結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
|
提出日時 | 2021-08-14 22:31:08 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 66 ms / 2,000 ms |
コード長 | 5,825 bytes |
コンパイル時間 | 1,884 ms |
コンパイル使用メモリ | 181,768 KB |
実行使用メモリ | 9,364 KB |
最終ジャッジ日時 | 2024-10-05 23:49:09 |
合計ジャッジ時間 | 4,403 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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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>#define rep(i,n) for(int i = 0; i < (n); i++)using namespace std;typedef long long ll;ll modpow(ll a,ll b,ll mod){ll ans = 1;a %= mod;while(b){if(b&1) ans = ans * a % mod;a = a * a % mod;b >>= 1;}return ans;}int get_root(int p) {vector<int> ds;for(int i = 1; i * i <= p - 1; i++){if((p - 1) % i == 0){ds.push_back(i);if(i * i != p - 1) ds.push_back((p - 1) / i);}}sort(ds.begin(), ds.end());ds.pop_back();for(int i = 1; i <= p - 1; i++){for(auto &d : ds) if(modpow(i, d, p) == 1) goto fail;return i;fail:;}return -1;}template< int mod >struct Fp {int x;Fp() : x(0) {}Fp(int64_t y) : x(y >= 0 ? y % mod : (mod + y % mod) % mod) {}Fp &operator+=(const Fp &p) { if((x += p.x) >= mod) x -= mod; return *this; }Fp &operator-=(const Fp &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; }Fp &operator*=(const Fp &p) { x = (int)(1LL * x * p.x % mod); return *this; }Fp &operator/=(const Fp &p) { *this *= p.inv(); return *this; }Fp operator-() const { return Fp(-x); }Fp operator+(const Fp &p) const { return Fp(*this) += p; }Fp operator-(const Fp &p) const { return Fp(*this) -= p; }Fp operator*(const Fp &p) const { return Fp(*this) *= p; }Fp operator/(const Fp &p) const { return Fp(*this) /= p; }bool operator==(const Fp &p) const { return x == p.x; }bool operator!=(const Fp &p) const { return x != p.x; }Fp inv() 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 Fp(u);}Fp pow(int64_t n) const {Fp ret(1), mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const Fp &p) { return os << p.x; }friend istream &operator>>(istream &is, Fp &a) {int64_t t;is >> t;a = Fp< mod > (t);return (is);}static int get_mod() { return mod; }};using mint = Fp<998244353>;template< int mod > struct NTT {vector< int > rev, rts;int base, max_base, root;NTT() : base(1), rev{0, 1}, rts{0, 1} {assert(mod >= 3 && mod % 2 == 1);auto tmp = mod - 1;max_base = 0;while(tmp % 2 == 0) tmp >>= 1, max_base++;root = 2;while(mod_pow(root, (mod - 1) >> 1) == 1) ++root;assert(mod_pow(root, mod - 1) == 1);root = mod_pow(root, (mod - 1) >> max_base);}inline int mod_pow(int x, int n) {int ret = 1;while(n > 0) {if(n & 1) ret = mul(ret, x);x = mul(x, x);n >>= 1;}return ret;}inline int inverse(int x) { return mod_pow(x, mod - 2); }inline unsigned add(unsigned x, unsigned y) {x += y; if(x >= mod) x -= mod; return x;}inline unsigned mul(unsigned a, unsigned b) {return 1ull * a * b % (unsigned long long) mod;}void ensure_base(int nbase) {if(nbase <= base) return;rev.resize(1 << nbase);rts.resize(1 << nbase);for(int i = 0; i < (1 << nbase); i++) {rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));}assert(nbase <= max_base);while(base < nbase) {int z = mod_pow(root, 1 << (max_base - 1 - base));for(int i = 1 << (base - 1); i < (1 << base); i++) {rts[i << 1] = rts[i];rts[(i << 1) + 1] = mul(rts[i], z);}++base;}}void ntt(vector< int > &a) {const int n = (int) a.size();assert((n & (n - 1)) == 0);int zeros = __builtin_ctz(n);ensure_base(zeros);int shift = base - zeros;for(int i = 0; i < n; i++) {if(i < (rev[i] >> shift)) {swap(a[i], a[rev[i] >> shift]);}}for(int k = 1; k < n; k <<= 1) {for(int i = 0; i < n; i += 2 * k) {for(int j = 0; j < k; j++) {int z = mul(a[i + j + k], rts[j + k]);a[i + j + k] = add(a[i + j], mod - z);a[i + j] = add(a[i + j], z);}}}}vector< int > multiply(vector< int > a, vector< int > b) {int need = a.size() + b.size() - 1;int nbase = 1;while((1 << nbase) < need) nbase++;ensure_base(nbase);int sz = 1 << nbase;a.resize(sz, 0);b.resize(sz, 0);ntt(a);ntt(b);int inv_sz = inverse(sz);for(int i = 0; i < sz; i++) {a[i] = mul(a[i], mul(b[i], inv_sz));}reverse(a.begin() + 1, a.end());ntt(a);a.resize(need);return a;}};int main(){cin.tie(0);ios::sync_with_stdio(0);int P; cin >> P;vector<int> A(P), B(P);for(int i = 1; i < P; i++) cin >> A[i];for(int i = 1; i < P; i++) cin >> B[i];int g = get_root(P);vector<int> va(P - 1), vb(P - 1);int x = 1;rep(i,P-1){va[i] = A[x];vb[i] = B[x];x = (ll)x * g % P;}NTT<998244353> ntt;auto vc = ntt.multiply(va, vb);rep(i,vc.size()) if(i >= P - 1) {vc[i - (P - 1)] += vc[i];}vector<mint> ans(P);x = 1;rep(i,P-1){ans[x] = vc[i];x = (ll)x * g % P;}for(int i = 1; i < P; i++){if(i > 1) cout << " ";cout << ans[i];}cout << endl;}