結果

問題 No.931 Multiplicative Convolution
ユーザー Haar
提出日時 2020-11-07 03:19:40
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 149 ms / 2,000 ms
コード長 9,351 bytes
コンパイル時間 2,479 ms
コンパイル使用メモリ 208,524 KB
最終ジャッジ日時 2025-01-15 21:24:20
ジャッジサーバーID
(参考情報)
judge3 / judge2
このコードへのチャレンジ
(要ログイン)
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

#line 1 "main.cpp"
#include <bits/stdc++.h>
#line 4 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Mint/mint.cpp"
namespace haar_lib {
template <int32_t M>
class modint {
uint32_t val_;
public:
constexpr static auto mod(){return M;}
constexpr modint(): val_(0){}
constexpr modint(int64_t n){
if(n >= M) val_ = n % M;
else if(n < 0) val_ = n % M + M;
else val_ = n;
}
constexpr auto& operator=(const modint &a){val_ = a.val_; return *this;}
constexpr auto& operator+=(const modint &a){
if(val_ + a.val_ >= M) val_ = (uint64_t)val_ + a.val_ - M;
else val_ += a.val_;
return *this;
}
constexpr auto& operator-=(const modint &a){
if(val_ < a.val_) val_ += M;
val_ -= a.val_;
return *this;
}
constexpr auto& operator*=(const modint &a){
val_ = (uint64_t)val_ * a.val_ % M;
return *this;
}
constexpr auto& operator/=(const modint &a){
val_ = (uint64_t)val_ * a.inv().val_ % M;
return *this;
}
constexpr auto operator+(const modint &a) const {return modint(*this) += a;}
constexpr auto operator-(const modint &a) const {return modint(*this) -= a;}
constexpr auto operator*(const modint &a) const {return modint(*this) *= a;}
constexpr auto operator/(const modint &a) const {return modint(*this) /= a;}
constexpr bool operator==(const modint &a) const {return val_ == a.val_;}
constexpr bool operator!=(const modint &a) const {return val_ != a.val_;}
constexpr auto& operator++(){*this += 1; return *this;}
constexpr auto& operator--(){*this -= 1; return *this;}
constexpr auto operator++(int){auto t = *this; *this += 1; return t;}
constexpr auto operator--(int){auto t = *this; *this -= 1; return t;}
constexpr static modint pow(int64_t n, int64_t p){
if(p < 0) return pow(n, -p).inv();
int64_t ret = 1, e = n % M;
for(; p; (e *= e) %= M, p >>= 1) if(p & 1) (ret *= e) %= M;
return ret;
}
constexpr static modint inv(int64_t a){
int64_t b = M, u = 1, v = 0;
while(b){
int64_t t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
u %= M;
if(u < 0) u += M;
return u;
}
constexpr static auto frac(int64_t a, int64_t b){return modint(a) / modint(b);}
constexpr auto pow(int64_t p) const {return pow(val_, p);}
constexpr auto inv() const {return inv(val_);}
friend constexpr auto operator-(const modint &a){return modint(M - a.val_);}
friend constexpr auto operator+(int64_t a, const modint &b){return modint(a) + b;}
friend constexpr auto operator-(int64_t a, const modint &b){return modint(a) - b;}
friend constexpr auto operator*(int64_t a, const modint &b){return modint(a) * b;}
friend constexpr auto operator/(int64_t a, const modint &b){return modint(a) / b;}
friend std::istream& operator>>(std::istream &s, modint &a){s >> a.val_; return s;}
friend std::ostream& operator<<(std::ostream &s, const modint &a){s << a.val_; return s;}
template <int N>
static auto div(){
static auto value = inv(N);
return value;
}
explicit operator int32_t() const noexcept {return val_;}
explicit operator int64_t() const noexcept {return val_;}
};
}
#line 7 "/home/haar/Downloads/kyopro-lib/Mylib/Convolution/ntt_convolution.cpp"
namespace haar_lib {
template <typename T, int PRIM_ROOT, int MAX_SIZE>
class number_theoretic_transform {
public:
using value_type = T;
constexpr static int primitive_root = PRIM_ROOT;
constexpr static int max_size = MAX_SIZE;
private:
const int MAX_POWER_;
std::vector<T> BASE_, INV_BASE_;
public:
number_theoretic_transform():
MAX_POWER_(__builtin_ctz(MAX_SIZE)),
BASE_(MAX_POWER_ + 1),
INV_BASE_(MAX_POWER_ + 1)
{
static_assert((MAX_SIZE & (MAX_SIZE - 1)) == 0, "MAX_SIZE must be power of 2.");
T t = T::pow(PRIM_ROOT, (T::mod() - 1) >> (MAX_POWER_ + 2));
T s = t.inv();
for(int i = MAX_POWER_; --i >= 0;){
t *= t;
s *= s;
BASE_[i] = -t;
INV_BASE_[i] = -s;
}
}
void run(std::vector<T> &f, bool INVERSE = false) const {
const int n = f.size();
assert((n & (n - 1)) == 0 and n <= MAX_SIZE); // 2
if(INVERSE){
for(int b = 1; b < n; b <<= 1){
T w = 1;
for(int j = 0, k = 1; j < n; j += 2 * b, ++k){
for(int i = 0; i < b; ++i){
const auto s = f[i + j];
const auto t = f[i + j + b];
f[i + j] = s + t;
f[i + j + b] = (s - t) * w;
}
w *= INV_BASE_[__builtin_ctz(k)];
}
}
const T t = T::inv(n);
for(auto &x : f) x *= t;
}else{
for(int b = n >> 1; b; b >>= 1){
T w = 1;
for(int j = 0, k = 1; j < n; j += 2 * b, ++k){
for(int i = 0; i < b; ++i){
const auto s = f[i + j];
const auto t = f[i + j + b] * w;
f[i + j] = s + t;
f[i + j + b] = s - t;
}
w *= BASE_[__builtin_ctz(k)];
}
}
}
}
template <typename U>
std::vector<T> convolve(std::vector<U> f, std::vector<U> g) const {
const int m = f.size() + g.size() - 1;
int n = 1;
while(n < m) n *= 2;
std::vector<T> f2(n), g2(n);
for(int i = 0; i < (int)f.size(); ++i) f2[i] = (int64_t)f[i];
for(int i = 0; i < (int)g.size(); ++i) g2[i] = (int64_t)g[i];
run(f2);
run(g2);
for(int i = 0; i < n; ++i) f2[i] *= g2[i];
run(f2, true);
return f2;
}
template <typename U>
std::vector<T> operator()(std::vector<U> f, std::vector<U> g) const {
return convolve(f, g);
}
};
template <typename T>
std::vector<T> convolve_general_mod(std::vector<T> f, std::vector<T> g){
static constexpr int M1 = 167772161, P1 = 3;
static constexpr int M2 = 469762049, P2 = 3;
static constexpr int M3 = 1224736769, P3 = 3;
auto res1 = number_theoretic_transform<modint<M1>, P1, 1 << 20>().convolve(f, g);
auto res2 = number_theoretic_transform<modint<M2>, P2, 1 << 20>().convolve(f, g);
auto res3 = number_theoretic_transform<modint<M3>, P3, 1 << 20>().convolve(f, g);
const int n = res1.size();
std::vector<T> ret(n);
const int64_t M12 = (int64_t)modint<M2>::inv(M1);
const int64_t M13 = (int64_t)modint<M3>::inv(M1);
const int64_t M23 = (int64_t)modint<M3>::inv(M2);
for(int i = 0; i < n; ++i){
const int64_t r[3] = {(int64_t)res1[i], (int64_t)res2[i], (int64_t)res3[i]};
const int64_t t0 = r[0] % M1;
const int64_t t1 = (r[1] - t0 + M2) * M12 % M2;
const int64_t t2 = ((r[2] - t0 + M3) * M13 % M3 - t1 + M3) * M23 % M3;
ret[i] = T(t0) + T(t1) * M1 + T(t2) * M1 * M2;
}
return ret;
}
}
#line 3 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Mod/mod_pow.cpp"
namespace haar_lib {
constexpr int64_t mod_pow(int64_t n, int64_t p, int64_t m){
int64_t ret = 1;
while(p > 0){
if(p & 1) (ret *= n) %= m;
(n *= n) %= m;
p >>= 1;
}
return ret;
}
}
#line 3 "/home/haar/Downloads/kyopro-lib/Mylib/Number/Prime/primitive_root.cpp"
namespace haar_lib {
constexpr int primitive_root(int p){
int pf[30] = {};
int k = 0;
{
int n = p - 1;
for(int64_t i = 2; i * i <= p; ++i){
if(n % i == 0){
pf[k++] = i;
while(n % i == 0) n /= i;
}
}
if(n != 1)
pf[k++] = n;
}
for(int g = 2; g <= p; ++g){
bool ok = true;
for(int i = 0; i < k; ++i){
if(mod_pow(g, (p - 1) / pf[i], p) == 1){
ok = false;
break;
}
}
if(not ok) continue;
return g;
}
return -1;
}
}
#line 5 "/home/haar/Downloads/kyopro-lib/Mylib/IO/join.cpp"
namespace haar_lib {
template <typename Iter>
std::string join(Iter first, Iter last, std::string delim = " "){
std::stringstream s;
for(auto it = first; it != last; ++it){
if(it != first) s << delim;
s << *it;
}
return s.str();
}
}
#line 8 "main.cpp"
#ifdef DEBUG
#include <Mylib/Debug/debug.cpp>
#else
#define dump(...)
#endif
using namespace haar_lib;
constexpr int mod = 998244353;
constexpr int prim_root = primitive_root(mod);
using mint = modint<mod>;
using NTT = number_theoretic_transform<mint, prim_root, 1 << 20>;
const static auto ntt = NTT();
int main(){
std::cin.tie(0);
std::ios::sync_with_stdio(false);
int P; std::cin >> P;
std::vector<mint> A(P), B(P);
for(int i = 1; i < P; ++i) std::cin >> A[i];
for(int i = 1; i < P; ++i) std::cin >> B[i];
int p_root = primitive_root(P);
std::vector<int> index(P);
{
int s = 1;
for(int i = 0; i < P; ++i){
index[s] = i;
(s *= p_root) %= P;
}
}
std::vector<mint> a(P), b(P);
for(int i = 1; i < P; ++i){
a[index[i]] = A[i];
b[index[i]] = B[i];
}
auto c = ntt(a, b);
//dump(p_root, a, b, c);
std::vector<mint> ans(P);
for(int i = 0; i < (int)c.size(); ++i){
ans[mod_pow(p_root, i, P)] += c[i];
}
std::cout << join(ans.begin() + 1, ans.end()) << "\n";
return 0;
}
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