test/yosupo-judge/subset_convolution/main.test.cpp

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• Last update: 2021-04-23 23:44:44+09:00
• Problem: https://judge.yosupo.jp/problem/subset_convolution
• Link: View error logs on GitHub Actions

Depends on

• Fast Möbius transform (Subsets) (Mylib/Convolution/fast_mobius_transform_subset.cpp)
• Fast Zeta transform (Subsets) (Mylib/Convolution/fast_zeta_transform_subset.cpp)
• Subset convolution (Mylib/Convolution/subset_convolution.cpp)
• Input vector (Mylib/IO/input_vector.cpp)
• join function (Mylib/IO/join.cpp)
• Modint (Mylib/Number/Mint/mint.cpp)

Code

#define PROBLEM "https://judge.yosupo.jp/problem/subset_convolution"

#include <iostream>
#include "Mylib/Convolution/subset_convolution.cpp"
#include "Mylib/IO/input_vector.cpp"
#include "Mylib/IO/join.cpp"
#include "Mylib/Number/Mint/mint.cpp"

namespace hl = haar_lib;

using mint = hl::modint<998244353>;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int N;
  std::cin >> N;
  auto a = hl::input_vector<mint>(1 << N);
  auto b = hl::input_vector<mint>(1 << N);

  auto ans = hl::subset_convolution(a, b);

  std::cout << hl::join(ans.begin(), ans.end()) << "\n";

  return 0;
}

#line 1 "test/yosupo-judge/subset_convolution/main.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/subset_convolution"

#include <iostream>
#line 2 "Mylib/Convolution/subset_convolution.cpp"
#include <cassert>
#include <vector>
#line 3 "Mylib/Convolution/fast_mobius_transform_subset.cpp"
#include <functional>
#line 5 "Mylib/Convolution/fast_mobius_transform_subset.cpp"

namespace haar_lib {
  template <typename T, typename Func = std::minus<T>>
  std::vector<T> fast_mobius_transform_subset(std::vector<T> f, const Func &op = std::minus<T>()) {
    const int N = f.size();
    assert((N & (N - 1)) == 0 && "N must be a power of 2");
    for (int i = 1; i < N; i <<= 1) {
      for (int j = 0; j < N; ++j) {
        if (j & i) f[j] = op(f[j], f[j ^ i]);
      }
    }
    return f;
  }
}  // namespace haar_lib
#line 5 "Mylib/Convolution/fast_zeta_transform_subset.cpp"

namespace haar_lib {
  template <typename T, typename Func = std::plus<T>>
  std::vector<T> fast_zeta_transform_subset(std::vector<T> f, const Func &op = std::plus<T>()) {
    const int N = f.size();
    assert((N & (N - 1)) == 0 && "N must be a power of 2");
    for (int i = 1; i < N; i <<= 1) {
      for (int j = 0; j < N; ++j) {
        if (j & i) f[j] = op(f[j], f[j ^ i]);
      }
    }
    return f;
  }
}  // namespace haar_lib
#line 6 "Mylib/Convolution/subset_convolution.cpp"

namespace haar_lib {
  template <typename T>
  std::vector<T> subset_convolution(std::vector<T> f, std::vector<T> g) {
    const int N = f.size();
    assert((N & (N - 1)) == 0 && "N must be a power of 2");
    assert(f.size() == g.size());

    const int K = __builtin_ctz(N);

    std::vector<std::vector<T>> F(K + 1), G(K + 1);

    for (int i = 0; i <= K; ++i) {
      F[i].resize(N);
      G[i].resize(N);

      for (int j = 0; j < N; ++j) {
        if (__builtin_popcount(j) == i) {
          F[i][j] = f[j];
          G[i][j] = g[j];
        }
      }

      F[i] = fast_zeta_transform_subset(F[i]);
      G[i] = fast_zeta_transform_subset(G[i]);
    }

    std::vector<std::vector<T>> H(K + 1, std::vector<T>(N));
    for (int i = 0; i <= K; ++i) {
      for (int j = 0; j < N; ++j) {
        for (int s = 0; s <= i; ++s) {
          H[i][j] += F[s][j] * G[i - s][j];
        }
      }
    }

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

    for (int i = 0; i <= K; ++i) {
      auto h = fast_mobius_transform_subset(H[i]);
      for (int j = 0; j < N; ++j) {
        if (__builtin_popcount(j) == i) ret[j] += h[j];
      }
    }

    return ret;
  }
}  // namespace haar_lib
#line 4 "Mylib/IO/input_vector.cpp"

namespace haar_lib {
  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;
  }
}  // namespace haar_lib
#line 3 "Mylib/IO/join.cpp"
#include <sstream>
#include <string>

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();
  }
}  // namespace haar_lib
#line 3 "Mylib/Number/Mint/mint.cpp"
#include <utility>

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_; }
  };
}  // namespace haar_lib
#line 8 "test/yosupo-judge/subset_convolution/main.test.cpp"

namespace hl = haar_lib;

using mint = hl::modint<998244353>;

int main() {
  std::cin.tie(0);
  std::ios::sync_with_stdio(false);

  int N;
  std::cin >> N;
  auto a = hl::input_vector<mint>(1 << N);
  auto b = hl::input_vector<mint>(1 << N);

  auto ans = hl::subset_convolution(a, b);

  std::cout << hl::join(ans.begin(), ans.end()) << "\n";

  return 0;
}

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