test/verify/yosupo-bitwise-and-convolution-3.test.cpp

• View this file on GitHub
• Last update: 2026-08-10 14:37:08+00:00
• Problem: https://judge.yosupo.jp/problem/bitwise_and_convolution

Depends on

• Superset Zeta/Moebius Transform SIMD (上位集合のゼータ/メビウス変換, (math/fft/superset-zeta-moebius-transform-simd.hpp)
• Printer(高速出力) (other/printer.hpp)
• Scanner(高速入力) (other/scanner.hpp)

Code

// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/bitwise_and_convolution
// clang-format on

#include <cstdio>
#include <vector>

#include "../../math/fft/superset-zeta-moebius-transform-simd.hpp"
#include "../../other/printer.hpp"
#include "../../other/scanner.hpp"

using namespace std;

const int MOD = 998244353;

int main() {
  Scanner in(stdin);
  Printer out(stdout);
  int N;
  in.read(N);
  int a[1 << N], b[1 << N];
  for (int i = 0; i < (1 << N); i++) in.read(a[i]);
  for (int i = 0; i < (1 << N); i++) in.read(b[i]);
  bitwise_and_convolution_simd<MOD>(a, b, 1 << N);
  for (int i = 0; i < (1 << N); i++) {
    if (i) out.write(' ');
    out.write(a[i]);
  }
  out.writeln();
}

#line 1 "test/verify/yosupo-bitwise-and-convolution-3.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/bitwise_and_convolution
// clang-format on

#include <cstdio>
#include <vector>

#line 2 "math/fft/superset-zeta-moebius-transform-simd.hpp"

#include <immintrin.h>

#include <cassert>

/**
 * @brief Superset Zeta/Moebius Transform SIMD (上位集合のゼータ/メビウス変換,
 * SIMD)
 */
__attribute__((target("avx2"))) void superset_zeta_transform_simd(int* buf,
                                                                  int mod,
                                                                  int n) {
  assert((n & (n - 1)) == 0);
  auto m_zero = _mm256_set1_epi32(0);
  auto m_mod_one = _mm256_set1_epi32(mod - 1);
  auto m_mod = _mm256_set1_epi32(mod);
  auto m_zero2 = _mm_set1_epi32(0);
  auto m_mod_one2 = _mm_set1_epi32(mod - 1);
  auto m_mod2 = _mm_set1_epi32(mod);
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j += i << 1) {
      if (i <= 2) {
        for (int k = 0; k < i; k++) {
          buf[j + k] += buf[j + k + i];
          if (buf[j + k] >= mod) buf[j + k] -= mod;
        }
      } else if (i == 4) {
        for (int k = 0; k < i; k += 4) {
          auto a = _mm_loadu_si128((__m128i*)(buf + j + k));
          auto b = _mm_loadu_si128((__m128i*)(buf + j + k + i));
          a = _mm_add_epi32(a, b);
          a = _mm_sub_epi32(
              a, _mm_and_si128(_mm_cmpgt_epi32(a, m_mod_one2), m_mod2));
          _mm_storeu_si128((__m128i*)(buf + j + k), a);
        }
      } else {
        for (int k = 0; k < i; k += 8) {
          auto a = _mm256_loadu_si256((__m256i*)(buf + j + k));
          auto b = _mm256_loadu_si256((__m256i*)(buf + j + k + i));
          a = _mm256_add_epi32(a, b);
          a = _mm256_sub_epi32(
              a, _mm256_and_si256(_mm256_cmpgt_epi32(a, m_mod_one), m_mod));
          _mm256_storeu_si256((__m256i*)(buf + j + k), a);
        }
      }
    }
  }
}

__attribute__((target("avx2"))) void superset_moebius_transform_simd(int* buf,
                                                                     int mod,
                                                                     int n) {
  assert((n & (n - 1)) == 0);
  auto m_zero = _mm256_set1_epi32(0);
  auto m_mod = _mm256_set1_epi32(mod);
  auto m_zero2 = _mm_set1_epi32(0);
  auto m_mod2 = _mm_set1_epi32(mod);
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j += i << 1) {
      if (i <= 2) {
        for (int k = 0; k < i; k++) {
          buf[j + k] += mod - buf[j + k + i];
          if (buf[j + k] >= mod) buf[j + k] -= mod;
        }
      } else if (i == 4) {
        for (int k = 0; k < i; k += 4) {
          auto a = _mm_loadu_si128((__m128i*)(buf + j + k));
          auto b = _mm_loadu_si128((__m128i*)(buf + j + k + i));
          a = _mm_sub_epi32(a, b);
          a = _mm_add_epi32(a,
                            _mm_and_si128(_mm_cmpgt_epi32(m_zero2, a), m_mod2));
          _mm_storeu_si128((__m128i*)(buf + j + k), a);
        }
      } else {
        for (int k = 0; k < i; k += 8) {
          auto a = _mm256_loadu_si256((__m256i*)(buf + j + k));
          auto b = _mm256_loadu_si256((__m256i*)(buf + j + k + i));
          a = _mm256_sub_epi32(a, b);
          a = _mm256_add_epi32(
              a, _mm256_and_si256(_mm256_cmpgt_epi32(m_zero, a), m_mod));
          _mm256_storeu_si256((__m256i*)(buf + j + k), a);
        }
      }
    }
  }
}

template <int mod>
int* bitwise_and_convolution_simd(int* f, int* g, int n) {
  assert((n & (n - 1)) == 0);
  superset_zeta_transform_simd(f, mod, n);
  superset_zeta_transform_simd(g, mod, n);
  for (int i = 0; i < n; i++) f[i] = (1uLL * f[i] * g[i]) % mod;
  superset_moebius_transform_simd(f, mod, n);
  return f;
}
#line 2 "other/printer.hpp"

#include <charconv>
#include <cstddef>
#line 6 "other/printer.hpp"
#include <string>
#include <type_traits>
#line 9 "other/printer.hpp"

/**
 * @brief Printer(高速出力)
 */
struct Printer {
 public:
  explicit Printer(FILE* fp) : fp(fp) {}

  ~Printer() { flush(); }

  template <bool f = false, typename T, typename... E>
  void write(const T& t, const E&... e) {
    if (f) write_single(' ');
    write_single(t);
    write<true>(e...);
  }

  template <typename... T>
  void writeln(const T&... t) {
    write(t...);
    write_single('\n');
  }

  void flush() {
    fwrite(line, 1, st - line, fp);
    st = line;
  }

 private:
  FILE* fp = nullptr;
  static constexpr std::size_t line_size = 1 << 16;
  static constexpr std::size_t int_digits = 20;
  char line[line_size + 1] = {};
  char* st = line;

  template <bool f = false>
  void write() {}

  void write_single(const char& t) {
    if (st + 1 >= line + line_size) flush();
    *st++ = t;
  }

  template <typename T, std::enable_if_t<std::is_integral<T>::value, int> = 0>
  void write_single(T s) {
    if (st + int_digits >= line + line_size) flush();
    st += std::to_chars(st, st + int_digits, s).ptr - st;
  }

  void write_single(const std::string& s) {
    for (auto& c : s) write_single(c);
  }

  void write_single(const char* s) {
    while (*s != 0) write_single(*s++);
  }

  template <typename T>
  void write_single(const std::vector<T>& s) {
    for (std::size_t i = 0; i < s.size(); i++) {
      if (i) write_single(' ');
      write_single(s[i]);
    }
  }
};
#line 2 "other/scanner.hpp"

#line 5 "other/scanner.hpp"
#include <cstring>
#line 9 "other/scanner.hpp"

/**
 * @brief Scanner(高速入力)
 */
struct Scanner {
 public:
  explicit Scanner(std::FILE* fp) : fp(fp) {}

  template <typename T, typename... E>
  void read(T& t, E&... e) {
    read_single(t);
    read(e...);
  }

 private:
  static constexpr std::size_t line_size = 1 << 16;
  static constexpr std::size_t int_digits = 20;
  char line[line_size + 1] = {};
  std::FILE* fp = nullptr;
  char* st = line;
  char* ed = line;

  void read() {}

  static inline bool is_space(char c) { return c <= ' '; }

  void reread() {
    std::ptrdiff_t len = ed - st;
    std::memmove(line, st, len);
    char* tmp = line + len;
    ed = tmp + std::fread(tmp, 1, line_size - len, fp);
    *ed = 0;
    st = line;
  }

  void skip_space() {
    while (true) {
      if (st == ed) reread();
      while (*st && is_space(*st)) ++st;
      if (st != ed) return;
    }
  }

  template <typename T, std::enable_if_t<std::is_integral<T>::value, int> = 0>
  void read_single(T& s) {
    skip_space();
    if (st + int_digits >= ed) reread();
    bool neg = false;
    if (std::is_signed<T>::value && *st == '-') {
      neg = true;
      ++st;
    }
    typename std::make_unsigned<T>::type y = *st++ - '0';
    while (*st >= '0') {
      y = 10 * y + *st++ - '0';
    }
    s = (neg ? -y : y);
  }

  template <typename T,
            std::enable_if_t<std::is_same<T, std::string>::value, int> = 0>
  void read_single(T& s) {
    s = "";
    skip_space();
    while (true) {
      char* base = st;
      while (*st && !is_space(*st)) ++st;
      s += std::string(base, st);
      if (st != ed) return;
      reread();
    }
  }

  template <typename T>
  void read_single(std::vector<T>& s) {
    for (auto& d : s) read(d);
  }
};
#line 11 "test/verify/yosupo-bitwise-and-convolution-3.test.cpp"

using namespace std;

const int MOD = 998244353;

int main() {
  Scanner in(stdin);
  Printer out(stdout);
  int N;
  in.read(N);
  int a[1 << N], b[1 << N];
  for (int i = 0; i < (1 << N); i++) in.read(a[i]);
  for (int i = 0; i < (1 << N); i++) in.read(b[i]);
  bitwise_and_convolution_simd<MOD>(a, b, 1 << N);
  for (int i = 0; i < (1 << N); i++) {
    if (i) out.write(' ');
    out.write(a[i]);
  }
  out.writeln();
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	2 ms	4 MB
g++	max_random_00	AC	57 ms	12 MB
g++	max_random_01	AC	54 ms	12 MB
g++	max_random_02	AC	53 ms	12 MB
g++	random_00	AC	4 ms	4 MB
g++	random_01	AC	5 ms	4 MB
g++	random_02	AC	14 ms	6 MB
g++	small_00	AC	2 ms	4 MB
g++	small_01	AC	2 ms	4 MB
g++	small_02	AC	2 ms	4 MB
g++	tiny_00	AC	2 ms	4 MB
g++	tiny_01	AC	2 ms	4 MB
g++	tiny_02	AC	2 ms	4 MB
clang++	example_00	AC	3 ms	4 MB
clang++	max_random_00	AC	55 ms	12 MB
clang++	max_random_01	AC	54 ms	12 MB
clang++	max_random_02	AC	51 ms	12 MB
clang++	random_00	AC	4 ms	4 MB
clang++	random_01	AC	5 ms	4 MB
clang++	random_02	AC	15 ms	6 MB
clang++	small_00	AC	2 ms	4 MB
clang++	small_01	AC	2 ms	4 MB
clang++	small_02	AC	2 ms	4 MB
clang++	tiny_00	AC	2 ms	4 MB
clang++	tiny_01	AC	2 ms	4 MB
clang++	tiny_02	AC	2 ms	4 MB

Back to top page