結果

問題 No.931 Multiplicative Convolution
ユーザー kuhaku
提出日時 2020-08-21 01:18:20
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 669 ms / 2,000 ms
コード長 4,104 bytes
コンパイル時間 2,526 ms
コンパイル使用メモリ 206,488 KB
最終ジャッジ日時 2025-01-13 04:34:08
ジャッジサーバーID
(参考情報)
judge5 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 14
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
using Vec = vector<ll>;
#define REP(i, m, n) for(ll i = (m); i < (n); ++i)
#define rep(i, n) REP(i, 0, n)
template <typename T>
bool chmax(T &a, const T b){if(a < b){a = b; return true;} return false;}
template <typename T>
bool chmin(T &a, const T b){if(a > b){a = b; return true;} return false;}
constexpr ll LINF = 1e18L+1;
constexpr ll MOD = 998244353;
const double PI = acos(-1.0);
template <int mod>
struct ModInt {
int x;
ModInt() : x(0) {}
ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int) (1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt &operator++() {
if((++x) >= mod) x -= mod;
return *this;
}
ModInt operator++(int) {
ModInt tmp(*this);
operator++();
return tmp;
}
ModInt &operator--() {
if((x += mod - 1) >= mod) x -= mod;
return *this;
}
ModInt operator--(int) {
ModInt tmp(*this);
operator--();
return tmp;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const {
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
ModInt pow(int64_t n) const {
ModInt res(1), mul(x);
while(n > 0) {
if(n & 1) res *= mul;
mul *= mul;
n >>= 1;
}
return res;
}
friend ostream &operator<<(ostream &os, const ModInt &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt &a) {
int64_t t;
is >> t;
a = ModInt< mod >(t);
return (is);
}
static int get_mod() { return mod; }
};
using Mint = ModInt<MOD>;
void ntt(vector<Mint> &a, bool inv){
int N = a.size();
int n = 2, d = N / 2;
vector<Mint> cp(N);
while (n <= N) {
for (int p = 0; p < d; ++p) {
Mint omega = Mint(3).pow((MOD - 1) / n);
if (inv) omega = omega.inverse();
Mint pow_omega = 1;
for (int i = 0; i < n / 2; ++i) {
cp[p + d * i] = a[p + 2 * d * i] + pow_omega * a[p + 2 * d * i + d];
cp[p + d * i + N / 2] = a[p + 2 * d * i] - pow_omega * a[p + 2 * d * i + d];
pow_omega *= omega;
}
}
for (int i = 0; i < N; ++i) a[i] = cp[i];
n <<= 1, d >>= 1;
}
}
void conv(vector<Mint> &a, vector<Mint> b){
int n = a.size() + b.size();
int N = 1;
while (N <= n) N <<= 1;
a.resize(N);
b.resize(N);
ntt(a, false);
ntt(b, false);
for (int i = 0; i < N; ++i) {
a[i] *= b[i] / N;
}
ntt(a, true);
}
ll find_root(ll p){
for(ll i = 2; i < p; ++i){
unordered_set<ll> used;
ll t = 1;
bool flg = true;
for(ll j = 0; j < p - 2; ++j){
used.insert(t);
(t *= i) %= p;
if(used.find(t) != used.end()) {
flg = false;
break;
}
}
if(flg) return i;
}
return 0;
}
int main(void) {
ll p;
cin >> p;
Vec a(p), b(p);
rep(i, p - 1) cin >> a[i + 1];
rep(i, p - 1) cin >> b[i + 1];
ll r = find_root(p);
cerr << r << endl;
ll t = 1;
vector<Mint> u(p), v(p);
rep(i, p - 1){
v[i] = a[t];
u[i] = b[t];
(t *= r) %= p;
}
conv(v, u);
t = 1;
vector<Mint> ans(p);
rep(i, v.size()){
// cerr << v[i] << endl;
ans[t] += v[i];
(t *= r) %= p;
}
rep(i, p - 1) cout << ans[i + 1] << " ";
cout << endl;
return 0;
}
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