh/cantor.hpp"



#line 1 "src/code/ds/fenwick.hpp"



#line 1 "src/code/bit/lowbit.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/bit/lowbit.hpp"

namespace tifa_libs::bit {

template <class T>
constexpr T lowbit(T x) { return T(1) << std::countr_zero(x); }

}  // namespace tifa_libs::bit


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

namespace tifa_libs::ds {

template <class T>
class fenwick {
  vec<T> a;

 public:
  //! [1, sz)
  explicit constexpr fenwick(u32 sz) : a(sz) { assert(sz > 1); }

  //! [pos, sz), pos > 0
  constexpr void add(u32 pos, T const &x) {
    if (!pos) return;
    for (; pos < a.size(); pos += bit::lowbit(pos)) a[pos] += x;
  }
  //! [1, pos)
  constexpr T sum(u32 pos) {
    T ret = 0;
    for (pos = std::min(pos, (u32)a.size() - 1); pos; pos -= bit::lowbit(pos)) ret += a[pos];
    return ret;
  }
  //! for weighted fenwick
  constexpr T kth_max(u32 k) {
    u32 now = 0, n = std::bit_ceil(a.size());
    T s{};
    while (n) {
      u32 to = now | n;
      if (to >= a.size()) continue;
      if (T x = s + a[to]; x < k) {
        now = to;
        s = x;
      }
    }
    return now + 1;
  }
};

}  // namespace tifa_libs::ds


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

namespace tifa_libs {

//! [0, n)
//! p \in [1, n], a_i == a_j \iff i == j
constexpr vecu cantor_seq(vecu const &p) {
  u32 n = (u32)p.size();
  ds::fenwick<u32> tr(n + 1);
  vecu s(n);
  for (u32 i = n - 1; ~i; --i) {
    s[i] = tr.sum(p[i]);
    tr.add(p[i], 1);
  }
  return s;
}

}  // namespace tifa_libs


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



#line 1 "src/code/ds/weighted_segtree.hpp"



#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


#line 1 "src/code/edh/cantor_seq2val.hpp"



#line 1 "src/code/comb/gen_fact.hpp"



#line 1 "src/code/math/mul_mod_u.hpp"



#line 5 "src/code/math/mul_mod_u.hpp"

namespace tifa_libs::math {

constexpr u64 mul_mod_u(u64 a, u64 b, u64 mod) {
  if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
  else return (u64)((u128)a * b % mod);
}

}  // namespace tifa_libs::math


#line 5 "src/code/comb/gen_fact.hpp"

namespace tifa_libs::math {

// i! from i=0..n-1
constexpr vecu64 gen_fact(u32 n, u64 mod) {
  if (n == 0) return {};
  if (n == 1) return {1};
  vecu64 ans(n);
  ans[0] = ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = mul_mod_u(ans[i - 1], i, mod);
  return ans;
}
// i! from i=0..n-1
template <class mint>
constexpr vec<mint> gen_fact(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_fact(n, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 5 "src/code/edh/cantor_seq2val.hpp"

namespace tifa_libs {

constexpr u64 cantor_seq2val(vecu const &s, vecu64 const &fact, u64 mod = -1_u64) {
  u32 n = (u32)s.size();
  u64 ret = 1;
  for (u32 i = 0; i < n; ++i) (ret += math::mul_mod_u(s[i], fact[n - i - 1], mod)) %= mod;
  return ret;
}
constexpr u64 cantor_seq2val(vecu const &s, u64 mod = -1_u64) { return cantor_seq2val(s, math::gen_fact((u32)s.size(), mod), mod); }

}  // namespace tifa_libs


#line 1 "src/code/edh/cantor_val2seq.hpp"



#line 5 "src/code/edh/cantor_val2seq.hpp"

namespace tifa_libs {

constexpr vecu cantor_val2seq(u64 cv, vecu64 const &fact) {
  u32 n = (u32)fact.size();
  --cv;
  vecu s;
  s.reserve(n);
  for (u32 i = 0; i < n; cv %= fact[n - i - 1], ++i) s.push_back(u32(cv / fact[n - i - 1]));
  return s;
}
constexpr vecu cantor_val2seq(u64 cv, u32 n) { return cantor_val2seq(cv, math::gen_fact(n, -1_u64)); }

}  // namespace tifa_libs


#line 1 "src/code/io/ios_container.hpp"



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



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<typename T::iterator>;
  { v.end() } -> std::same_as<typename T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
constexpr bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
constexpr bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
constexpr bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
constexpr bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
constexpr bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
constexpr bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
constexpr bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = typename to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 5 "src/code/io/ios_container.hpp"

template <tifa_libs::container_c T>
std::istream &operator>>(std::istream &is, T &x) {
  for (auto &i : x) is >> i;
  return is;
}
template <tifa_libs::container_c T>
std::ostream &operator<<(std::ostream &os, T const &x) {
  if (x.begin() == x.end()) return os;
  auto it = x.begin();
  os << *it++;
  for (; it != x.end(); ++it) os << ' ' << *it;
  return os;
}


#line 8 "src/test_cpverifier/aizu/itp2_5_c.test.cpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n;
  std::cin >> n;
  vecu p(n);
  std::cin >> p;
  auto s = tifa_libs::cantor_seq(p);
  auto fact = tifa_libs::math::gen_fact((u32)s.size(), -1_u64);
  u64 v = tifa_libs::cantor_seq2val(s, fact);
  if (v > 1) std::cout << tifa_libs::cantor_inv_seq(tifa_libs::cantor_val2seq(v - 1, fact)) << '\n';
  std::cout << p << '\n';
  if (v < fact.back() * n) std::cout << tifa_libs::cantor_inv_seq(tifa_libs::cantor_val2seq(v + 1, fact)) << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 00_sample_00.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 00_sample_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 01_corner_00.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 01_corner_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 01_corner_02.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_00.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 02_all_01.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 02_all_02.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_04.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_05.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 02_all_06.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_07.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 02_all_08.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_09.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_10.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_11.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_12.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_13.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 02_all_14.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_15.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_16.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_17.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_18.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_19.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_20.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_21.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_22.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 02_all_23.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_00.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 03_random_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_02.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 03_random_04.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 03_random_05.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 04_maximum_00.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 04_maximum_01.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 04_maximum_02.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 04_maximum_03.in :heavy_check_mark: AC 8 ms 4 MB
g++-12 04_maximum_04.in :heavy_check_mark: AC 8 ms 4 MB
Back to top page