結果

問題 No.931 Multiplicative Convolution
ユーザー pekempey
提出日時 2019-11-23 06:46:47
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 72 ms / 2,000 ms
コード長 4,685 bytes
コンパイル時間 1,989 ms
コンパイル使用メモリ 183,816 KB
実行使用メモリ 12,080 KB
最終ジャッジ日時 2024-10-11 06:46:34
合計ジャッジ時間 4,079 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
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;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define repr(i, n) for (int i = (n) - 1; i >= 0; i--)
#define repe(i, l, r) for (int i = (l); i < (r); i++)
#define reper(i, l, r) for (int i = (r) - 1; i >= (l); i--)
#define repi(i, l, r) for (int i = (l); i <= (r); i++)
#define repir(i, l, r) for (int i = (r); i >= (l); i--)
#define range(a) a.begin(), a.end()
void initio() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); }
constexpr int MOD = 998244353;
constexpr int ROOT = 3;
class mint {
int n;
public:
mint(int n_ = 0) : n(n_) {}
explicit operator int() { return n; }
friend mint operator-(mint a) { return -a.n + MOD * (a.n != 0); }
friend mint operator+(mint a, mint b) { int x = a.n + b.n; return x - (x >= MOD) * MOD; }
friend mint operator-(mint a, mint b) { int x = a.n - b.n; return x + (x < 0) * MOD; }
friend mint operator*(mint a, mint b) { return (long long)a.n * b.n % MOD; }
friend mint &operator+=(mint &a, mint b) { return a = a + b; }
friend mint &operator-=(mint &a, mint b) { return a = a - b; }
friend mint &operator*=(mint &a, mint b) { return a = a * b; }
friend bool operator==(mint a, mint b) { return a.n == b.n; }
friend bool operator!=(mint a, mint b) { return a.n != b.n; }
friend istream &operator>>(istream &i, mint &a) { return i >> a.n; }
friend ostream &operator<<(ostream &o, mint a) { return o << a.n; }
};
mint modpow(mint a, long long b) {
mint res = 1;
while (b > 0) {
if (b & 1) res *= a;
a *= a;
b >>= 1;
}
return res;
}
int modpow2(int a, long long b, int p) {
int res = 1;
while (b > 0) {
if (b & 1) res = (ll)res * a % p;
a = (ll)a * a % p;
b >>= 1;
}
return res;
}
mint modinv(mint n) {
int a = (int)n, b = MOD;
int s = 1, t = 0;
while (b != 0) {
int q = a / b;
a -= q * b;
s -= q * t;
swap(a, b);
swap(s, t);
}
return s >= 0 ? s : s + MOD;
}
template<int N>
struct NTT {
mint rots[N];
NTT() {
mint w = modpow(ROOT, (MOD - 1) / N);
mint ws = 1;
for (int i = 0; i < N / 2; i++) {
rots[i + N / 2] = ws;
ws *= w;
}
for (int i = N / 2 - 1; i >= 1; i--) {
rots[i] = rots[i * 2];
}
}
void ntt(vector<mint> &a) {
const int n = a.size();
int i = 0;
for (int j = 1; j < n - 1; j++) {
for (int k = n >> 1; k > (i ^= k); k >>= 1);
if (j < i) swap(a[i], a[j]);
}
for (int i = 1; i < n; i *= 2) {
for (int j = 0; j < n; j += i * 2) {
for (int k = 0; k < i; k++) {
mint s = a[j + k];
mint t = a[j + k + i] * rots[i + k];
a[j + k ] = s + t;
a[j + k + i] = s - t;
}
}
}
}
void invntt(vector<mint> &a) {
const int n = a.size();
ntt(a);
reverse(a.begin() + 1, a.end());
mint inv_n = modinv(n);
for (int i = 0; i < n; i++) {
a[i] *= inv_n;
}
}
vector<mint> convolution(vector<mint> a, vector<mint> b) {
const int n = a.size() + b.size() - 1;
int t = 1;
while (t < n) t *= 2;
a.resize(t);
b.resize(t);
ntt(a);
ntt(b);
for (int i = 0; i < t; i++) {
a[i] *= b[i];
}
invntt(a);
a.resize(n);
return a;
}
};
NTT<1 << 20> ntt;
vector<long long> divisors(long long n) {
vector<long long> res;
for (long long i = 1; i * i <= n; i++) {
if (n % i == 0) {
res.push_back(i);
if (i * i != n) {
res.push_back(n / i);
}
}
}
sort(range(res));
return res;
}
int primitive_root(int p) {
auto ds = divisors(p - 1);
ds.pop_back();
for (int i = 1; i <= p - 1; i++) {
bool all = true;
for (int d : ds) {
all &= modpow2(i, d, p) != 1;
}
if (all) return i;
}
abort();
}
int main() { initio();
int P; cin >> P;
vector<mint> A(P - 1), B(P - 1);
rep(i, P - 1) cin >> A[i];
rep(i, P - 1) cin >> B[i];
int g = primitive_root(P);
vector<int> table(P - 1);
table[0] = 1;
for (int i = 1; i <= P - 2; i++) {
table[i] = (ll)table[i - 1] * g % P;
}
vector<int> inv(P);
for (int i = 0; i <= P - 2; i++) {
inv[table[i]] = i;
}
vector<mint> F(P - 1);
vector<mint> G(P - 1);
for (int i = 0; i <= P - 2; i++) {
F[inv[i + 1]] = A[i];
G[inv[i + 1]] = B[i];
}
auto ans = ntt.convolution(F, G);
for (int i = P - 1; i < ans.size(); i++) {
ans[i % (P - 1)] += ans[i];
}
vector<mint> true_ans(P);
for (int i = 0; i < P - 1; i++) {
true_ans[table[i]] = ans[i];
}
for (int i = 1; i < true_ans.size(); i++) {
cout << true_ans[i] << " \n"[i == true_ans.size() - 1];
}
}
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