tests/Bitwise_Subset_Convolution.test.cpp

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Last update: 2025-11-28 12:47:29+07:00
Problem: https://judge.yosupo.jp/problem/subset_convolution

Depends on

Code

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

#include "../misc/macros.h"
#include "../math/ModInt.h"
#include "../math/FST.h"

using namespace FST;
using Fp = modint<998244353>;

void solve() {
  int n;
  cin >> n;
  vector<Fp> a(1 << n), b(1 << n);
  for (int i = 0; i < (1 << n); ++i) cin >> a[i];
  for (int i = 0; i < (1 << n); ++i) cin >> b[i];
  auto c = subsetConv(a, b);
  for(auto e: c) cout << e << ' ';
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tc = 1;
  // cin >> tc;
  while (tc--) solve();
}

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

#line 1 "misc/macros.h"
// #pragma GCC optimize("Ofast,unroll-loops")       // unroll long, simple loops
// #pragma GCC target("avx2,fma")                   // vectorizing code
// #pragma GCC target("lzcnt,popcnt,abm,bmi,bmi2")  // for fast bitset operation

#include <bits/extc++.h>
#include <tr2/dynamic_bitset>

using namespace std;
using namespace __gnu_pbds;  // ordered_set, gp_hash_table
// using namespace __gnu_cxx; // rope

// for templates to work
#define all(x) (x).begin(), (x).end()
#define sz(x) (int) (x).size()
#define pb push_back
#define eb emplace_back
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using pii = pair<i32, i32>;
using vi = vector<i32>;

// fast map
const int RANDOM = chrono::high_resolution_clock::now().time_since_epoch().count();
struct chash {  // customize hash function for gp_hash_table
  int operator()(int x) const { return x ^ RANDOM; }
};
gp_hash_table<int, int, chash> table;

/* ordered set
    find_by_order(k): returns an iterator to the k-th element (0-based)
    order_of_key(k): returns the number of elements in the set that are strictly less than k
*/
template <class T>
using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

/*  rope
    rope <int> cur = v.substr(l, r - l + 1);
    v.erase(l, r - l + 1);
    v.insert(v.mutable_begin(), cur);
*/
#line 2 "math/ModInt.h"

template <int mod>
struct modint {
  using M = modint;
  static_assert(mod > 0 && mod <= 2147483647);
  static constexpr int modulo = mod;
  static constexpr u32 r1 = []() {
    u32 r1 = mod;
    for (int i = 0; i < 5; ++i) r1 *= 2 - mod * r1;
    return -r1;
  }();
  static constexpr u32 r2 = -u64(mod) % mod;
  static u32 reduce(u64 x) {
    u32 y = u32(x) * r1, r = (x + u64(y) * mod) >> 32;
    return r >= mod ? r - mod : r;
  }
  u32 x;
  modint() : x(0) {}
  modint(i64 x) : x(reduce(u64(x % mod + mod) * r2)) {}
  M& operator+=(const M& a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  M& operator-=(const M& a) {
    if ((x += mod - a.x) >= mod) x -= mod;
    return *this;
  }
  M& operator*=(const M& a) {
    x = reduce(u64(x) * a.x);
    return *this;
  }
  M& operator/=(const M& a) { return *this *= a.inv(); }
  M operator-() const { return M(0) - *this; }
  M operator+(const M& a) const { return M(*this) += a; }
  M operator-(const M& a) const { return M(*this) -= a; }
  M operator*(const M& a) const { return M(*this) *= a; }
  M operator/(const M& a) const { return M(*this) /= a; }
  bool operator==(const M& a) const { return x == a.x; }
  bool operator!=(const M& a) const { return x != a.x; }
  M pow(u64 k) const {
    M res(1), b = *this;
    while (k) {
      if (k & 1) res *= b;
      b *= b, k >>= 1;
    }
    return res;
  }
  M inv() const { return pow(mod - 2); }
  friend ostream& operator<<(ostream& os, const M& a) {
    return os << reduce(a.x);
  }
  friend istream& operator>>(istream& is, M& a) {
    i64 v;
    is >> v;
    a = M(v);
    return is;
  }
};

u64 modmul(u64 x, u64 y, u64 m) { return u128(x) * y % m; }
u64 modpow(u64 x, u64 k, u64 m) {
  u64 res = 1;
  while (k) {
    if (k & 1) res = modmul(res, x, m);
    x = modmul(x, x, m);
    k >>= 1;
  }
  return res;
}
#line 1 "math/FST.h"
#define pc __builtin_popcount

namespace FST {
  enum { OR, AND, XOR };
  template<class T>
  void fwht(vector<T>& a, int op, int inv) {
    int n = sz(a);
    for (int l = 1; l < n; l <<= 1)
      for (int i = 0; i < n; i += 2 * l)
        for (int j = 0; j < l; ++j) {
          T u = a[i + j], v = a[i + j + l];
          if (op == OR) a[i + j + l] += inv ? -u : u;
          else if (op == AND) a[i + j] += inv ? -v : v;
          else a[i + j] = u + v, a[i + j + l] = u - v;
        }
    if (op == XOR && inv) {
      T in = T(1) / n;
      for (auto& x : a) x *= in;
    }
  }
  template<class T>
  vector<T> conv(vector<T> a, vector<T> b, int op) {
    int n = 1; while (n < max(sz(a), sz(b))) n <<= 1;
    a.resize(n), b.resize(n);
    fwht(a, op, 0), fwht(b, op, 0);
    for (int i = 0; i < n; ++i) a[i] *= b[i];
    fwht(a, op, 1);
    return a;
  }
  template<class T>
  vector<T> subsetConv(const vector<T>& a, const vector<T>& b) {
    int n = 1, k = 0;
    while (n < max(sz(a), sz(b))) n <<= 1, k++;
    vector<vector<T>> fa(k + 1, vector<T>(n)), fb(k + 1, vector<T>(n)), h(k + 1, vector<T>(n));
    for (int i = 0; i < n; ++i) {
      if (i < sz(a)) fa[pc(i)][i] = a[i];
      if (i < sz(b)) fb[pc(i)][i] = b[i];
    }
    for (int i = 0; i <= k; ++i) fwht(fa[i], OR, 0), fwht(fb[i], OR, 0);
    for (int i = 0; i <= k; ++i)
      for (int j = 0; j <= i; ++j)
        for (int x = 0; x < n; ++x) h[i][x] += fa[j][x] * fb[i - j][x];
    for (int i = 0; i <= k; ++i) fwht(h[i], OR, 1);
    vector<T> res(n);
    for (int i = 0; i < n; ++i) res[i] = h[pc(i)][i];
    return res;
  }
}
#line 6 "tests/Bitwise_Subset_Convolution.test.cpp"

using namespace FST;
using Fp = modint<998244353>;

void solve() {
  int n;
  cin >> n;
  vector<Fp> a(1 << n), b(1 << n);
  for (int i = 0; i < (1 << n); ++i) cin >> a[i];
  for (int i = 0; i < (1 << n); ++i) cin >> b[i];
  auto c = subsetConv(a, b);
  for(auto e: c) cout << e << ' ';
}

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int tc = 1;
  // cin >> tc;
  while (tc--) solve();
}