#491504 (C++17) No.1067 #いろいろな色 / Red and Blue and more various colors (Middle)

提出ソース

結果

問題	No.1067 #いろいろな色 / Red and Blue and more various colors (Middle)
ユーザー	Haar
提出日時	2020-06-04 08:04:09
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	10,188 bytes
コンパイル時間	2,848 ms
コンパイル使用メモリ	224,056 KB
実行使用メモリ	133,608 KB
最終ジャッジ日時	2023-08-18 14:55:36
合計ジャッジ時間	6,322 ms
ジャッジサーバーID （参考情報）	judge14 / judge15

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	1 ms 8,760 KB
testcase_01	AC	1 ms 4,384 KB
testcase_02	AC	2 ms 4,380 KB
testcase_03	AC	2 ms 4,376 KB
testcase_04	AC	2 ms 4,376 KB
testcase_05	AC	2 ms 4,380 KB
testcase_06	AC	1 ms 4,376 KB
testcase_07	AC	1 ms 4,376 KB
testcase_08	AC	2 ms 4,380 KB
testcase_09	AC	1 ms 4,376 KB
testcase_10	AC	1 ms 4,376 KB
testcase_11	TLE	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-

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ソースコード

raw source code

#include <bits/stdc++.h>

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

/**
 * @docs input_vector.md
 */
template <typename T>
std::vector<T> input_vector(int N){
  std::vector<T> ret(N);
  for(int i = 0; i < N; ++i) std::cin >> ret[i];
  return ret;
}

template <typename T>
std::vector<std::vector<T>> input_vector(int N, int M){
  std::vector<std::vector<T>> ret(N);
  for(int i = 0; i < N; ++i) ret[i] = input_vector<T>(M);
  return ret;
}

/**
 * @docs input_tuple_vector.md
 */
template <typename T, size_t ... I>
void input_tuple_vector_init(T &val, int N, std::index_sequence<I...>){
  (void)std::initializer_list<int>{
    (void(std::get<I>(val).resize(N)), 0)...
      };
}

template <typename T, size_t ... I>
void input_tuple_vector_helper(T &val, int i, std::index_sequence<I...>){
  (void)std::initializer_list<int>{
    (void(std::cin >> std::get<I>(val)[i]), 0)...
      };
}

template <typename ... Args>
auto input_tuple_vector(int N){
  std::tuple<std::vector<Args>...> ret;

  input_tuple_vector_init(ret, N, std::make_index_sequence<sizeof...(Args)>());
  for(int i = 0; i < N; ++i){
    input_tuple_vector_helper(ret, i, std::make_index_sequence<sizeof...(Args)>());
  }

  return ret;
}

/**
 * @docs input_tuples.md
 */
template <typename ... Args>
class InputTuples{
  template <typename T, size_t ... I>
  static void input_tuple_helper(T &val, std::index_sequence<I...>){
    (void)std::initializer_list<int>{(void(std::cin >> std::get<I>(val)), 0)...};
  }
  
  struct iter{
    using value_type = std::tuple<Args ...>;
    value_type value;
    bool get = false;
    int N;
    int c = 0;

    value_type operator*(){
      if(get) return value;
      else{
        input_tuple_helper(value, std::make_index_sequence<sizeof...(Args)>());
        return value;
      }
    }

    void operator++(){
      ++c;
      get = false;
    }

    bool operator!=(iter &) const {
      return c < N;
    }

    iter(int N): N(N){}
  };

  int N;

public:
  InputTuples(int N): N(N){}

  iter begin() const {return iter(N);}
  iter end() const {return iter(N);}
};

template <typename ... Args>
auto input_tuples(int N){
  return InputTuples<Args ...>(N);
}


/**
 * @title modint
 * @docs mint.md
 */
template <uint32_t M> class ModInt{
public:
  constexpr static uint32_t MOD = M;
  uint64_t val;
  
  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;
  }
  
  inline constexpr auto operator+(const ModInt &a) const {return ModInt(val + a.val);}
  inline constexpr auto operator-(const ModInt &a) const {return ModInt(val - a.val);}
  inline constexpr auto operator*(const ModInt &a) const {return ModInt(val * a.val);}
  inline constexpr auto operator/(const ModInt &a) const {return ModInt(val * a.inv().val);}
  
  inline constexpr auto& operator=(const ModInt &a){val = a.val; return *this;}
  inline constexpr auto& operator+=(const ModInt &a){if((val += a.val) >= M) val -= M; return *this;}
  inline constexpr auto& operator-=(const ModInt &a){if(val < a.val) val += M; val -= a.val; return *this;}
  inline constexpr auto& operator*=(const ModInt &a){(val *= a.val) %= M; return *this;}
  inline constexpr auto& operator/=(const ModInt &a){(val *= a.inv().val) %= M; return *this;}
  
  inline constexpr bool operator==(const ModInt &a) const {return val == a.val;}
  inline constexpr bool operator!=(const ModInt &a) const {return val != a.val;}
  
  inline constexpr auto& operator++(){*this += 1; return *this;}
  inline constexpr auto& operator--(){*this -= 1; return *this;}
  
  inline constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
  inline constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}
  
  inline constexpr static ModInt power(int64_t n, int64_t p){
    if(p < 0) return power(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;
  }
  
  inline 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;
  }
  
  inline constexpr static auto frac(int64_t a, int64_t b){return ModInt(a) / ModInt(b);}
  
  inline constexpr auto power(int64_t p) const {return power(val, p);}
  inline constexpr auto inv() const {return inv(val);}
  
  friend inline constexpr auto operator-(const ModInt &a){return ModInt(-a.val);}
  
  friend inline constexpr auto operator+(int64_t a, const ModInt &b){return ModInt(a) + b;}
  friend inline constexpr auto operator-(int64_t a, const ModInt &b){return ModInt(a) - b;}
  friend inline constexpr auto operator*(int64_t a, const ModInt &b){return ModInt(a) * b;}
  friend inline constexpr auto operator/(int64_t a, const ModInt &b){return ModInt(a) / b;}
  
  friend std::istream& operator>>(std::istream &s, ModInt<M> &a){s >> a.val; return s;}
  friend std::ostream& operator<<(std::ostream &s, const ModInt<M> &a){s << a.val; return s;}

  template <int N>
  inline 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;}
};


/**
 * @title NumberTheoreticTransform
 * @docs ntt_convolution.md
 */
template <typename T, int PRIM_ROOT, int MAX_SIZE>
class NumberTheoreticTransform{
  const int MAX_POWER;
  std::vector<T> BASE, INV_BASE;
  
public:
  NumberTheoreticTransform():
    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::power(PRIM_ROOT, (T::MOD-1) >> (MAX_POWER + 2));
    T s = t.inv();
    
    for(int i = MAX_POWER - 1; i >= 0; --i){
      t *= t;
      s *= s;
      BASE[i] = -t;
      INV_BASE[i] = -s;
    }
  }

  void run_ntt(std::vector<T> &f, bool INVERSE = false){
    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> run_convolution(std::vector<U> f, std::vector<U> g){
    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] = f[i];
    for(int i = 0; i < (int)g.size(); ++i) g2[i] = g[i];
    
    run_ntt(f2);
    run_ntt(g2);
    
    for(int i = 0; i < n; ++i) f2[i] *= g2[i];
    run_ntt(f2, true);
    
    return f2;
  }
};

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

  for(auto &x : f) x %= T::MOD;
  for(auto &x : g) x %= T::MOD;
  
  auto res1 = NumberTheoreticTransform<ModInt<M1>, P1, 1 << 20>().run_convolution(f, g);
  auto res2 = NumberTheoreticTransform<ModInt<M2>, P2, 1 << 20>().run_convolution(f, g);
  auto res3 = NumberTheoreticTransform<ModInt<M3>, P3, 1 << 20>().run_convolution(f, g);

  const int n = res1.size();

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

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

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

    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;
}


constexpr int mod = 998244353;
using mint = ModInt<mod>;

auto ntt = NumberTheoreticTransform<mint, 3, 1 << 20>();

std::vector<mint> mul(std::vector<mint> a, std::vector<mint> b){
  auto ret = ntt.run_convolution(a, b);
  return ret;
}


int main(){
  int N, Q; std::cin >> N >> Q;

  auto A = input_vector<int>(N);

  std::vector<int> ord(N);
  std::iota(ord.begin(), ord.end(), 0);
  std::sort(ord.begin(), ord.end(), [&](int i, int j){return A[i] < A[j];});

  std::vector<int> c(A);
  std::sort(c.begin(), c.end());

  std::vector<std::vector<mint>> right(N+1);
  std::vector<std::vector<mint>> left(N+1);

  right[0] = {1};
  
  for(int i = 0; i < N; ++i){
    right[i + 1] = {A[ord[i]]};
  }

  for(int i = 0; i < N; ++i){
    right[i + 1] = mul(right[i + 1], right[i]);
    if((int)right[i + 1].size() > N + 1) right[i + 1].resize(N + 1);
  }

  left[N] = {1};
  for(int i = 0; i < N; ++i){
    left[i] = {A[ord[i]] - 1, 1};
  }

  for(int i = N; i > 0; --i){
    left[i - 1] = mul(left[i - 1], left[i]);
    if((int)left[i - 1].size() > N + 1) left[i - 1].resize(N + 1);
  }

  std::vector<std::vector<mint>> f(N+1);

  for(int i = 0; i < N + 1; ++i){
    f[i] = mul(right[i], left[i]);
    f[i].resize(N + 1);
  }

  
  //  dump(f);
  

  for(auto [l, r, p] : input_tuples<int, int, int>(Q)){
    int ans = 0;

    for(int i = l; i <= r; ++i){
      int j = std::lower_bound(c.begin(), c.end(), i) - c.begin();
      //dump(f[j][p]);
      ans ^= f[j][p].val;
    }

    ans %= mod;
    
    std::cout << ans << "\n";
  }
  
  return 0;
}

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結果

テストケース

ソースコード