結果
| 問題 | No.931 Multiplicative Convolution |
| ユーザー |
 lumc_
|
| 提出日時 | 2019-11-22 22:28:49 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 769 ms / 2,000 ms |
| コード長 | 12,207 bytes |
| コンパイル時間 | 1,248 ms |
| コンパイル使用メモリ | 119,388 KB |
| 実行使用メモリ | 14,592 KB |
| 最終ジャッジ日時 | 2024-10-11 04:14:07 |
| 合計ジャッジ時間 | 7,221 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 14 |
ソースコード
// includes {{{
#include<iostream>
#include<iomanip>
#include<algorithm>
#include<vector>
#include<stack>
#include<queue>
#include<map>
#include<set>
#include<tuple>
#include<cmath>
#include<random>
#include<cassert>
#include<bitset>
#include<cstdlib>
// #include<deque>
// #include<multiset>
// #include<cstring>
// #include<bits/stdc++.h>
// }}}
using namespace std;
using ll = long long;
// #undef DEBUG
// #define DEBUG
// DEBUG {{{
#include <array>
#include <deque>
#include <iostream>
#include <list>
#include <queue>
#include <stack>
#include <tuple>
#include <valarray>
#include <vector>
template < int n, class... T >
typename std::enable_if< (n >= sizeof...(T)) >::type __output_tuple(
std::ostream &, std::tuple< T... > const &) {}
template < int n, class... T >
typename std::enable_if< (n < sizeof...(T)) >::type __output_tuple(
std::ostream &os, std::tuple< T... > const &t) {
os << (n == 0 ? "" : ", ") << std::get< n >(t);
__output_tuple< n + 1 >(os, t);
}
template < class... T >
std::ostream &operator<<(std::ostream &os, std::tuple< T... > const &t) {
os << "(";
__output_tuple< 0 >(os, t);
os << ")";
return os;
}
template < class T, class U >
std::ostream &operator<<(std::ostream &os, std::pair< T, U > const &p) {
os << "(" << p.first << ", " << p.second << ")";
return os;
}
template < class T >
std::ostream &operator<<(std::ostream &os, const std::stack< T > &a) {
os << "{";
for(auto tmp = a; tmp.size(); tmp.pop())
os << (a.size() == tmp.size() ? "" : ", ") << tmp.top();
os << "}";
return os;
}
template < class T, class Container, class Compare >
std::ostream &operator<<(std::ostream &os,
std::priority_queue< T, Container, Compare > a) {
os << "{ (top) ";
while(a.size()) os << a.top() << (a.size() == 1 ? "" : ", "), a.pop();
os << " }";
return os;
}
template < class T, class Container >
std::ostream &operator<<(std::ostream &os, std::queue< T, Container > a) {
os << "{ ";
while(a.size()) os << a.front() << (a.size() == 1 ? "" : ", "), a.pop();
os << " }";
return os;
}
#ifdef DEBUG
#if !defined(DEBUG_OUT)
#define DEBUG_OUT std::cerr
#endif
#define dump(...) \
[&]() { \
auto __debug_tap = std::make_tuple(__VA_ARGS__); \
DEBUG_OUT << "[" << __LINE__ << "] " << #__VA_ARGS__ << " = " << __debug_tap \
<< std::endl; \
}()
template < class T >
inline void dump2D(T &d, size_t sizey, size_t sizex) {
for(size_t i = 0; i < sizey; i++) {
DEBUG_OUT << "\t";
for(size_t j = 0; j < sizex; j++)
DEBUG_OUT << d[i][j] << (j + 1 == sizex ? "" : "\t");
DEBUG_OUT << std::endl;
}
}
template < class T >
inline void dump1D(T &d, size_t sizey) {
for(size_t i = 0; i < sizey; i++) {
DEBUG_OUT << d[i] << (i + 1 == sizey ? "" : " ");
}
DEBUG_OUT << std::endl;
}
template <
class T, class = typename std::iterator_traits< decltype(begin(T())) >::value_type,
class = typename std::enable_if< !std::is_same< T, std::string >::value >::type >
std::ostream &operator<<(std::ostream &os, const T &a) {
os << "{";
for(auto ite = begin(a); ite != end(a); ++ite)
os << (ite == begin(a) ? "" : ", ") << *ite;
os << "}";
return os;
}
#else
#define dump(...) ((void) 42)
#define dump2D(...) ((void) 42)
#define dump1D(...) ((void) 42)
template <
class T, class = typename std::iterator_traits< decltype(begin(T())) >::value_type,
class = typename std::enable_if< !std::is_same< T, std::string >::value >::type >
std::ostream &operator<<(std::ostream &os, const T &a) {
for(auto ite = begin(a); ite != end(a); ++ite)
os << (ite == begin(a) ? "" : " ") << *ite;
return os;
}
#endif
// }}}
// MAX_N is max size of OUTPUT, DOUBLED INPUT
// MAX_RES_VALUE = MAX_VALUE^2 * MAX_N
// if MAX_N > 2^20, comment out primes!
// NTT {{{
#include <cassert>
#include <cstdint>
#include <vector>
namespace NTT {
using uint = uint_fast32_t;
// NTT_PRIMES {{{
constexpr ll NTT_PRIMES[][2] = {
{1224736769, 3}, // 2^24 * 73 + 1,
{1053818881, 7}, // 2^20 * 3 * 5 * 67 + 1
{1051721729, 6}, // 2^20 * 17 * 59 + 1
{1045430273, 3}, // 2^20 * 997 + 1
{1012924417, 5}, // 2^21 * 3 * 7 * 23 + 1
{1007681537, 3}, // 2^20 * 31^2 + 1
{1004535809, 3}, // 2^21 * 479 + 1
{998244353, 3}, // 2^23 * 7 * 17 + 1
{985661441, 3}, // 2^22 * 5 * 47 + 1
{976224257, 3}, // 2^20 * 7^2 * 19 + 1
{975175681, 17}, // 2^21 * 3 * 5 * 31 + 1
{962592769, 7}, // 2^21 * 3^3 * 17 + 1
{950009857, 7}, // 2^21 * 4 * 151 + 1
{943718401, 7}, // 2^22 * 3^2 * 5^2 + 1
{935329793, 3}, // 2^22 * 223 + 1
{924844033, 5}, // 2^21 * 3^2 * 7^2 + 1
{469762049, 3}, // 2^26 * 7 + 1
{167772161, 3}, // 2^25 * 5 + 1
};
// }}}
// general math {{{
ll extgcd(ll a, ll b, ll &x, ll &y) {
ll d;
return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
: (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
}
ll modinv(ll a, ll mod) {
ll x, y;
extgcd(a, mod, x, y);
x %= mod;
return x < 0 ? x + mod : x;
}
ll modpow(ll a, ll b, ll mod) {
ll r = 1;
a %= mod;
while(b) {
if(b & 1) r = r * a % mod;
a = a * a % mod;
b >>= 1;
}
return r;
}
// }}}
// NTT Core {{{
template < int MAX_H >
struct Pool {
static ll *tmp, *A, *B;
};
template < int MAX_H >
ll *Pool< MAX_H >::tmp = new ll[1 << MAX_H];
template < int MAX_H >
ll *Pool< MAX_H >::A = new ll[1 << MAX_H];
template < int MAX_H >
ll *Pool< MAX_H >::B = new ll[1 << MAX_H];
template < int MAX_H, ll mod, ll primitive >
class Core {
public:
static_assert((mod & ((1 << MAX_H) - 1)) == 1, "mod is too small; comment out");
// ord zetaList[i] = 2^(i + 1)
ll zetaList[MAX_H], zetaInvList[MAX_H];
// constexpr
Core() {
zetaList[MAX_H - 1] = modpow(primitive, (mod - 1) / (1 << MAX_H), mod);
zetaInvList[MAX_H - 1] = modinv(zetaList[MAX_H - 1], mod);
for(int ih = MAX_H - 2; ih >= 0; --ih) {
zetaList[ih] = zetaList[ih + 1] * zetaList[ih + 1] % mod;
zetaInvList[ih] = zetaInvList[ih + 1] * zetaInvList[ih + 1] % mod;
}
}
void fft(ll *a, uint n, uint nh, bool inverse) const {
ll *tmp = Pool< MAX_H >::tmp;
uint mask = n - 1;
for(uint i = n >> 1, ih = nh - 1; i >= 1; i >>= 1, --ih) {
ll zeta = inverse ? zetaInvList[nh - 1 - ih] : zetaList[nh - 1 - ih];
ll powZeta = 1;
for(uint j = 0; j < n; j += i) {
for(uint k = 0; k < i; ++k) {
tmp[j | k] =
(a[((j << 1) & mask) | k] + powZeta * a[(((j << 1) | i) & mask) | k]) % mod;
}
powZeta = powZeta * zeta % mod;
}
swap(a, tmp);
}
if(nh & 1) {
swap(a, tmp);
for(uint i = 0; i < n; ++i) a[i] = tmp[i];
}
if(inverse) {
ll invN = modinv(n, mod);
for(uint i = 0; i < n; ++i) a[i] = a[i] * invN % mod;
}
}
vector< ll > conv(const vector< ll > &a, const vector< ll > &b) const {
uint t = a.size() + b.size() - 1;
uint n = 1, nh = 0;
while(n < t) n <<= 1, ++nh;
return convStrict(a, b, n, nh);
}
vector< ll > convStrict(const vector< ll > &a, const vector< ll > &b, uint n,
uint nh) const {
ll *A = Pool< MAX_H >::A, *B = Pool< MAX_H >::B;
for(uint i = 0; i < n; ++i) A[i] = B[i] = 0;
copy(a.begin(), a.end(), A);
copy(b.begin(), b.end(), B);
fft(A, n, nh, 0), fft(B, n, nh, 0);
for(uint i = 0; i < n; ++i) A[i] = A[i] * B[i] % mod;
fft(A, n, nh, 1);
return vector< ll >(A, A + n);
}
};
// }}}
// Convolution With Garner {{{
template < int MAX_H, int I >
class ConvolutionWithGarnerCore {
public:
static void conv_for(uint n, uint nh, const vector< ll > &a, const vector< ll > &b,
vector< ll > &mods, vector< ll > &coeffs,
vector< vector< ll > > &constants) {
static const Core< MAX_H, NTT_PRIMES[I][0], NTT_PRIMES[I][1] > ntt;
auto c = ntt.convStrict(a, b, n, nh);
mods[I] = NTT_PRIMES[I][0];
ConvolutionWithGarnerCore< MAX_H, I - 1 >::conv_for(
n, nh, a, b, mods, coeffs, constants);
// garner
for(size_t i = 0; i < c.size(); ++i) {
ll v = (c[i] - constants[I][i]) * modinv(coeffs[I], mods[I]) % mods[I];
if(v < 0) v += mods[I];
for(size_t j = I + 1; j < mods.size(); ++j) {
constants[j][i] = (constants[j][i] + coeffs[j] * v) % mods[j];
}
}
for(size_t j = I + 1; j < mods.size(); ++j) {
coeffs[j] = (coeffs[j] * mods[I]) % mods[j];
}
}
};
template < int MAX_H >
class ConvolutionWithGarnerCore< MAX_H, -1 > {
public:
static void conv_for(uint, uint, const vector< ll > &, const vector< ll > &,
vector< ll > &, vector< ll > &, vector< vector< ll > > &) {}
};
template < int MAX_H >
class ConvolutionWithGarner {
public:
template < int USE >
static vector< ll > conv(const vector< ll > &a, const vector< ll > &b, ll mod) {
static_assert(USE >= 1, "USE must be positive");
static_assert(USE <= sizeof(NTT_PRIMES) / sizeof(*NTT_PRIMES), "USE is too big");
uint nt = a.size() + b.size() - 1;
uint n = 1, nh = 0;
while(n < nt) n <<= 1, ++nh;
vector< ll > coeffs(USE + 1, 1);
vector< vector< ll > > constants(USE + 1, vector< ll >(n));
vector< ll > mods(USE + 1, mod);
ConvolutionWithGarnerCore< MAX_H, USE - 1 >::conv_for(
n, nh, a, b, mods, coeffs, constants);
return constants.back();
}
};
// }}}
} // namespace NTT
// }}}
// 1st param is MAX_H
NTT::Core< 18, NTT::NTT_PRIMES[0][0], NTT::NTT_PRIMES[0][1] > nttBig;
NTT::Core< 18, 998244353, 5 > ntt;
using nttconv = NTT::ConvolutionWithGarner< 18 >;
// nttconv::conv< USE >(a, b, mod)
constexpr ll mod = 998244353;
int a[112345];
int b[112345];
int c[112345];
int modlog[112345];
int modexp[112345];
// O(N^.5)
/// --- divisor {{{ ///
#include <vector>
vector< ll > divisor(ll n) {
vector< ll > res;
for(ll i = 1; i * i <= n; i++) {
if(n % i == 0) {
res.emplace_back(i);
if(i != n / i) res.emplace_back(n / i);
}
}
return res;
}
/// }}}--- ///
/// --- math {{{ ///
ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a % b); }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
ll extgcd(ll a, ll b, ll &x, ll &y) {
ll d;
return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
: (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
}
ll modinv(ll a, ll mod) {
ll x, y;
extgcd(a, mod, x, y);
if(x < 0) x += mod;
return x;
}
ll modpow(ll a, ll b, ll mod) {
ll r = 1;
a %= mod;
while(b) {
if(b & 1) r = r * a % mod;
a = a * a % mod;
b >>= 1;
}
return r;
}
/// }}}--- ///
// O(log p)
/// --- isPrimitive {{{ ///
bool isPrimitive(ll x, ll p) {
auto ds = divisor(p - 1);
for(ll d : ds)
if(d != p - 1) {
if(modpow(x, d, p) == 1) return false;
}
return true;
}
/// }}}--- ///
int main() {
std::ios::sync_with_stdio(false), std::cin.tie(0);
int p;
cin >> p;
for(int i = 1; i < p; i++) cin >> a[i];
for(int i = 1; i < p; i++) cin >> b[i];
int g = 0;
for(int i = 1; i < p; i++) if(isPrimitive(i, p)) g = i;
dump(g);
for(int i = 0, now = 1; i < p - 1; i++, now = (ll) now * g % p) modlog[now] = i, modexp[i] = now;
vector<ll> A(p), B(p);
for(int i = 1; i < p; i++) A[modlog[i]] = a[i];
for(int i = 1; i < p; i++) B[modlog[i]] = b[i];
auto C = ntt.conv(A, B);
for(int i = p - 1; i < C.size(); i++) (C[i % (p - 1)] += C[i]) %= mod;
dump(C);
for(int i = 1; i < p; i++) {
cout << C[modlog[i] % (p - 1)] << " \n"[i == p - 1];
}
return 0;
}