#538124 (C++17) No.1193 Penguin Sequence

• 問題: No.1193 Penguin Sequence
• ユーザー: KoD
• 提出日時: 2020-08-22 16:30:16
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 174 ms / 2,000 ms
• コード長: 10,427 bytes
• コンパイル時間: 1,088 ms
• コンパイル使用メモリ: 85,712 KB
• 最終ジャッジ日時: 2025-01-13 10:12:47
• ジャッジサーバーID （参考情報）: judge5 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 38

ソースコード

#line 1 "main.cpp"

/**
 * @title Template
 */

#include <iostream>
#include <algorithm>
#include <utility>
#include <numeric>
#include <vector>
#include <array>
#include <cassert>

#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/chmin_chmax.cpp"

template <class T, class U>
constexpr bool chmin(T &lhs, const U &rhs) {
  if (lhs > rhs) { lhs = rhs; return true; }
  return false;
}

template <class T, class U>
constexpr bool chmax(T &lhs, const U &rhs) {
  if (lhs < rhs) { lhs = rhs; return true; }
  return false;
}

/**
 * @title Chmin/Chmax
 */
#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/range.cpp"

#line 4 "/Users/kodamankod/Desktop/Programming/Library/other/range.cpp"

class range {
public:
  class iterator {
  private:
    int64_t M_position;

  public:
    constexpr iterator(int64_t position) noexcept: M_position(position) { }
    constexpr void operator ++ () noexcept { ++M_position; }
    constexpr bool operator != (iterator other) const noexcept { return M_position != other.M_position; }
    constexpr int64_t operator * () const noexcept { return M_position; }

  };

  class reverse_iterator {
  private:
    int64_t M_position;
  
  public:
    constexpr reverse_iterator(int64_t position) noexcept: M_position(position) { }
    constexpr void operator ++ () noexcept { --M_position; }
    constexpr bool operator != (reverse_iterator other) const noexcept { return M_position != other.M_position; }
    constexpr int64_t operator * () const noexcept { return M_position; }

  };
  
private:
  const iterator M_first, M_last;

public:
  constexpr range(int64_t first, int64_t last) noexcept: M_first(first), M_last(std::max(first, last)) { }
  constexpr iterator begin() const noexcept { return M_first; }
  constexpr iterator end() const noexcept { return M_last; }
  constexpr reverse_iterator rbegin() const noexcept { return reverse_iterator(*M_last - 1); } 
  constexpr reverse_iterator rend() const noexcept { return reverse_iterator(*M_first - 1); } 

};

/**
 * @title Range
 */
#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/rev.cpp"

#include <type_traits>
#include <iterator>
#line 6 "/Users/kodamankod/Desktop/Programming/Library/other/rev.cpp"

template <class T>
class rev_impl {
public:
  using iterator = decltype(std::rbegin(std::declval<T>()));

private:
  const iterator M_begin;
  const iterator M_end;

public:
  constexpr rev_impl(T &&cont) noexcept: M_begin(std::rbegin(cont)), M_end(std::rend(cont)) { }
  constexpr iterator begin() const noexcept { return M_begin; }
  constexpr iterator end() const noexcept { return M_end; }

};

template <class T>
constexpr decltype(auto) rev(T &&cont) {
  return rev_impl<T>(std::forward<T>(cont));
}

/**
 * @title Reverser
 */
#line 2 "/Users/kodamankod/Desktop/Programming/Library/algebraic/modular.cpp"

#include <cstdint>
#line 5 "/Users/kodamankod/Desktop/Programming/Library/algebraic/modular.cpp"

template <class Modulus>
class modular {
public:
  using value_type = uint32_t;
  using cover_type = uint64_t;
  static constexpr value_type mod() { return Modulus::value(); }

  template <class T>
  static constexpr value_type normalize(T value_) noexcept {
    if (value_ < 0) {
      value_ = -value_;
      value_ %= mod();
      if (value_ == 0) return 0;
      return mod() - value_;
    }
    return value_ % mod();
  }

private:
  value_type value;

public:
  constexpr modular() noexcept : value(0) { }
  template <class T>
  explicit constexpr modular(T value_) noexcept : value(normalize(value_)) { }
  template <class T>
  explicit constexpr operator T() const noexcept { return static_cast<T>(value); }

  constexpr value_type get() const noexcept { return value; }
  constexpr value_type &extract() noexcept { return value; }
  constexpr modular operator - () const noexcept { return modular(mod() - value); }
  constexpr modular operator ~ () const noexcept { return inverse(*this); }

  constexpr modular operator + (const modular &rhs) const noexcept { return modular(*this) += rhs; }
  constexpr modular& operator += (const modular &rhs) noexcept { 
    if ((value += rhs.value) >= mod()) value -= mod(); 
    return *this; 
  }

  constexpr modular operator - (const modular &rhs) const noexcept { return modular(*this) -= rhs; }
  constexpr modular& operator -= (const modular &rhs) noexcept { 
    if ((value += mod() - rhs.value) >= mod()) value -= mod(); 
    return *this; 
  }

  constexpr modular operator * (const modular &rhs) const noexcept { return modular(*this) *= rhs; }
  constexpr modular& operator *= (const modular &rhs) noexcept { 
    value = (cover_type) value * rhs.value % mod();
    return *this;
  }

  constexpr modular operator / (const modular &rhs) const noexcept { return modular(*this) /= rhs; }
  constexpr modular& operator /= (const modular &rhs) noexcept { return (*this) *= inverse(rhs); }

  constexpr bool zero() const noexcept { return value == 0; }
  constexpr bool operator == (const modular &rhs) const noexcept { return value == rhs.value; }
  constexpr bool operator != (const modular &rhs) const noexcept { return value != rhs.value; }

  friend std::ostream& operator << (std::ostream &stream, const modular &rhs) { return stream << rhs.value; }
  friend constexpr modular inverse(modular val) noexcept { return power(val, mod() - 2); }
  friend constexpr modular power(modular val, cover_type exp) noexcept { 
    modular res(1);
    for (; exp > 0; exp >>= 1, val *= val) if (exp & 1) res *= val;
    return res;
  }

};

template <uint32_t Val>
struct modulus_impl { static constexpr uint32_t value() noexcept { return Val; } };
template <uint32_t Val>
using mint32_t = modular<modulus_impl<Val>>;

struct runtime_mod { static uint32_t &value() noexcept { static uint32_t val = 0; return val; } };
using rmint32_t = modular<runtime_mod>;

/**
 * @title Modint
 */
#line 2 "/Users/kodamankod/Desktop/Programming/Library/algebraic/factorials.cpp"

#include <cstddef>
#line 5 "/Users/kodamankod/Desktop/Programming/Library/algebraic/factorials.cpp"

template <class T, size_t N>
class factorials {
public:
  using value_type = T;
  static constexpr size_t size = N;

public:
  std::array<value_type, size + 1> fact{};
  std::array<value_type, size + 1> fact_inv{};

  factorials() {
    fact.front() = value_type(1);
    for (size_t i = 1; i <= size; ++i) {
      fact[i] = fact[i - 1] * value_type(i);
    }
    fact_inv.back() = ~fact.back();
    for (size_t i = size; i > 0; --i) {
      fact_inv[i - 1] = fact_inv[i] * value_type(i);
    }
  }

  value_type operator () (size_t n, size_t r) const {
    return fact[n] * fact_inv[n - r] * fact_inv[r];
  }

};

/**
 * @title Factorial
 */
#line 2 "/Users/kodamankod/Desktop/Programming/Library/container/fenwick_tree.cpp"

#line 2 "/Users/kodamankod/Desktop/Programming/Library/other/bit_operation.cpp"

#line 5 "/Users/kodamankod/Desktop/Programming/Library/other/bit_operation.cpp"

constexpr size_t   bit_ppc(const uint64_t x)   { return __builtin_popcountll(x); }
constexpr size_t   bit_ctzr(const uint64_t x)  { return x == 0 ? 64 : __builtin_ctzll(x); }
constexpr size_t   bit_ctzl(const uint64_t x)  { return x == 0 ? 64 : __builtin_clzll(x); }
constexpr size_t   bit_width(const uint64_t x) { return 64 - bit_ctzl(x); }
constexpr uint64_t bit_msb(const uint64_t x)   { return x == 0 ? 0 : uint64_t(1) << (bit_width(x) - 1); }
constexpr uint64_t bit_lsb(const uint64_t x)   { return x & (-x); }
constexpr uint64_t bit_cover(const uint64_t x) { return x == 0 ? 0 : bit_msb(2 * x - 1); }

constexpr uint64_t bit_rev(uint64_t x) {
  x = ((x >> 1) & 0x5555555555555555) | ((x & 0x5555555555555555) << 1);
  x = ((x >> 2) & 0x3333333333333333) | ((x & 0x3333333333333333) << 2);
  x = ((x >> 4) & 0x0F0F0F0F0F0F0F0F) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);
  x = ((x >> 8) & 0x00FF00FF00FF00FF) | ((x & 0x00FF00FF00FF00FF) << 8);
  x = ((x >> 16) & 0x0000FFFF0000FFFF) | ((x & 0x0000FFFF0000FFFF) << 16);
  x = (x >> 32) | (x << 32);
  return x;
}

/**
 * @title Bit Operations
 */
#line 4 "/Users/kodamankod/Desktop/Programming/Library/container/fenwick_tree.cpp"

#line 7 "/Users/kodamankod/Desktop/Programming/Library/container/fenwick_tree.cpp"

template <class T>
class fenwick_tree {
public:
  using value_type = T;
  using size_type = size_t;

private:
  std::vector<value_type> M_tree;

public:
  fenwick_tree() = default;
  explicit fenwick_tree(size_type size) { initialize(size); }

  void initialize(size_type size) {
    M_tree.assign(size + 1, value_type{});
  }

  void add(size_type index, const value_type& x) {
    ++index;
    while (index <= size()) {
      M_tree[index] += x;
      index += bit_lsb(index);
    }
  }

  value_type get(size_type index) const {
    ++index;
    value_type res{};
    while (index > 0) {
      res += M_tree[index];
      index -= bit_lsb(index);
    }
    return res;
  }
  value_type fold(size_type l, size_type r) const {
    if (l == 0 && r == 0) return value_type{};
    if (l == 0) return get(r - 1);
    return get(r - 1) - get(l - 1);
  }

  size_type size() const {
    return M_tree.size() - 1;
  }

};

/**
 * @title Fenwick Tree
 */
#line 20 "main.cpp"

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;

constexpr i32 inf32 = (i32(1) << 30) - 1;
constexpr i64 inf64 = (i64(1) << 62) - 1;

using m32 = mint32_t<998244353>;
factorials<m32, 200000> fact;

int main() {
  i32 N;
  std::cin >> N;
  std::vector<i32> A(N);
  for (auto &x: A) {
    std::cin >> x;
  }
  auto nums = A;
  std::sort(nums.begin(), nums.end());
  nums.erase(std::unique(nums.begin(), nums.end()), nums.end());
  for (auto &x: A) {
    x = std::lower_bound(nums.begin(), nums.end(), x) - nums.begin();
  }
  i64 inv = 0, sum = 0;
  {
    fenwick_tree<i32> fen(nums.size());
    for (auto i: range(0, N)) {
      inv += fen.fold(A[i] + 1, nums.size());
      fen.add(A[i], 1);
    }
    sum = inv;
    fen.initialize(nums.size());
    for (auto i: rev(range(0, N))) {
      sum += fen.fold(A[i] + 1, nums.size());
      fen.add(A[i], 1);
    }
  }
  m32 ans, coeff, prev(1);
  for (auto i: range(1, N + 1)) {
    m32 add = m32(sum) * coeff * fact(N - 1, i - 1); 
    if (i > 1) {
      add += m32(inv) * prev * fact(N - 2, i - 2);
    }
    ans = fact(N, i) * ans + add;
    coeff = coeff * fact(N, i) + prev * fact(N - 1, i - 1);
    prev *= fact(N, i);
  }
  std::cout << ans << '\n';
  return 0;
}