結果
| 問題 | No.931 Multiplicative Convolution |
| ユーザー |
 satanic
|
| 提出日時 | 2019-11-23 00:17:43 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 167 ms / 2,000 ms |
| コード長 | 9,586 bytes |
| コンパイル時間 | 1,869 ms |
| コンパイル使用メモリ | 146,344 KB |
| 実行使用メモリ | 22,704 KB |
| 最終ジャッジ日時 | 2024-10-11 06:36:44 |
| 合計ジャッジ時間 | 4,374 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / 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
// need
#include <iostream>
#include <algorithm>
// data structure
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <complex>
//#include <deque>
#include <valarray>
#include <unordered_map>
#include <unordered_set>
#include <array>
// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>
#include <fstream>
// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest& ...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w_=0; w_<n; ++w_){MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest& ...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest& ...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& R:c)for(auto& w:R)std::cin>>w;
// output
template<typename T>void MACRO_OUT(const T t) { std::cout << t; }
template<typename First, typename...Rest>void MACRO_OUT(const First first, const Rest...rest) { std::cout << first << " "; MACRO_OUT(rest...); }
#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define FOUT(n, dist) std::cout<<std::fixed<<std::setprecision(n)<<(dist);
#define SOUT(n, c, dist) std::cout<<std::setw(n)<<std::setfill(c)<<(dist);
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(w, n) std::cout<<(w + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(dist) {std::cerr << #dist << "\t: " << (dist) << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t: ";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t: ";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";}
#define SHOWSTACK(a) {auto tmp(a);std::cerr << #a << "\t: ";while(!tmp.empty()){std::cerr << tmp.top() << " ";tmp.pop();}std::cerr << "\n";}
// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(w, a, n) for(int w=(a);w<(n);++w)
#define RFOR(w, a, n) for(int w=(n)-1;w>=(a);--w)
#define REP(w, n) for(int w=0;w<int(n);++w)
#define RREP(w, n) for(int w=int(n)-1;w>=0;--w)
#define IN(a, x, b) (a<=x && x<b)
template<class T> inline T CHMAX(T & a, const T b) { return a = (a < b) ? b : a; }
template<class T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
// test
template<class T> using V = std::vector<T>;
template<class T> using VV = V<V<T>>;
template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
os << "(" << p.first << ", " << p.second << ")"; return os;
}
// type/const
#define int ll
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = (1 << 30) - 1; // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60; // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-10;
constexpr int MOD = 998244353;
constexpr double PI = 3.141592653589793238462643383279;
template<class T, size_t N> void FILL(T(&a)[N], const T & val) { for (auto& x : a) x = val; }
template<class ARY, size_t N, size_t M, class T> void FILL(ARY(&a)[N][M], const T & val) { for (auto& b : a) FILL(b, val); }
template<class T> void FILL(std::vector<T> & a, const T & val) { for (auto& x : a) x = val; }
template<class ARY, class T> void FILL(std::vector<std::vector<ARY>> & a, const T & val) { for (auto& b : a) FILL(b, val); }
// ------------>8------------------------------------->8------------
ll powMod(ll n, ll p, ll mod) {
n %= mod;
ll res = 1;
while (p) {
if (p & 1) res *= n, res %= mod;
n *= n, n %= mod;
p >>= 1;
}
return res;
}
int generator(int p) {
std::vector<int> fact;
int phi = p - 1, n = phi;
for (int i = 2; i * i <= n; ++i)
if (n % i == 0) {
fact.push_back(i);
while (n % i == 0)
n /= i;
}
if (n > 1)
fact.push_back(n);
for (int res = 2; res <= p; ++res) {
bool ok = true;
for (size_t i = 0; i < fact.size() && ok; ++i)
ok &= powMod(res, phi / fact[i], p) != 1;
if (ok) return res;
}
return -1;
}
// find x such that g^x == y (mod p)
int BabyStepGiantStep(int p, int g, int y) {
int m = std::ceil(std::sqrt(p));
std::unordered_map<int, int> mp; mp.reserve(m);
ll gj = 1;
for (int j = 0; j < m; ++j) {
mp[gj] = j;
(gj *= g) %= p;
}
ll gm = powMod(g, p - 1 - m, p);
ll ga = y;
for (int i = 0; i < m; ++i) {
auto it = mp.find(ga);
if (it != mp.end()) return i * m + it->second;
(ga *= gm) %= p;
}
return -1;
}
// Description: 整数列a[i],b[i]から列c[k]=sum{a[i]*b[k-i]}を生成する.任意modに対応.O(NlogN).
namespace NTT {
std::vector<int> tmp;
size_t sz = 1;
inline int powMod(int n, int p, int m) {
int res = 1;
while (p) {
if (p & 1) res = (ll)res * n % m;
n = (ll)n * n % m;
p >>= 1;
}
return (int)res;
}
inline int invMod(int n, int m) {
return powMod(n, m - 2, m);
}
template <int Mod, int PrimitiveRoot>
struct NTTPart {
static std::vector<int> ntt(std::vector<int> a, bool inv = false) {
size_t mask = sz - 1;
size_t p = 0;
for (size_t i = sz >> 1; i >= 1; i >>= 1) {
auto& cur = (p & 1) ? tmp : a;
auto& nex = (p & 1) ? a : tmp;
int e = powMod(PrimitiveRoot, (Mod - 1) / sz * i, Mod);
if (inv) e = invMod(e, Mod);
int w = 1;
for (size_t j = 0; j < sz; j += i) {
for (size_t k = 0; k < i; ++k) {
nex[j + k] = (cur[((j << 1) & mask) + k] + (ll)w * cur[(((j << 1) + i) & mask) + k]) % Mod;
}
w = (ll)w * e % Mod;
}
++p;
}
if (p & 1) std::swap(a, tmp);
if (inv) {
int invSz = invMod(sz, Mod);
for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * invSz % Mod;
}
return a;
}
static std::vector<int> mul(std::vector<int> a, std::vector<int> b) {
a = ntt(a);
b = ntt(b);
for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * b[i] % Mod;
a = ntt(a, true);
return a;
}
};
constexpr int M[] = { 1224736769, 469762049, 167772161 };
constexpr int PR[] = { 3, 3, 3 };
constexpr int NTT_CONVOLUTION_TIME = 3;
/*
X := max(a)*max(b)*min(|a|, |b|) のとき,
NTT_CONVOLUTION_TIME <- 1: X < 1224736769 = 1.2*10^ 9 ~ 2^30
NTT_CONVOLUTION_TIME <- 2: X < 575334854091079681 = 5.8*10^17 ~ 2^59
NTT_CONVOLUTION_TIME <- 3: X < 2^86 (32bit * 32bit * 10^7くらいまで)
*/
inline void garner(std::vector<int> * c, int mod) {
if (NTT_CONVOLUTION_TIME == 1) {
for (auto& x : c[0]) x %= mod;
}
else if (NTT_CONVOLUTION_TIME == 2) {
const int r01 = invMod(M[0], M[1]);
for (size_t i = 0; i < sz; ++i) {
c[1][i] = (c[1][i] - c[0][i]) * (ll)r01 % M[1];
if (c[1][i] < 0) c[1][i] += M[1];
c[0][i] = (c[0][i] + (ll)c[1][i] * M[0]) % mod;
}
}
else if (NTT_CONVOLUTION_TIME == 3) {
const int R01 = invMod(M[0], M[1]);
const int R02 = invMod(M[0], M[2]);
const int R12 = invMod(M[1], M[2]);
const int M01 = (ll)M[0] * M[1] % mod;
for (size_t i = 0; i < sz; ++i) {
c[1][i] = (c[1][i] - c[0][i]) * (ll)R01 % M[1];
if (c[1][i] < 0) c[1][i] += M[1];
c[2][i] = ((c[2][i] - c[0][i]) * (ll)R02 % M[2] - c[1][i]) * R12 % M[2];
if (c[2][i] < 0) c[2][i] += M[2];
c[0][i] = (c[0][i] + (ll)c[1][i] * M[0] + (ll)c[2][i] * M01) % mod;
}
}
}
std::vector<int> mul(std::vector<int> a, std::vector<int> b, int mod) {
for (auto& x : a) x %= mod;
for (auto& x : b) x %= mod;
size_t m = a.size() + b.size() - 1;
sz = 1;
while (m > sz) sz <<= 1;
tmp.resize(sz);
a.resize(sz, 0);
b.resize(sz, 0);
std::vector<int> c[NTT_CONVOLUTION_TIME];
if (NTT_CONVOLUTION_TIME >= 1) c[0] = NTTPart<M[0], PR[0]>::mul(a, b);
if (NTT_CONVOLUTION_TIME >= 2) c[1] = NTTPart<M[1], PR[1]>::mul(a, b);
if (NTT_CONVOLUTION_TIME >= 3) c[2] = NTTPart<M[2], PR[2]>::mul(a, b);
for (auto& v : c) v.resize(m);
garner(c, mod);
return c[0];
}
}; // !!! CHECK NTT_CONVOLUTION_TIME !!!
signed main() {
INIT;
VAR(int, p);
VEC(int, a, p - 1);
VEC(int, b, p - 1);
a.insert(a.begin(), 0);
b.insert(b.begin(), 0);
int g = generator(p);
V<int> A(p - 1), B(p - 1);
{
int t = 1;
REP(i, p - 1) {
A[i] = a[t];
B[i] = b[t];
(t *= g) %= p;
}
}
auto C = NTT::mul(A, B, MOD);
{
FOR(i, p - 1, C.size()) {
(C[i % (p - 1)] += C[i]) %= MOD;
C[i] = 0;
}
}
V<int> c(p, 0);
{
int t = 1;
REP(i, p - 1) {
c[t] = C[i];
(t *= g) %= p;
}
}
FOR(i, 1, p) {
OUT(c[i])SPBR(i, p)
}
return 0;
}