#585115 (C++17) No.1300 Sum of Inversions

• 問題: No.1300 Sum of Inversions
• ユーザー: KoD
• 提出日時: 2020-11-27 21:33:00
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 178 ms / 2,000 ms
• コード長: 10,416 bytes
• コンパイル時間: 1,081 ms
• コンパイル使用メモリ: 91,948 KB
• 実行使用メモリ: 9,472 KB
• 最終ジャッジ日時: 2024-07-26 11:46:17
• 合計ジャッジ時間: 7,761 ms
• ジャッジサーバーID （参考情報）: judge1 / judge4

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 6,816 KB
testcase_01	AC	2 ms; 6,944 KB
testcase_02	AC	2 ms; 6,940 KB
testcase_03	AC	139 ms; 8,064 KB
testcase_04	AC	136 ms; 8,064 KB
testcase_05	AC	110 ms; 7,296 KB
testcase_06	AC	155 ms; 8,704 KB
testcase_07	AC	150 ms; 8,448 KB
testcase_08	AC	167 ms; 8,960 KB
testcase_09	AC	163 ms; 8,832 KB
testcase_10	AC	88 ms; 6,944 KB
testcase_11	AC	93 ms; 6,940 KB
testcase_12	AC	135 ms; 8,064 KB
testcase_13	AC	130 ms; 7,936 KB
testcase_14	AC	178 ms; 9,344 KB
testcase_15	AC	163 ms; 8,832 KB
testcase_16	AC	140 ms; 8,192 KB
testcase_17	AC	86 ms; 6,944 KB
testcase_18	AC	99 ms; 6,940 KB
testcase_19	AC	116 ms; 7,424 KB
testcase_20	AC	121 ms; 7,552 KB
testcase_21	AC	118 ms; 7,552 KB
testcase_22	AC	108 ms; 7,168 KB
testcase_23	AC	153 ms; 8,704 KB
testcase_24	AC	114 ms; 7,424 KB
testcase_25	AC	95 ms; 6,940 KB
testcase_26	AC	95 ms; 6,944 KB
testcase_27	AC	105 ms; 7,168 KB
testcase_28	AC	168 ms; 9,088 KB
testcase_29	AC	116 ms; 7,424 KB
testcase_30	AC	161 ms; 8,832 KB
testcase_31	AC	106 ms; 7,168 KB
testcase_32	AC	114 ms; 7,424 KB
testcase_33	AC	38 ms; 6,944 KB
testcase_34	AC	89 ms; 6,944 KB
testcase_35	AC	113 ms; 9,472 KB
testcase_36	AC	133 ms; 9,472 KB

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/cpp_programming/Library/other/range.cpp"

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

class range {
  struct iter {
    std::size_t itr;
    constexpr iter(std::size_t pos) noexcept: itr(pos) { }
    constexpr void operator ++ () noexcept { ++itr; }
    constexpr bool operator != (iter other) const noexcept { return itr != other.itr; }
    constexpr std::size_t operator * () const noexcept { return itr; }
  };

  struct reviter {
    std::size_t itr;
    constexpr reviter(std::size_t pos) noexcept: itr(pos) { }
    constexpr void operator ++ () noexcept { --itr; }
    constexpr bool operator != (reviter other) const noexcept { return itr != other.itr; }
    constexpr std::size_t operator * () const noexcept { return itr; }
  };

  const iter first, last;

public:
  constexpr range(std::size_t first, std::size_t last) noexcept: first(first), last(std::max(first, last)) { }
  constexpr iter begin() const noexcept { return first; }
  constexpr iter end() const noexcept { return last; }
  constexpr reviter rbegin() const noexcept { return reviter(*last - 1); } 
  constexpr reviter rend() const noexcept { return reviter(*first - 1); } 
};

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

#line 2 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/mod_inv.cpp"

#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/mod_inv.cpp"
#include <cstdint>

constexpr std::pair<int64_t, int64_t> mod_inv(int64_t a, int64_t b) {
  if ((a %= b) == 0) return { b, 0 };
  int64_t s = b, t = (a < 0 ? a + b : a);
  int64_t m0 = 0, m1 = 1, tmp = 0;
  while (t > 0) {
    const auto u = s / t;
    s -= t * u; m0 -= m1 * u;
    tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp;
  }
  return { s, (m0 < 0 ? m0 + b / s : m0) };
}

/**
 * @title Extended GCD
 */
#line 4 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"

#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/algebraic/modular.cpp"
#include <type_traits>

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

  template <bool IsPrime, std::enable_if_t<IsPrime>* = nullptr>
  constexpr modular inverse_helper() const noexcept { return power(*this, mod() - 2); }
  template <bool IsPrime, std::enable_if_t<!IsPrime>* = nullptr>
  constexpr modular inverse_helper() const noexcept {
    const auto tmp = mod_inv(value, mod());
    assert(tmp.first == 1);
    return modular(tmp.second);
  }

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(const modular &val) noexcept { return val.inverse_helper<Modulus::is_prime>(); }
  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 Mod, bool IsPrime = true>
struct static_modulus { 
  static constexpr uint32_t mod() noexcept { return Mod; } 
  static constexpr bool is_prime = IsPrime;
};

template <uint32_t Id = 0, bool IsPrime = false>
struct dynamic_modulus {
  static uint32_t &mod() noexcept { static uint32_t val = 0; return val; }
  static constexpr bool is_prime = IsPrime;
};

template <uint32_t Mod, bool IsPrime = true>
using mint32_t = modular<static_modulus<Mod, IsPrime>>;
using rmint32_t = modular<dynamic_modulus<>>;

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

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

#include <cstddef>
#line 5 "/Users/kodamankod/Desktop/cpp_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/cpp_programming/Library/container/fenwick_tree.cpp"

#line 8 "/Users/kodamankod/Desktop/cpp_programming/Library/container/fenwick_tree.cpp"
#include <type_traits>

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) {
    assert(index < size());
    ++index;
    while (index <= size()) {
      M_tree[index] += x;
      index += bit_lsb(index);
    }
  }

  template <size_type Indexed = 1>
  value_type get(size_type index) const {
    assert(index < size());
    index += Indexed;
    value_type res{ };
    while (index > 0) {
      res += M_tree[index];
      index -= bit_lsb(index);
    }
    return res;
  }
  value_type fold(size_type first, size_type last) const {
    assert(first <= last);
    assert(last <= size());
    value_type res{};
    while (first < last) {
      res += M_tree[last];
      last -= bit_lsb(last);
    }
    while (last < first) {
      res -= M_tree[first];
      first -= bit_lsb(first);
    }
    return res;
  }

  template <class Func>
  size_type satisfies(const size_type left, Func &&func) const {
    assert(left <= size());
    if (func(value_type { })) return left;
    value_type val = -get<0>(left);
    size_type res = 0;
    for (size_type cur = bit_cover(size() + 1) >> 1; cur > 0; cur >>= 1) {
      if ((res + cur <= left) || (res + cur <= size() && !func(val + M_tree[res + cur]))) {
        val += M_tree[res + cur];
        res += cur;
      }
    }
    return res + 1;
  }

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

/**
 * @title Fenwick Tree
 */
#line 17 "main.cpp"

using i32 = std::int32_t;
using i64 = std::int64_t;
using u32 = std::uint32_t;
using u64 = std::uint64_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

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

using Fp = mint32_t<998244353>;

int main() {
  usize N;
  std::cin >> N;
  std::vector<u32> A(N);
  for (auto &x: A) {
    std::cin >> x;
  }
  auto cmp = A;
  std::sort(cmp.begin(), cmp.end());
  cmp.erase(std::unique(cmp.begin(), cmp.end()), cmp.end());
  std::vector<usize> idx(N);
  for (auto i: range(0, N)) {
    idx[i] = std::lower_bound(cmp.begin(), cmp.end(), A[i]) - cmp.begin();
  }
  fenwick_tree<Fp> lcnt(cmp.size()), rcnt(cmp.size());
  fenwick_tree<Fp> lsum(cmp.size()), rsum(cmp.size());
  for (auto i: range(0, N)) {
    rcnt.add(idx[i], Fp(1));
    rsum.add(idx[i], Fp(A[i]));
  }
  Fp ans;
  for (auto i: range(0, N)) {
    rcnt.add(idx[i], -Fp(1));
    rsum.add(idx[i], -Fp(A[i]));
    const auto L = lcnt.fold(idx[i] + 1, cmp.size());
    const auto R = rcnt.fold(0, idx[i]);
    ans += L * rsum.fold(0, idx[i]) + R * lsum.fold(idx[i] + 1, cmp.size()) + L * R * Fp(A[i]);
    lcnt.add(idx[i], Fp(1));
    lsum.add(idx[i], Fp(A[i]));
  }
  std::cout << ans << '\n';
  return 0;
}