結果

問題 No.1239 Multiplication -2
コンテスト
ユーザー KoD
提出日時 2020-09-25 22:24:21
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 59 ms / 2,000 ms
コード長 9,256 bytes
コンパイル時間 872 ms
コンパイル使用メモリ 86,568 KB
最終ジャッジ日時 2025-01-14 21:06:11
ジャッジサーバーID
（参考情報） 		judge5 / judge4
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ファイルパターン 結果
sample AC * 3
other AC * 34
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ソースコード

diff # 

#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/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/cpp_programming/Library/other/range.cpp"

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

#include <type_traits>
#include <iterator>
#line 6 "/Users/kodamankod/Desktop/cpp_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/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;
 
  template <class T>
  static constexpr value_type normalize(T value_) noexcept {
    if (value_ < 0) {
      value_ = -value_;
      value_ %= Modulus::mod();
      if (value_ == 0) return 0;
      return Modulus::mod() - value_;
    }
    return value_ % Modulus::mod();
  }

private:
  value_type value;

  template <bool IsPrime, std::enable_if_t<IsPrime>* = nullptr>
  constexpr modular inverse_helper() const noexcept { return power(*this, Modulus::mod() - 2); }
  template <bool IsPrime, std::enable_if_t<!IsPrime>* = nullptr>
  constexpr modular inverse_helper() const noexcept {
    const auto tmp = mod_inv(value, Modulus::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(Modulus::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) >= Modulus::mod()) value -= Modulus::mod(); 
    return *this; 
  }
 
  constexpr modular operator - (const modular &rhs) const noexcept { return modular(*this) -= rhs; }
  constexpr modular& operator -= (const modular &rhs) noexcept { 
    if ((value += Modulus::mod() - rhs.value) >= Modulus::mod()) value -= Modulus::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 % Modulus::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>
using mint32_t = modular<static_modulus<Mod>>;
using rmint32_t = modular<dynamic_modulus<>>;

/*
 * @title Modint
 */
#line 18 "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>;

int main() {
  i32 N;
  std::cin >> N;
  std::vector<i32> A(N);
  for (auto &x: A) {
    std::cin >> x;
  }
  std::vector<i32> two, zero;
  for (auto i: range(0, N)) {
    if (std::abs(A[i]) == 2) {
      two.push_back(i);
    }
    if (A[i] == 0) {
      zero.push_back(i);
    }
  }
  m32 ans;
  for (auto step: range(0, two.size())) {
    i32 l = (step == 0 ? 0 : two[step - 1] + 1);
    i32 m = two[step];
    i32 r = (step + 1 == two.size() ? N - 1 : two[step + 1] - 1);
    {
      auto itr = std::lower_bound(zero.begin(), zero.end(), m);
      if (itr != zero.begin()) {
        chmax(l, *(--itr) + 1);
      }
    }
    {
      auto itr = std::upper_bound(zero.begin(), zero.end(), m);
      if (itr != zero.end()) {
        chmin(r, *itr - 1);
      }
    }
    bool all = false;
    const auto lsize = m - l + 1;
    std::vector<m32> ldp(lsize);
    std::vector<bool> lflag(lsize);
    ldp[0] = power(m32(2), (l == 0 ? 0 : l - 1));
    {
      i32 idx = 0;
      for (auto i: range(l, m)) {
        all ^= (A[i] < 0);
        lflag[idx + 1] = lflag[idx] ^ (A[i] < 0);
        ldp[idx + 1] = ldp[idx] * m32(i == 0 ? 1 : 2);
        ++idx;
      }
    }
    const auto rsize = r - m + 1;
    std::vector<m32> rdp(rsize);
    std::vector<bool> rflag(rsize);
    rdp[0] = power(m32(2), (r + 1 == N ? 0 : N - r - 2));
    {
      i32 idx = 0;
      for (auto i: rev(range(m + 1, r + 1))) {
        all ^= (A[i] < 0);
        rflag[idx + 1] = rflag[idx] ^ (A[i] < 0);
        rdp[idx + 1] = rdp[idx] * m32(i + 1 == N ? 1 : 2);
        ++idx;
      }
    }
    std::array<m32, 2> sum{};
    for (auto i: range(0, rsize)) {
      sum[rflag[i]] += rdp[i];
    }
    for (auto i: range(0, lsize)) {
      ans += ldp[i] * sum[lflag[i] ^ (A[m] > 0) ^ all];
    }
  }
  std::cout << ans / power(m32(2), N - 1) << '\n';
  return 0;
}
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