tests/GCD_Convolution.test.cpp

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Last update: 2025-11-28 02:09:51+07:00
Problem: https://judge.yosupo.jp/problem/gcd_convolution

Depends on

Code

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

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

void solve() {
  using Fp = modint<998244353>;
  int n;
  cin >> n;
  sieve(n);
  vector<Fp> a(n + 1), b(n + 1);
  for(int i = 1; i <= n; ++i) cin >> a[i];
  for(int i = 1; i <= n; ++i) cin >> b[i];
  auto c = convolution(a, b, 0);
  // cerr << "ok";
  for(int i = 1; i <= n; ++i) cout << c[i] << ' ';
}

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

#line 1 "tests/GCD_Convolution.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/gcd_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 1 "math/ZetaMobius.h"
constexpr int MAXN = 1e6 + 5;
vector<int> P;
bitset<MAXN> is_p;

void sieve(int n) {
  is_p.set(); is_p[0] = is_p[1] = 0;
  for (int i = 2; i <= n; ++i) {
    if (is_p[i]) P.pb(i);
    for (int p : P) {
      if (i * p > n) break;
      is_p[i * p] = 0;
      if (i % p == 0) break;
    }
  }
}

// div=0: Multiple (GCD), div=1: Divisor (LCM)
template <class Fp>
void zeta(vector<Fp>& f, bool div) {
  int n = sz(f) - 1;
  for (int p : P) {
    if (p > n) break;
    if (!div) for (int j = n / p; j >= 1; --j) f[j] += f[j * p];
    else      for (int j = 1; j * p <= n; ++j) f[j * p] += f[j];
  }
}

template <class Fp>
void mobius(vector<Fp>& f, bool div) {
  int n = sz(f) - 1;
  for (int p : P) {
    if (p > n) break;
    if (!div) for (int j = 1; j <= n / p; ++j) f[j] -= f[j * p];
    else      for (int j = n / p; j >= 1; --j) f[j * p] -= f[j];
  }
}

template <class Fp>
vector<Fp> convolution(vector<Fp> f, vector<Fp> g, bool div) {
  int n = min(sz(f), sz(g)) - 1;
  f.resize(n + 1); g.resize(n + 1);
  zeta(f, div), zeta(g, div);
  vector<Fp> h(n + 1);
  for(int i = 1; i <= n; ++i) h[i] = f[i] * g[i];
  mobius(h, div);
  return h;
}
#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 6 "tests/GCD_Convolution.test.cpp"

void solve() {
  using Fp = modint<998244353>;
  int n;
  cin >> n;
  sieve(n);
  vector<Fp> a(n + 1), b(n + 1);
  for(int i = 1; i <= n; ++i) cin >> a[i];
  for(int i = 1; i <= n; ++i) cin >> b[i];
  auto c = convolution(a, b, 0);
  // cerr << "ok";
  for(int i = 1; i <= n; ++i) cout << c[i] << ' ';
}

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