結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
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提出日時 | 2019-11-23 00:18:11 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 131 ms / 2,000 ms |
コード長 | 7,283 bytes |
コンパイル時間 | 2,883 ms |
コンパイル使用メモリ | 212,788 KB |
最終ジャッジ日時 | 2025-01-08 05:25:15 |
ジャッジサーバーID (参考情報) |
judge3 / 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>using namespace std;using int64 = long long;const int mod = 998244353;const int64 infll = (1LL << 62) - 1;const int inf = (1 << 30) - 1;struct IoSetup {IoSetup() {cin.tie(nullptr);ios::sync_with_stdio(false);cout << fixed << setprecision(10);cerr << fixed << setprecision(10);}} iosetup;template< typename T1, typename T2 >ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {os << p.first << " " << p.second;return os;}template< typename T1, typename T2 >istream &operator>>(istream &is, pair< T1, T2 > &p) {is >> p.first >> p.second;return is;}template< typename T >ostream &operator<<(ostream &os, const vector< T > &v) {for(int i = 0; i < (int) v.size(); i++) {os << v[i] << (i + 1 != v.size() ? " " : "");}return os;}template< typename T >istream &operator>>(istream &is, vector< T > &v) {for(T &in : v) is >> in;return is;}template< typename T1, typename T2 >inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }template< typename T1, typename T2 >inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }template< typename T = int64 >vector< T > make_v(size_t a) {return vector< T >(a);}template< typename T, typename... Ts >auto make_v(size_t a, Ts... ts) {return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));}template< typename T, typename V >typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {t = v;}template< typename T, typename V >typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {for(auto &e : t) fill_v(e, v);}template< typename F >struct FixPoint : F {FixPoint(F &&f) : F(forward< F >(f)) {}template< typename... Args >decltype(auto) operator()(Args &&... args) const {return F::operator()(*this, forward< Args >(args)...);}};template< typename F >inline decltype(auto) MFP(F &&f) {return FixPoint< F >{forward< F >(f)};}template< typename Mint >struct NumberTheoreticTransformFriendlyModInt {vector< int > rev;vector< Mint > rts;int base, max_base;Mint root;NumberTheoreticTransformFriendlyModInt() : base(1), rev{0, 1}, rts{0, 1} {const int mod = Mint::get_mod();assert(mod >= 3 && mod % 2 == 1);auto tmp = mod - 1;max_base = 0;while(tmp % 2 == 0) tmp >>= 1, max_base++;root = 2;while(root.pow((mod - 1) >> 1) == 1) root += 1;assert(root.pow(mod - 1) == 1);root = root.pow((mod - 1) >> max_base);}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) {Mint z = root.pow(1 << (max_base - 1 - base));for(int i = 1 << (base - 1); i < (1 << base); i++) {rts[i << 1] = rts[i];rts[(i << 1) + 1] = rts[i] * z;}++base;}}void ntt(vector< Mint > &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++) {Mint z = a[i + j + k] * rts[j + k];a[i + j + k] = a[i + j] - z;a[i + j] = a[i + j] + z;}}}}void intt(vector< Mint > &a) {const int n = (int) a.size();ntt(a);reverse(a.begin() + 1, a.end());Mint inv_sz = Mint(1) / n;for(int i = 0; i < n; i++) a[i] *= inv_sz;}vector< Mint > multiply(vector< Mint > a, vector< Mint > 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);Mint inv_sz = Mint(1) / sz;for(int i = 0; i < sz; i++) {a[i] *= b[i] * inv_sz;}reverse(a.begin() + 1, a.end());ntt(a);a.resize(need);return a;}};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-() 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 ret(1), mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}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 modint = ModInt< mod >;int64_t mod_pow(int64_t x, int64_t n, int64_t mod) {int64_t ret = 1;while(n > 0) {if(n & 1) (ret *= x) %= mod;(x *= x) %= mod;n >>= 1;}return ret;}map< int64_t, int > prime_factor(int64_t n) {map< int64_t, int > ret;for(int64_t i = 2; i * i <= n; i++) {while(n % i == 0) {ret[i]++;n /= i;}}if(n != 1) ret[n] = 1;return (ret);}int main() {int P;cin >> P;vector< modint > A(P), B(P);for(int i = 1; i < P; i++) cin >> A[i];for(int i = 1; i < P; i++) cin >> B[i];if(P == 2) {cout << A[1] * B[1] << endl;return 0;}int root = 2;auto d = prime_factor(P - 1);for(; root < P; root++) {bool ok = true;for(const auto &p : d) {const uint q = p.first;const uint per = (P - 1) / q;if(mod_pow(root, per, P) == 1) {ok = false;break;}}if(ok) { break; }}vector< modint > C(P - 1), D(P - 1);int tap = 1;for(int i = 0; i < P - 1; i++) {C[i] = A[tap];D[i] = B[tap];(tap *= root) %= P;}NumberTheoreticTransformFriendlyModInt< modint > ntt;auto E = ntt.multiply(C, D);tap = 1;vector< modint > F(P - 1);for(int i = 0; i < E.size(); i++) {F[tap - 1] += E[i];(tap *= root) %= P;}cout << F << endl;}