結果

問題 No.931 Multiplicative Convolution
ユーザー ei1333333
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
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 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;
}
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