#589087 (C++17) No.1307 Rotate and Accumulate

提出ソース
結果

問題	No.1307 Rotate and Accumulate
ユーザー	Haar
提出日時	2020-12-04 12:05:15
言語	C++17 (gcc 13.2.0 + boost 1.83.0)
結果	AC
実行時間	88 ms / 5,000 ms
コード長	16,380 bytes
コンパイル時間	3,375 ms
コンパイル使用メモリ	218,984 KB
実行使用メモリ	12,952 KB
最終ジャッジ日時	2023-10-13 00:19:57
合計ジャッジ時間	5,834 ms
ジャッジサーバーID （参考情報）	judge11 / judge12
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 4,352 KB
testcase_01	AC	1 ms 4,352 KB
testcase_02	AC	2 ms 4,352 KB
testcase_03	AC	2 ms 4,352 KB
testcase_04	AC	1 ms 4,352 KB
testcase_05	AC	2 ms 4,348 KB
testcase_06	AC	2 ms 4,356 KB
testcase_07	AC	1 ms 4,348 KB
testcase_08	AC	43 ms 8,648 KB
testcase_09	AC	45 ms 9,104 KB
testcase_10	AC	48 ms 8,136 KB
testcase_11	AC	40 ms 8,456 KB
testcase_12	AC	47 ms 8,164 KB
testcase_13	AC	12 ms 4,348 KB
testcase_14	AC	25 ms 5,828 KB
testcase_15	AC	87 ms 12,952 KB
testcase_16	AC	87 ms 12,896 KB
testcase_17	AC	88 ms 12,860 KB
testcase_18	AC	82 ms 12,872 KB
testcase_19	AC	88 ms 12,940 KB
testcase_20	AC	88 ms 12,928 KB
testcase_21	AC	2 ms 4,356 KB
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ソースコード

raw source code
#line 1 "main.cpp"
#include <bits/stdc++.h>

#ifdef DEBUG
#include <Mylib/Debug/debug.cpp>
#else
#define dump(...) ((void)0)
#endif

template <typename T, typename U>
bool chmin(T &a, const U &b){
  return (a > b ? a = b, true : false);
}

template <typename T, typename U>
bool chmax(T &a, const U &b){
  return (a < b ? a = b, true : false);
}

template <typename T, size_t N, typename U>
void fill_array(T (&a)[N], const U &v){
  std::fill((U*)a, (U*)(a + N), v);
}

template <typename T, size_t N, size_t I = N>
auto make_vector(const std::array<int, N> &a, T value = T()){
  static_assert(I >= 1);
  static_assert(N >= 1);
  if constexpr (I == 1){
    return std::vector<T>(a[N - I], value);
  }else{
    return std::vector(a[N - I], make_vector<T, N, I - 1>(a, value));
  }
}

template <typename T>
std::ostream& operator<<(std::ostream &s, const std::vector<T> &a){
  for(auto it = a.begin(); it != a.end(); ++it){
    if(it != a.begin()) s << " ";
    s << *it;
  }
  return s;
}

template <typename T>
std::istream& operator>>(std::istream &s, std::vector<T> &a){
  for(auto &x : a) s >> x;
  return s;
}

std::string YesNo(bool value){return value ? "Yes" : "No";}
std::string YESNO(bool value){return value ? "YES" : "NO";}
std::string yesno(bool value){return value ? "yes" : "no";}

template <typename T>
void putl(const T &value){
  std::cout << value << "\n";
}

template <typename Head, typename ... Tail>
void putl(const Head head, const Tail &... tail){
  std::cout << head << " ";
  putl(tail ...);
}

#line 4 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Mint/mint.cpp"

namespace haar_lib {
  template <int32_t M>
  class modint {
    uint32_t val_;

  public:
    constexpr static auto mod(){return M;}

    constexpr modint(): val_(0){}
    constexpr modint(int64_t n){
      if(n >= M) val_ = n % M;
      else if(n < 0) val_ = n % M + M;
      else val_ = n;
    }

    constexpr auto& operator=(const modint &a){val_ = a.val_; return *this;}
    constexpr auto& operator+=(const modint &a){
      if(val_ + a.val_ >= M) val_ = (uint64_t)val_ + a.val_ - M;
      else val_ += a.val_;
      return *this;
    }
    constexpr auto& operator-=(const modint &a){
      if(val_ < a.val_) val_ += M;
      val_ -= a.val_;
      return *this;
    }
    constexpr auto& operator*=(const modint &a){
      val_ = (uint64_t)val_ * a.val_ % M;
      return *this;
    }
    constexpr auto& operator/=(const modint &a){
      val_ = (uint64_t)val_ * a.inv().val_ % M;
      return *this;
    }

    constexpr auto operator+(const modint &a) const {return modint(*this) += a;}
    constexpr auto operator-(const modint &a) const {return modint(*this) -= a;}
    constexpr auto operator*(const modint &a) const {return modint(*this) *= a;}
    constexpr auto operator/(const modint &a) const {return modint(*this) /= a;}

    constexpr bool operator==(const modint &a) const {return val_ == a.val_;}
    constexpr bool operator!=(const modint &a) const {return val_ != a.val_;}

    constexpr auto& operator++(){*this += 1; return *this;}
    constexpr auto& operator--(){*this -= 1; return *this;}

    constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
    constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}

    constexpr static modint pow(int64_t n, int64_t p){
      if(p < 0) return pow(n, -p).inv();

      int64_t ret = 1, e = n % M;
      for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;
      return ret;
    }

    constexpr static modint inv(int64_t a){
      int64_t b = M, u = 1, v = 0;

      while(b){
        int64_t t = a / b;
        a -= t * b; std::swap(a, b);
        u -= t * v; std::swap(u, v);
      }

      u %= M;
      if(u < 0) u += M;

      return u;
    }

    constexpr static auto frac(int64_t a, int64_t b){return modint(a) / modint(b);}

    constexpr auto pow(int64_t p) const {return pow(val_, p);}
    constexpr auto inv() const {return inv(val_);}

    friend constexpr auto operator-(const modint &a){return modint(M - a.val_);}

    friend constexpr auto operator+(int64_t a, const modint &b){return modint(a) + b;}
    friend constexpr auto operator-(int64_t a, const modint &b){return modint(a) - b;}
    friend constexpr auto operator*(int64_t a, const modint &b){return modint(a) * b;}
    friend constexpr auto operator/(int64_t a, const modint &b){return modint(a) / b;}

    friend std::istream& operator>>(std::istream &s, modint &a){s >> a.val_; return s;}
    friend std::ostream& operator<<(std::ostream &s, const modint &a){s << a.val_; return s;}

    template <int N>
    static auto div(){
      static auto value = inv(N);
      return value;
    }

    explicit operator int32_t() const noexcept {return val_;}
    explicit operator int64_t() const noexcept {return val_;}
  };
}
#line 7 "/home/haar/Downloads/kyopro-lib/Mylib/Convolution/ntt_convolution.cpp"

namespace haar_lib {
  template <typename T, int PRIM_ROOT, int MAX_SIZE>
  class number_theoretic_transform {
  public:
    using value_type = T;
    constexpr static int primitive_root = PRIM_ROOT;
    constexpr static int max_size = MAX_SIZE;

  private:
    const int MAX_POWER_;
    std::vector<T> BASE_, INV_BASE_;

  public:
    number_theoretic_transform():
      MAX_POWER_(__builtin_ctz(MAX_SIZE)),
      BASE_(MAX_POWER_ + 1),
      INV_BASE_(MAX_POWER_ + 1)
    {
      static_assert((MAX_SIZE & (MAX_SIZE - 1)) == 0, "MAX_SIZE must be power of 2.");

      T t = T::pow(PRIM_ROOT, (T::mod() - 1) >> (MAX_POWER_ + 2));
      T s = t.inv();

      for(int i = MAX_POWER_; --i >= 0;){
        t *= t;
        s *= s;
        BASE_[i] = -t;
        INV_BASE_[i] = -s;
      }
    }

    void run(std::vector<T> &f, bool INVERSE = false) const {
      const int n = f.size();
      assert((n & (n - 1)) == 0 and n <= MAX_SIZE); // データ数は2の冪乗個

      if(INVERSE){
        for(int b = 1; b < n; b <<= 1){
          T w = 1;
          for(int j = 0, k = 1; j < n; j += 2 * b, ++k){
            for(int i = 0; i < b; ++i){
              const auto s = f[i + j];
              const auto t = f[i + j + b];

              f[i + j] = s + t;
              f[i + j + b] = (s - t) * w;
            }
            w *= INV_BASE_[__builtin_ctz(k)];
          }
        }

        const T t = T::inv(n);
        for(auto &x : f) x *= t;
      }else{
        for(int b = n >> 1; b; b >>= 1){
          T w = 1;
          for(int j = 0, k = 1; j < n; j += 2 * b, ++k){
            for(int i = 0; i < b; ++i){
              const auto s = f[i + j];
              const auto t = f[i + j + b] * w;

              f[i + j] = s + t;
              f[i + j + b] = s - t;
            }
            w *= BASE_[__builtin_ctz(k)];
          }
        }
      }
    }

    template <typename U>
    std::vector<T> convolve(std::vector<U> f, std::vector<U> g) const {
      const int m = f.size() + g.size() - 1;
      int n = 1;
      while(n < m) n *= 2;

      std::vector<T> f2(n), g2(n);

      for(int i = 0; i < (int)f.size(); ++i) f2[i] = (int64_t)f[i];
      for(int i = 0; i < (int)g.size(); ++i) g2[i] = (int64_t)g[i];

      run(f2);
      run(g2);

      for(int i = 0; i < n; ++i) f2[i] *= g2[i];
      run(f2, true);

      return f2;
    }

    template <typename U>
    std::vector<T> operator()(std::vector<U> f, std::vector<U> g) const {
      return convolve(f, g);
    }
  };

  template <typename T>
  std::vector<T> convolve_general_mod(std::vector<T> f, std::vector<T> g){
    static constexpr int M1 = 167772161, P1 = 3;
    static constexpr int M2 = 469762049, P2 = 3;
    static constexpr int M3 = 1224736769, P3 = 3;

    auto res1 = number_theoretic_transform<modint<M1>, P1, 1 << 20>().convolve(f, g);
    auto res2 = number_theoretic_transform<modint<M2>, P2, 1 << 20>().convolve(f, g);
    auto res3 = number_theoretic_transform<modint<M3>, P3, 1 << 20>().convolve(f, g);

    const int n = res1.size();

    std::vector<T> ret(n);

    const int64_t M12 = (int64_t)modint<M2>::inv(M1);
    const int64_t M13 = (int64_t)modint<M3>::inv(M1);
    const int64_t M23 = (int64_t)modint<M3>::inv(M2);

    for(int i = 0; i < n; ++i){
      const int64_t r[3] = {(int64_t)res1[i], (int64_t)res2[i], (int64_t)res3[i]};

      const int64_t t0 = r[0] % M1;
      const int64_t t1 = (r[1] - t0 + M2) * M12 % M2;
      const int64_t t2 = ((r[2] - t0 + M3) * M13 % M3 - t1 + M3) * M23 % M3;

      ret[i] = T(t0) + T(t1) * M1 + T(t2) * M1 * M2;
    }

    return ret;
  }
}
#line 4 "/home/haar/Downloads/kyopro-lib/Mylib/Math/formal_power_series.cpp"
#include <initializer_list>
#line 6 "/home/haar/Downloads/kyopro-lib/Mylib/Math/formal_power_series.cpp"

namespace haar_lib {
  template <typename T, const auto &convolve>
  class formal_power_series {
  public:
    using value_type = T;

  private:
    std::vector<T> data_;

  public:
    formal_power_series(){}
    explicit formal_power_series(int N): data_(N){}
    formal_power_series(const std::vector<T> &data_): data_(data_){}
    formal_power_series(std::initializer_list<T> init): data_(init.begin(), init.end()){}
    formal_power_series(const formal_power_series &a): data_(a.data_){}
    formal_power_series(formal_power_series &&a) noexcept {*this = std::move(a);}

    size_t size() const {
      return data_.size();
    }

    const T& operator[](int i) const {
      return data_[i];
    }

    T& operator[](int i){
      return data_[i];
    }

    auto begin() {return data_.begin();}
    auto end() {return data_.end();}

    const auto& data() const {return data_;}

    void resize(int n){
      data_.resize(n);
    }

    auto& operator=(formal_power_series &&rhs) noexcept {
      if(this != &rhs){
        data_ = std::move(rhs.data_);
      }
      return *this;
    }

    auto& operator+=(const formal_power_series &rhs){
      if(data_.size() < rhs.size()) data_.resize(rhs.size());
      for(int i = 0; i < rhs.size(); ++i) data_[i] += rhs[i];
      return *this;
    }

    auto& operator+=(T rhs){
      data_[0] += rhs;
      return *this;
    }

    auto operator+(T rhs) const {
      auto ret = *this;
      return ret += rhs;
    }

    auto operator+(const formal_power_series &rhs) const {
      auto ret = *this;
      return ret += rhs;
    }

    auto& operator-=(const formal_power_series &rhs){
      if(data_.size() < rhs.size()) data_.resize(rhs.size());
      for(int i = 0; i < rhs.size(); ++i) data_[i] -= rhs[i];
      return *this;
    }

    auto& operator-=(T rhs){
      data_[0] -= rhs;
      return *this;
    }

    auto operator-(T rhs) const {
      auto ret = *this;
      return ret -= rhs;
    }

    auto operator-(const formal_power_series &rhs) const {
      auto ret = *this;
      return ret -= rhs;
    }

    auto operator-() const {
      auto ret = *this;
      for(auto &x : ret) x = -x;
      return ret;
    }

    auto& operator*=(const formal_power_series &rhs){
      data_ = convolve(data_, rhs.data_);
      return *this;
    }

    auto operator*(const formal_power_series &rhs) const {
      auto ret = convolve(data_, rhs.data_);
      return formal_power_series(ret);
    }

    auto& operator*=(T rhs){
      for(auto &x : data_) x *= rhs;
      return *this;
    }

    auto operator*(T rhs) const {
      auto ret = *this;
      return ret *= rhs;
    }

    auto differentiate() const {
      const int n = data_.size();
      std::vector<T> ret(n - 1);
      for(int i = 0; i < n - 1; ++i){
        ret[i] = data_[i + 1] * (i + 1);
      }

      return formal_power_series(ret);
    }

    auto integrate() const {
      const int n = data_.size();
      std::vector<T> ret(n + 1);
      for(int i = 0; i < n; ++i){
        ret[i + 1] = data_[i] / (i + 1);
      }

      return formal_power_series(ret);
    }

    auto inv() const {
      assert(data_[0] != 0);
      const int n = data_.size();

      int t = 1;
      std::vector<T> ret = {data_[0].inv()};
      ret.reserve(n * 2);

      while(t <= n * 2){
        std::vector<T> c(data_.begin(), data_.begin() + std::min(t, n));
        c = convolve(c, convolve(ret, ret));

        c.resize(t);
        ret.resize(t);

        for(int i = 0; i < t; ++i){
          ret[i] = ret[i] * 2 - c[i];
        }

        t <<= 1;
      }

      ret.resize(n);

      return formal_power_series(ret);
    }

    auto log() const {
      assert(data_[0] == 1);
      const int n = data_.size();
      auto ret = (differentiate() * inv()).integrate();
      ret.resize(n);
      return ret;
    }

    auto exp() const {
      const int n = data_.size();

      int t = 1;
      formal_power_series b({1});

      while(t <= n * 2){
        t <<= 1;
        auto temp = b.log();
        temp.resize(t);

        for(int i = 0; i < t; ++i) temp[i] = -temp[i];
        temp[0] += 1;
        for(int i = 0; i < std::min(t, n); ++i) temp[i] += data_[i];

        b = b * temp;
        b.resize(t);
      }

      b.resize(n);

      return b;
    }

    auto shift(int64_t k) const {
      const int64_t n = data_.size();
      formal_power_series ret(n);

      if(k >= 0){
        for(int64_t i = k; i < n; ++i){
          ret[i] = data_[i - k];
        }
      }else{
        for(int64_t i = 0; i < n + k; ++i){
          ret[i] = data_[i - k];
        }
      }

      return ret;
    }

    auto pow(int64_t M) const {
      assert(M >= 0);

      const int n = data_.size();
      int k = 0;
      for(; k < n; ++k){
        if(data_[k] != 0){
          break;
        }
      }

      if(k >= n) return *this;

      T a = data_[k];

      formal_power_series ret = *this;
      ret = (ret.shift(-k)) * a.inv();
      ret = (ret.log() * (T)M).exp();
      ret = (ret * a.pow(M)).shift(M * k);

      return ret;
    }

    std::optional<formal_power_series> sqrt() const;
  };
}
#line 3 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Mod/mod_pow.cpp"

namespace haar_lib {
  constexpr int64_t mod_pow(int64_t n, int64_t p, int64_t m){
    int64_t ret = 1;
    while(p > 0){
      if(p & 1) (ret *= n) %= m;
      (n *= n) %= m;
      p >>= 1;
    }
    return ret;
  }
}
#line 3 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Prime/primitive_root.cpp"

namespace haar_lib {
  constexpr int primitive_root(int p){
    int pf[30] = {};
    int k = 0;
    {
      int n = p - 1;
      for(int64_t i = 2; i * i <= p; ++i){
        if(n % i == 0){
          pf[k++] = i;
          while(n % i == 0) n /= i;
        }
      }
      if(n != 1)
        pf[k++] = n;
    }

    for(int g = 2; g <= p; ++g){
      bool ok = true;
      for(int i = 0; i < k; ++i){
        if(mod_pow(g, (p - 1) / pf[i], p) == 1){
          ok = false;
          break;
        }
      }

      if(not ok) continue;

      return g;
    }
    return -1;
  }
}
#line 5 "/home/haar/Downloads/kyopro-lib/Mylib/IO/join.cpp"

namespace haar_lib {
  template <typename Iter>
  std::string join(Iter first, Iter last, std::string delim = " "){
    std::stringstream s;

    for(auto it = first; it != last; ++it){
      if(it != first) s << delim;
      s << *it;
    }

    return s.str();
  }
}
#line 70 "main.cpp"


namespace haar_lib {}

namespace solver {
  using namespace haar_lib;

  constexpr int m1000000007 = 1000000007;
  constexpr int m998244353 = 998244353;

  void init(){
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(12);
    std::cerr << std::fixed << std::setprecision(12);
    std::cin.exceptions(std::ios_base::failbit);
  }

  using mint = modint<m998244353>;
  constexpr int prim_root = primitive_root(m998244353);
  const static auto ntt = number_theoretic_transform<mint, prim_root, 1 << 21>();
  using FPS = formal_power_series<mint, ntt>;

  void solve(){
    int N, Q; std::cin >> N >> Q;
    std::vector<int> a(N); std::cin >> a;
    std::vector<int> r(Q); std::cin >> r;

    std::vector<mint> s(N);
    for(int x : r){
      s[N - 1 - x] += 1;
    }

    std::vector<mint> t(a.begin(), a.end());

    t.insert(t.end(), a.begin(), a.end());

    auto res = FPS(s) * FPS(t);

    dump(res.data());

    std::cout << join(res.begin() + N - 1, res.begin() + (2 * N - 1)) << "\n";
  }
}

int main(){
  solver::init();
  while(true){
    try{
      solver::solve();
      std::cout << std::flush;
      std::cerr << std::flush;
    }catch(const std::istream::failure &e){
      break;
    }catch(...){
      break;
    }
  }
  return 0;
}
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結果

テストケース

ソースコード
