結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
|
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
#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;}