test/verify/yosupo-bitwise-xor-convolution.test.cpp

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• Last update: 2024-07-28 19:56:12+09:00
• Problem: https://judge.yosupo.jp/problem/bitwise_xor_convolution

Depends on

• math/combinatorics/montgomery-mod-int.hpp
• Bitwise Xor Convolution (Bitwise-XOR畳み込み) (math/fft/bitwise-xor-convolution.hpp)
• Fast Walsh Hadamard Transform (高速ウォルシュアダマール変換) (math/fft/fast-walsh-hadamard-transform.hpp)
• Printer(高速出力) (other/printer.hpp)
• Scanner(高速入力) (other/scanner.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution

#include "../../template/template.hpp"

#include "../../math/fft/bitwise-xor-convolution.hpp"
#include "../../math/combinatorics/montgomery-mod-int.hpp"

#include "../../other/scanner.hpp"
#include "../../other/printer.hpp"

using mint = modint998244353;

int main() {
  Scanner in(stdin);
  Printer out(stdout);
  int N;
  in.read(N);
  vector< mint > a(1 << N), b(1 << N);
  for(auto &x : a) {
    int p;
    in.read(p);
    x = p;
  }
  for(auto &x : b) {
    int p;
    in.read(p);
    x = p;
  }
  auto c = bitwise_xor_convolution(a, b);
  for(int i = 0; i < (1 << N); i++) {
    if(i) out.write(' ');
    out.write(c[i].val());
  }
  out.writeln();
}

#line 1 "test/verify/yosupo-bitwise-xor-convolution.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yosupo-bitwise-xor-convolution.test.cpp"

#line 1 "math/fft/fast-walsh-hadamard-transform.hpp"
/**
 * @brief Fast Walsh Hadamard Transform (高速ウォルシュアダマール変換)
 */
template <typename T>
void fast_walsh_hadamard_transform(vector<T> &f, bool inv = false) {
  const int n = (int)f.size();
  assert((n & (n - 1)) == 0);
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j += i << 1) {
      for (int k = 0; k < i; k++) {
        T s = f[j + k], t = f[j + k + i];
        f[j + k] = s + t;
        f[j + k + i] = s - t;
      }
    }
  }
  if (inv) {
    T inv_n = T(1) / n;
    for (auto &x : f) x *= inv_n;
  }
}
#line 2 "math/fft/bitwise-xor-convolution.hpp"

/**
 * @brief Bitwise Xor Convolution (Bitwise-XOR畳み込み)
 */
template <typename T>
vector<T> bitwise_xor_convolution(vector<T> f, vector<T> g) {
  const int n = (int)f.size();
  assert(f.size() == g.size());
  assert((n & (n - 1)) == 0);
  fast_walsh_hadamard_transform(f, false);
  fast_walsh_hadamard_transform(g, false);
  for (int i = 0; i < n; i++) f[i] *= g[i];
  fast_walsh_hadamard_transform(f, true);
  return f;
}
#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint &p) const { return mint(*this) += p; }

  mint operator-(const mint &p) const { return mint(*this) -= p; }

  mint operator*(const mint &p) const { return mint(*this) *= p; }

  mint operator/(const mint &p) const { return mint(*this) /= p; }

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 7 "test/verify/yosupo-bitwise-xor-convolution.test.cpp"

#line 1 "other/scanner.hpp"
/**
 * @brief Scanner(高速入力)
 */
struct Scanner {
 public:
  explicit Scanner(FILE *fp) : fp(fp) {}

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

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

  void read() {}

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

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

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

  template <typename T>
  void read_single(vector<T> &s) {
    for (auto &d : s) read(d);
  }
};
#line 1 "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 size_t line_size = 1 << 16;
  static constexpr 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, enable_if_t<is_integral<T>::value, int> = 0>
  void write_single(T s) {
    if (st + int_digits >= line + line_size) flush();
    st += to_chars(st, st + int_digits, s).ptr - st;
  }

  void write_single(const 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 vector<T> &s) {
    for (size_t i = 0; i < s.size(); i++) {
      if (i) write_single(' ');
      write_single(s[i]);
    }
  }
};
#line 10 "test/verify/yosupo-bitwise-xor-convolution.test.cpp"

using mint = modint998244353;

int main() {
  Scanner in(stdin);
  Printer out(stdout);
  int N;
  in.read(N);
  vector< mint > a(1 << N), b(1 << N);
  for(auto &x : a) {
    int p;
    in.read(p);
    x = p;
  }
  for(auto &x : b) {
    int p;
    in.read(p);
    x = p;
  }
  auto c = bitwise_xor_convolution(a, b);
  for(int i = 0; i < (1 << N); i++) {
    if(i) out.write(' ');
    out.write(c[i].val());
  }
  out.writeln();
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	5 ms	4 MB
g++	large_00	AC	7 ms	4 MB
g++	large_01	AC	9 ms	4 MB
g++	large_02	AC	25 ms	7 MB
g++	max_random_00	AC	76 ms	20 MB
g++	max_random_01	AC	79 ms	20 MB
g++	max_random_02	AC	76 ms	20 MB
g++	small_00	AC	5 ms	4 MB
g++	small_01	AC	5 ms	4 MB
g++	small_02	AC	5 ms	4 MB
g++	tiny_00	AC	4 ms	4 MB
g++	tiny_01	AC	5 ms	4 MB
g++	tiny_02	AC	5 ms	4 MB
clang++	example_00	AC	5 ms	4 MB
clang++	large_00	AC	8 ms	4 MB
clang++	large_01	AC	11 ms	4 MB
clang++	large_02	AC	32 ms	7 MB
clang++	max_random_00	AC	109 ms	20 MB
clang++	max_random_01	AC	106 ms	20 MB
clang++	max_random_02	AC	106 ms	20 MB
clang++	small_00	AC	5 ms	4 MB
clang++	small_01	AC	5 ms	4 MB
clang++	small_02	AC	4 ms	4 MB
clang++	tiny_00	AC	5 ms	4 MB
clang++	tiny_01	AC	4 ms	3 MB
clang++	tiny_02	AC	5 ms	4 MB

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