verify/verify-unit-test/set-function.test.cpp

View this file on GitHub
Last update: 2024-05-03 23:21:26+09:00
Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

Code

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

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

using namespace Nyaan;

#include "../../misc/rng.hpp"
#include "../../modint/montgomery-modint.hpp"
#include "../../set-function/and-convolution.hpp"
#include "../../set-function/or-convolution.hpp"
#include "../../set-function/xor-convolution.hpp"
using mint = LazyMontgomeryModInt<998244353>;

template <typename T>
void test(int n) {
  assert((n & (n - 1)) == 0);
  vector<T> a(n), b(n), c(n);

  rep(i, n) {
    a[i] = rng() & 0xFFFF;
    b[i] = rng() & 0xFFFF;
  }

  {
    auto d = a;
    subset_zeta_transform(d);
    subset_mobius_transform(d);
    assert(a == d && "subset");
  }

  {
    auto d = a;
    superset_zeta_transform(d);
    superset_mobius_transform(d);
    assert(a == d && "superset");
  }

  {
    auto d = a;
    walsh_hadamard_transform(d);
    walsh_hadamard_transform(d, true);
    assert(a == d && "hadamard");
  }

  // and convolution
  {
    auto d = and_convolution(a, b);
    fill(all(c), 0);
    rep(i, n) rep(j, n) c[i & j] += a[i] * b[j];
    assert(c == d && "and");
  }

  // or convolution
  {
    auto d = or_convolution(a, b);
    fill(all(c), 0);
    rep(i, n) rep(j, n) c[i | j] += a[i] * b[j];
    assert(c == d && "or");
  }

  // xor convolution
  {
    auto d = xor_convolution(a, b);
    fill(all(c), 0);
    rep(i, n) rep(j, n) c[i ^ j] += a[i] * b[j];
    assert(c == d && "xor");
  }
}

void Nyaan::solve() {
  for (int i = 1; i <= 1024; i *= 2) {
    test<ll>(i);
    test<mint>(i);
  }
  cerr << "ok" << endl;

  int a, b;
  cin >> a >> b;
  cout << a + b << endl;
}

#line 1 "verify/verify-unit-test/set-function.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 2 "template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  if(v.empty()) return {};
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan
#line 58 "template/template.hpp"

// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
#line 61 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

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

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan
#line 64 "template/template.hpp"

// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
  if (t == 0) cerr << 0;
  if (t < 0) cerr << '-', t = -t;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

void dump(__uint128_t t) {
  if (t == 0) cerr << 0;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(std::forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...)                           \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"

// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)
#line 70 "template/template.hpp"

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-unit-test/set-function.test.cpp"

using namespace Nyaan;

#line 2 "misc/rng.hpp"

#line 2 "internal/internal-seed.hpp"

#line 4 "internal/internal-seed.hpp"
using namespace std;

namespace internal {
unsigned long long non_deterministic_seed() {
  unsigned long long m =
      chrono::duration_cast<chrono::nanoseconds>(
          chrono::high_resolution_clock::now().time_since_epoch())
          .count();
  m ^= 9845834732710364265uLL;
  m ^= m << 24, m ^= m >> 31, m ^= m << 35;
  return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }

// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
  return deterministic_seed();
#else
  return non_deterministic_seed();
#endif
}

}  // namespace internal
#line 4 "misc/rng.hpp"

namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;

// [0, 2^64 - 1)
u64 rng() {
  static u64 _x = internal::seed();
  return _x ^= _x << 7, _x ^= _x >> 9;
}

// [l, r]
i64 rng(i64 l, i64 r) {
  assert(l <= r);
  return l + rng() % u64(r - l + 1);
}

// [l, r)
i64 randint(i64 l, i64 r) {
  assert(l < r);
  return l + rng() % u64(r - l);
}

// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
  assert(l <= r && n <= r - l);
  unordered_set<i64> s;
  for (i64 i = n; i; --i) {
    i64 m = randint(l, r + 1 - i);
    if (s.find(m) != s.end()) m = r - i;
    s.insert(m);
  }
  vector<i64> ret;
  for (auto& x : s) ret.push_back(x);
  sort(begin(ret), end(ret));
  return ret;
}

// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
  assert(l < r);
  return l + rnd() * (r - l);
}

template <typename T>
void randshf(vector<T>& v) {
  int n = v.size();
  for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}

}  // namespace my_rand

using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 2 "modint/montgomery-modint.hpp"

template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_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(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  static_assert(r * mod == 1, "this code has bugs.");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

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

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

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

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint operator+() const { return mint(*this); }

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

  constexpr mint inverse() const {
    int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
    while (y > 0) {
      t = x / y;
      x -= t * y, u -= t * v;
      tmp = x, x = y, y = tmp;
      tmp = u, u = v, v = tmp;
    }
    return mint{u};
  }

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

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }

  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};
#line 2 "set-function/and-convolution.hpp"

#line 2 "set-function/zeta-mobius-transform.hpp"

template <typename T>
void superset_zeta_transform(vector<T>& f) {
  int n = f.size();
  assert((n & (n - 1)) == 0);
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j++) {
      if ((j & i) == 0) {
        f[j] += f[j | i];
      }
    }
  }
}

template <typename T>
void superset_mobius_transform(vector<T>& f) {
  int n = f.size();
  assert((n & (n - 1)) == 0);
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j++) {
      if ((j & i) == 0) {
        f[j] -= f[j | i];
      }
    }
  }
}

template <typename T>
void subset_zeta_transform(vector<T>& f) {
  int n = f.size();
  assert((n & (n - 1)) == 0);
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j++) {
      if ((j & i) == 0) {
        f[j | i] += f[j];
      }
    }
  }
}

template <typename T>
void subset_mobius_transform(vector<T>& f) {
  int n = f.size();
  assert((n & (n - 1)) == 0);
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j++) {
      if ((j & i) == 0) {
        f[j | i] -= f[j];
      }
    }
  }
}

/**
 * @brief Zeta Transform / Moebius Transform
 */
#line 5 "set-function/and-convolution.hpp"

template <typename T>
vector<T> and_convolution(vector<T> a, vector<T> b) {
  superset_zeta_transform(a);
  superset_zeta_transform(b);
  for (int i = 0; i < (int)a.size(); i++) a[i] *= b[i];
  superset_mobius_transform(a);
  return a;
}

/**
 * @brief AND Convoluion
 */
#line 2 "set-function/or-convolution.hpp"

#line 5 "set-function/or-convolution.hpp"

template <typename T>
vector<T> or_convolution(vector<T> a, vector<T> b) {
  subset_zeta_transform(a);
  subset_zeta_transform(b);
  for (int i = 0; i < (int)a.size(); i++) a[i] *= b[i];
  subset_mobius_transform(a);
  return a;
}

/**
 * @brief OR Convoluion
 */
#line 2 "set-function/xor-convolution.hpp"

#line 2 "set-function/walsh-hadamard-transform.hpp"

template <typename T>
void walsh_hadamard_transform(vector<T>& f, bool inverse = false) {
  int n = f.size();
  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j++) {
      if ((j & i) == 0) {
        T x = f[j], y = f[j | i];
        f[j] = x + y, f[j | i] = x - y;
      }
    }
  }
  if (inverse) {
    if constexpr (is_integral<T>::value) {
      for (auto& x : f) x /= n;
    } else {
      T invn = T(1) / T(f.size());
      for (auto& x : f) x *= invn;
    }
  }
}

/**
 * @brief Walsh Hadamard Transform
 */
#line 5 "set-function/xor-convolution.hpp"

template <typename T>
vector<T> xor_convolution(vector<T> a, vector<T> b) {
  walsh_hadamard_transform(a);
  walsh_hadamard_transform(b);
  for (int i = 0; i < (int)a.size(); i++) a[i] *= b[i];
  walsh_hadamard_transform(a, true);
  return a;
}

/**
 * @brief XOR Convoluion
 */
#line 12 "verify/verify-unit-test/set-function.test.cpp"
using mint = LazyMontgomeryModInt<998244353>;

template <typename T>
void test(int n) {
  assert((n & (n - 1)) == 0);
  vector<T> a(n), b(n), c(n);

  rep(i, n) {
    a[i] = rng() & 0xFFFF;
    b[i] = rng() & 0xFFFF;
  }

  {
    auto d = a;
    subset_zeta_transform(d);
    subset_mobius_transform(d);
    assert(a == d && "subset");
  }

  {
    auto d = a;
    superset_zeta_transform(d);
    superset_mobius_transform(d);
    assert(a == d && "superset");
  }

  {
    auto d = a;
    walsh_hadamard_transform(d);
    walsh_hadamard_transform(d, true);
    assert(a == d && "hadamard");
  }

  // and convolution
  {
    auto d = and_convolution(a, b);
    fill(all(c), 0);
    rep(i, n) rep(j, n) c[i & j] += a[i] * b[j];
    assert(c == d && "and");
  }

  // or convolution
  {
    auto d = or_convolution(a, b);
    fill(all(c), 0);
    rep(i, n) rep(j, n) c[i | j] += a[i] * b[j];
    assert(c == d && "or");
  }

  // xor convolution
  {
    auto d = xor_convolution(a, b);
    fill(all(c), 0);
    rep(i, n) rep(j, n) c[i ^ j] += a[i] * b[j];
    assert(c == d && "xor");
  }
}

void Nyaan::solve() {
  for (int i = 1; i <= 1024; i *= 2) {
    test<ll>(i);
    test<mint>(i);
  }
  cerr << "ok" << endl;

  int a, b;
  cin >> a >> b;
  cout << a + b << endl;
}

Nyaan's Library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/verify-unit-test/set-function.test.cpp

Depends on

Code