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tests/Product_of_Polynomial_Sequence.test.cpp
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- Last update: 2025-11-28 02:09:51+07:00
- Problem: https://judge.yosupo.jp/problem/product_of_polynomial_sequence
Depends on
Code
#define PROBLEM "https://judge.yosupo.jp/problem/product_of_polynomial_sequence"
#include "../misc/macros.h"
#include "../math/Poly.h"
void solve() {
int n;
cin >> n;
if (n == 0) {
cout << 1;
return;
}
deque<Poly> dq;
for (int i = 0; i < n; ++i) {
int d;
cin >> d;
Poly p;
for (int j = 0; j <= d; ++j) {
int c;
cin >> c;
p.eb(c);
}
dq.push_back(p);
}
for (int i = 0; i < n - 1; ++i) {
auto f = dq.front();
dq.pop_front();
auto g = dq.front();
dq.pop_front();
dq.eb(f * g);
}
auto ans = dq.front();
for (auto v : ans) cout << v << ' ';
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
int tc = 1;
// cin >> tc;
while (tc--) solve();
}#line 1 "tests/Product_of_Polynomial_Sequence.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/product_of_polynomial_sequence"
#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 2 "math/Poly.h"
using Fp = modint<998244353>;
namespace ntt {
const Fp G = 3;
void ntt(vector<Fp>& a, bool inv) {
int n = sz(a);
for (int i = 1, j = 0; i < n; i++) {
int bit = n >> 1;
for (; j & bit; bit >>= 1) j ^= bit;
j ^= bit;
if (i < j) swap(a[i], a[j]);
}
for (int len = 1; len < n; len <<= 1) {
Fp wlen = G.pow((Fp::modulo - 1) / (2 * len));
if (inv) wlen = wlen.inv();
for (int i = 0; i < n; i += 2 * len) {
Fp w = 1;
for (int j = 0; j < len; j++) {
Fp u = a[i + j], v = a[i + j + len] * w;
a[i + j] = u + v, a[i + j + len] = u - v;
w *= wlen;
}
}
}
if (inv) {
Fp n_inv = Fp(n).inv();
for (auto& x : a) x *= n_inv;
}
}
vector<Fp> conv(vector<Fp> a, vector<Fp> b) {
if (a.empty() || b.empty()) return {};
int s = sz(a) + sz(b) - 1, n = 1;
while (n < s) n <<= 1;
a.resize(n), b.resize(n);
ntt(a, 0), ntt(b, 0);
for (int i = 0; i < n; i++) a[i] *= b[i];
ntt(a, 1), a.resize(s);
return a;
}
} // namespace ntt
struct Poly : vector<Fp> {
using vector::vector;
Poly(const vector<Fp>& v) : vector(v) {}
Poly cut(int n) const {
Poly res = *this;
res.resize(n);
return res;
}
Poly operator+(const Poly& r) const {
Poly res = *this;
res.resize(max(sz(*this), sz(r)));
for (int i = 0; i < sz(r); ++i) res[i] += r[i];
return res;
}
Poly operator-(const Poly& r) const {
Poly res = *this;
res.resize(max(sz(*this), sz(r)));
for (int i = 0; i < sz(r); ++i) res[i] -= r[i];
return res;
}
Poly operator*(const Poly& r) const { return ntt::conv(*this, r); }
Poly operator*(Fp v) const {
Poly res = *this;
for (auto& x : res) x *= v;
return res;
}
Poly& operator+=(const Poly& r) { return *this = *this + r; }
Poly& operator-=(const Poly& r) { return *this = *this - r; }
Poly& operator*=(const Poly& r) { return *this = *this * r; }
Poly deriv() const {
if (empty()) return {};
Poly res(sz(*this) - 1);
for (int i = 1; i < sz(*this); ++i) res[i - 1] = data()[i] * i;
return res;
}
Poly integ() const {
Poly res(sz(*this) + 1);
for (int i = 0; i < sz(*this); ++i) res[i + 1] = data()[i] * Fp(i + 1).inv();
return res;
}
Poly inv(int n) const {
Poly b = {data()[0].inv()};
for (int k = 1; k < n; k <<= 1) {
Poly a = cut(2 * k), prod = b * b * a;
b.resize(2 * k);
for (int i = 0; i < 2 * k; ++i) {
b[i] = b[i] * 2 - (i < sz(prod) ? prod[i] : Fp(0));
}
}
return b.cut(n);
}
Poly log(int n) const { return (deriv() * inv(n)).integ().cut(n); }
Poly exp(int n) const {
Poly b = {1};
for (int k = 1; k < n; k <<= 1) {
Poly ln_b = b.log(2 * k), a = cut(2 * k), diff = a - ln_b;
diff[0] += 1, b = (b * diff).cut(2 * k);
}
return b.cut(n);
}
Poly pow(i64 k, int n) const {
if (n == 0) return {};
if (k == 0) {
Poly res = {1};
res.resize(n);
return res;
}
int i = 0;
while (i < sz(*this) && data()[i].x == 0) i++;
if (i == sz(*this) || (i > 0 && k >= n / i + 2)) {
Poly res;
res.resize(n);
return res;
}
i64 shift = (i64) i * k;
if (shift >= n) {
Poly res;
res.resize(n);
return res;
}
Poly a = {begin() + i, end()};
int limit = n - shift;
a.resize(limit);
Fp lead = a[0];
Fp inv_lead = lead.inv();
a = a * inv_lead;
a = (a.log(limit) * Fp(k)).exp(limit);
a = a * lead.pow(k);
Poly res(shift, 0);
res.insert(res.end(), a.begin(), a.end());
res.resize(n);
return res;
}
friend ostream& operator<<(ostream& os, const Poly& p) {
for (auto x : p) os << x << " ";
return os;
}
};
#line 5 "tests/Product_of_Polynomial_Sequence.test.cpp"
void solve() {
int n;
cin >> n;
if (n == 0) {
cout << 1;
return;
}
deque<Poly> dq;
for (int i = 0; i < n; ++i) {
int d;
cin >> d;
Poly p;
for (int j = 0; j <= d; ++j) {
int c;
cin >> c;
p.eb(c);
}
dq.push_back(p);
}
for (int i = 0; i < n - 1; ++i) {
auto f = dq.front();
dq.pop_front();
auto g = dq.front();
dq.pop_front();
dq.eb(f * g);
}
auto ans = dq.front();
for (auto v : ans) cout << v << ' ';
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
int tc = 1;
// cin >> tc;
while (tc--) solve();
}