結果

問題 No.2833 Count Taiko Results
ユーザー 👑 emthrmemthrm
提出日時 2024-08-02 22:19:14
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 373 ms / 2,000 ms
コード長 15,803 bytes
コンパイル時間 3,233 ms
コンパイル使用メモリ 257,052 KB
実行使用メモリ 11,784 KB
最終ジャッジ日時 2024-08-02 22:19:27
合計ジャッジ時間 12,378 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
other AC * 58
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <unsigned int M>
struct MInt {
  unsigned int v;

  constexpr MInt() : v(0) {}
  constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
  static constexpr MInt raw(const int x) {
    MInt x_;
    x_.v = x;
    return x_;
  }

  static constexpr int get_mod() { return M; }
  static constexpr void set_mod(const int divisor) {
    assert(std::cmp_equal(divisor, M));
  }

  static void init(const int x) {
    inv<true>(x);
    fact(x);
    fact_inv(x);
  }

  template <bool MEMOIZES = false>
  static MInt inv(const int n) {
    // assert(0 <= n && n < M && std::gcd(n, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) return inverse[n];
    if constexpr (MEMOIZES) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[M % i] * raw(M / i);
      }
      return inverse[n];
    }
    int u = 1, v = 0;
    for (unsigned int a = n, b = M; b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }

  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    if (const int prev = factorial.size(); n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }

  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    if (const int prev = f_inv.size(); n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }

  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
  }

  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    inv<true>(k);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }

  constexpr MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  constexpr MInt& operator+=(const MInt& x) {
    if ((v += x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator-=(const MInt& x) {
    if ((v += M - x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator*=(const MInt& x) {
    v = (unsigned long long){v} * x.v % M;
    return *this;
  }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }

  constexpr auto operator<=>(const MInt& x) const = default;

  constexpr MInt& operator++() {
    if (++v == M) [[unlikely]] v = 0;
    return *this;
  }
  constexpr MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  constexpr MInt& operator--() {
    v = (v == 0 ? M - 1 : v - 1);
    return *this;
  }
  constexpr MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }

  constexpr MInt operator+() const { return *this; }
  constexpr MInt operator-() const { return raw(v ? M - v : 0); }

  constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt& x) const { return MInt(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
    return os << x.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }
};
using ModInt = MInt<MOD>;

template <typename T>
requires requires {
  typename T::Monoid;
  typename T::OperatorMonoid;
  {T::m_id()} -> std::same_as<typename T::Monoid>;
  {T::o_id()} -> std::same_as<typename T::OperatorMonoid>;
  {T::m_merge(std::declval<typename T::Monoid>(),
              std::declval<typename T::Monoid>())}
      -> std::same_as<typename T::Monoid>;
  {T::o_merge(std::declval<typename T::OperatorMonoid>(),
              std::declval<typename T::OperatorMonoid>())}
      -> std::same_as<typename T::OperatorMonoid>;
  {T::apply(std::declval<typename T::Monoid>(),
            std::declval<typename T::OperatorMonoid>())}
      -> std::same_as<typename T::Monoid>;
}
struct LazySegmentTree {
  using Monoid = typename T::Monoid;
  using OperatorMonoid = typename T::OperatorMonoid;

  explicit LazySegmentTree(const int n)
      : LazySegmentTree(std::vector<Monoid>(n, T::m_id())) {}

  explicit LazySegmentTree(const std::vector<Monoid>& a)
      : n(a.size()), height(std::countr_zero(std::bit_ceil(a.size()))),
        p2(1 << height) {
    lazy.assign(p2, T::o_id());
    data.assign(p2 << 1, T::m_id());
    std::copy(a.begin(), a.end(), data.begin() + p2);
    for (int i = p2 - 1; i > 0; --i) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
  }

  void set(int idx, const Monoid val) {
    idx += p2;
    for (int i = height; i > 0; --i) {
      propagate(idx >> i);
    }
    data[idx] = val;
    for (int i = 1; i <= height; ++i) {
      const int current_idx = idx >> i;
      data[current_idx] =
          T::m_merge(data[current_idx << 1], data[(current_idx << 1) + 1]);
    }
  }

  void apply(int idx, const OperatorMonoid val) {
    idx += p2;
    for (int i = height; i > 0; --i) {
      propagate(idx >> i);
    }
    data[idx] = T::apply(data[idx], val);
    for (int i = 1; i <= height; ++i) {
      const int current_idx = idx >> i;
      data[current_idx] =
          T::m_merge(data[current_idx << 1], data[(current_idx << 1) + 1]);
    }
  }

  void apply(int left, int right, const OperatorMonoid val) {
    if (right <= left) [[unlikely]] return;
    left += p2;
    right += p2;
    const int ctz_left = std::countr_zero(static_cast<unsigned int>(left));
    for (int i = height; i > ctz_left; --i) {
      propagate(left >> i);
    }
    const int ctz_right = std::countr_zero(static_cast<unsigned int>(right));
    for (int i = height; i > ctz_right; --i) {
      propagate(right >> i);
    }
    for (int l = left, r = right; l < r; l >>= 1, r >>= 1) {
      if (l & 1) apply_sub(l++, val);
      if (r & 1) apply_sub(--r, val);
    }
    for (int i = left >> (ctz_left + 1); i > 0; i >>= 1) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
    for (int i = right >> (ctz_right + 1); i > 0; i >>= 1) {
      data[i] = T::m_merge(data[i << 1], data[(i << 1) + 1]);
    }
  }

  Monoid get(int left, int right) {
    if (right <= left) [[unlikely]] return T::m_id();
    left += p2;
    right += p2;
    const int ctz_left = std::countr_zero(static_cast<unsigned int>(left));
    for (int i = height; i > ctz_left; --i) {
      propagate(left >> i);
    }
    const int ctz_right = std::countr_zero(static_cast<unsigned int>(right));
    for (int i = height; i > ctz_right; --i) {
      propagate(right >> i);
    }
    Monoid res_l = T::m_id(), res_r = T::m_id();
    for (; left < right; left >>= 1, right >>= 1) {
      if (left & 1) res_l = T::m_merge(res_l, data[left++]);
      if (right & 1) res_r = T::m_merge(data[--right], res_r);
    }
    return T::m_merge(res_l, res_r);
  }

  Monoid operator[](const int idx) {
    const int node = idx + p2;
    for (int i = height; i > 0; --i) {
      propagate(node >> i);
    }
    return data[node];
  }

  template <typename G>
  int find_right(int left, const G g) {
    if (left >= n) [[unlikely]] return n;
    left += p2;
    for (int i = height; i > 0; --i) {
      propagate(left >> i);
    }
    Monoid val = T::m_id();
    do {
      while (!(left & 1)) left >>= 1;
      Monoid nxt = T::m_merge(val, data[left]);
      if (!g(nxt)) {
        while (left < p2) {
          propagate(left);
          left <<= 1;
          nxt = T::m_merge(val, data[left]);
          if (g(nxt)) {
            val = nxt;
            ++left;
          }
        }
        return left - p2;
      }
      val = nxt;
      ++left;
    } while (!std::has_single_bit(static_cast<unsigned int>(left)));
    return n;
  }

  template <typename G>
  int find_left(int right, const G g) {
    if (right <= 0) [[unlikely]] return -1;
    right += p2;
    for (int i = height; i > 0; --i) {
      propagate((right - 1) >> i);
    }
    Monoid val = T::m_id();
    do {
      --right;
      while (right > 1 && (right & 1)) right >>= 1;
      Monoid nxt = T::m_merge(data[right], val);
      if (!g(nxt)) {
        while (right < p2) {
          propagate(right);
          right = (right << 1) + 1;
          nxt = T::m_merge(data[right], val);
          if (g(nxt)) {
            val = nxt;
            --right;
          }
        }
        return right - p2;
      }
      val = nxt;
    } while (!std::has_single_bit(static_cast<unsigned int>(right)));
    return -1;
  }

 private:
  const int n, height, p2;
  std::vector<Monoid> data;
  std::vector<OperatorMonoid> lazy;

  void apply_sub(const int idx, const OperatorMonoid& val) {
    data[idx] = T::apply(data[idx], val);
    if (idx < p2) lazy[idx] = T::o_merge(lazy[idx], val);
  }

  void propagate(const int idx) {
    // assert(1 <= idx && idx < p2);
    apply_sub(idx << 1, lazy[idx]);
    apply_sub((idx << 1) + 1, lazy[idx]);
    lazy[idx] = T::o_id();
  }
};

namespace monoid {

template <typename T>
struct RangeMinimumAndUpdateQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return std::numeric_limits<Monoid>::max(); }
  static constexpr OperatorMonoid o_id() {
    return std::numeric_limits<OperatorMonoid>::max();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return b == o_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return b == o_id() ? a : b;
  }
};

template <typename T>
struct RangeMaximumAndUpdateQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() {
    return std::numeric_limits<Monoid>::lowest();
  }
  static constexpr OperatorMonoid o_id() {
    return std::numeric_limits<OperatorMonoid>::lowest();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return b == o_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return b == o_id()? a : b;
  }
};

template <typename T, T Inf>
struct RangeMinimumAndAddQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return Inf; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return a + b;
  }
};

template <typename T, T Inf>
struct RangeMaximumAndAddQuery {
  using Monoid = T;
  using OperatorMonoid = T;
  static constexpr Monoid m_id() { return -Inf; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return a + b;
  }
};

template <typename T>
struct RangeSumAndUpdateQuery {
  using Monoid = struct { T sum; int len; };
  using OperatorMonoid = T;
  static std::vector<Monoid> init(const int n) {
    return std::vector<Monoid>(n, Monoid{0, 1});
  }
  static constexpr Monoid m_id() { return {0, 0}; }
  static constexpr OperatorMonoid o_id() {
    return std::numeric_limits<OperatorMonoid>::max();
  }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return Monoid{a.sum + b.sum, a.len + b.len};
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return b == o_id() ? a : b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return Monoid{b == o_id() ? a.sum : b * a.len, a.len};
  }
};

template <typename T>
struct RangeSumAndAddQuery {
  using Monoid = struct { T sum; int len; };
  using OperatorMonoid = T;
  static std::vector<Monoid> init(const int n) {
    return std::vector<Monoid>(n, Monoid{0, 1});
  }
  static constexpr Monoid m_id() { return {0, 0}; }
  static constexpr OperatorMonoid o_id() { return 0; }
  static Monoid m_merge(const Monoid& a, const Monoid& b) {
    return Monoid{a.sum + b.sum, a.len + b.len};
  }
  static OperatorMonoid o_merge(const OperatorMonoid& a,
                                const OperatorMonoid& b) {
    return a + b;
  }
  static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
    return Monoid{a.sum + b * a.len, a.len};
  }
};

}  // namespace monoid

int main() {
  struct S {
    using Monoid = ModInt;
    using OperatorMonoid = ModInt;
    static constexpr Monoid m_id() { return 0; }
    static constexpr OperatorMonoid o_id() { return 1; }
    static Monoid m_merge(const Monoid& a, const Monoid& b) { return a + b; }
    static OperatorMonoid o_merge(const OperatorMonoid& a,
                                  const OperatorMonoid& b) {
      return a * b;
    }
    static Monoid apply(const Monoid& a, const OperatorMonoid& b) {
      return a * b;
    }
  };

  int n, k; cin >> n >> k;
  vector<int> a(n + 1), b(n + 1);
  FOR(i, 1, n + 1) cin >> a[i];
  FOR(i, 1, n + 1) cin >> b[i];
  LazySegmentTree<S> dp0(n + 1), dp1(n + 1);
  dp0.set(0, 1);
  FOR(i, 1, n + 1) {  // i番目に失敗
    ModInt dp_i0 = 0, dp_i1 = 0;
    dp_i0 += dp0.get(max(i - k, 0), i) * b[i];  // Kコンボ達成できない
    if (i > k) dp_i1 += dp0[i - k - 1] * b[i];  // Kコンボ達成できる
    dp_i1 += dp1.get(max(i - k - 1, 0), i) * b[i];
    dp0.apply(0, i, a[i]);
    dp1.apply(0, i, a[i]);
    dp0.set(i, dp_i0);
    dp1.set(i, dp_i1);
    // REP(j, n + 1) cout << dp0[j] << " \n"[j == n];
    // REP(j, n + 1) cout << dp1[j] << " \n"[j == n];
    // cout << '\n';
  }
  cout << dp1.get(n - k, n + 1) + dp0[n - k] << '\n';
  return 0;
}
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