結果

問題 No.931 Multiplicative Convolution
ユーザー haruki_K
提出日時 2019-11-22 23:18:27
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 80 ms / 2,000 ms
コード長 9,126 bytes
コンパイル時間 2,061 ms
コンパイル使用メモリ 177,460 KB
実行使用メモリ 16,204 KB
最終ジャッジ日時 2024-10-11 04:52:54
合計ジャッジ時間 3,885 ms
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
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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

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int i = 0; i < int(n); i++)
#define rep1(i,n) for (int i = 1; i <= int(n); i++)
#define repR(i,n) for (int i = int(n)-1; i >= 0; i--)
#define rep1R(i,n) for (int i = int(n); i >= 1; i--)
#define loop(i,a,B) for (int i = a; i B; i++)
#define loopR(i,a,B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
#ifdef LOCAL
#define dump(...) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] ", dump_impl(#__VA_ARGS__, __VA_ARGS__)
#define say(x) cerr << "[" << __LINE__ << ":" << __FUNCTION__ << "] " << x << endl;
#define debug if (1)
void dump_impl(const char*) { cerr << endl; }
template <class T, class... U> void dump_impl(const char *s, T const& x, U const& ...y) { const char *o = "({[", *e = "]})"; for (int i = 0; *s !=
    '\0'; cerr << *s++) { if (count(o,o+3,*s)) i++; if (count(e,e+3,*s)) i--; if (!i && *s == ',') break; } cerr << " = " << x; if (*s == ',') cerr
    << ", ", s++; dump_impl(s, y...); }
#else
#define dump(...)
#define say(x)
#define debug if (0)
#endif
using ll = long long;
using ld = long double;
#define int ll
#define double ld
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
ostream& operator<<(ostream& os, T const& v) { os << "{"; for (auto const& x : v) os << " " << x; return os << " }"; }
template <class T> istream& operator>>(istream& is, vector<T>& v) { for (auto& x : v) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T,S> const& p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; }
template <size_t i, class T> typename enable_if<i >= tuple_size<T>::value>::type output_tuple(ostream&, T const&) { }
template <size_t i = 0, class T> typename enable_if<i < tuple_size<T>::value>::type
output_tuple(ostream& os, T const& t) { os << (i ? " " : "") << get<i>(t); output_tuple<i+1,T>(os,t); }
template <class... T> ostream& operator<<(ostream& os, tuple<T...> const& t) { return output_tuple(os,t), os; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class T, size_t d> struct vec_impl {
using type = vector<typename vec_impl<T,d-1>::type>;
template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T> constexpr bool chmin(T& x, T const& y) { if (x > y) { x = y; return true; } return false; }
template <class T> constexpr bool chmax(T& x, T const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); }
const ll INF = (1LL<<62)-1; // ~ 4.6e18
// <<<
int powmod (int a, int b, int p) {
int res = 1;
while (b)
if (b & 1)
res = int (res * 1ll * a % p), --b;
else
a = int (a * 1ll * a % p), b >>= 1;
return res;
}
int generator (int p) {
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;
}
// >>> runtime modint
using ll = long long;
class runtime_modint {
using M = runtime_modint;
ll x;
public:
static ll& mod() { static int mod = 0; return mod; }
runtime_modint(ll x = 0) {
assert(mod() > 0); this->x = ((x%=mod()) < 0 ? x+mod() : x);
}
ll val() const { return x; }
bool operator==(M r) const { return x == r.x; }
bool operator!=(M r) const { return x != r.x; }
M operator+() const { return *this; }
M operator-() const { return {mod()-x}; }
M& operator+=(M r) { if ((x += r.x) >= mod()) x -= mod(); return *this; }
M& operator-=(M r) { if ((x += mod()-r.x) >= mod()) x -= mod(); return *this; }
M& operator*=(M r) { (x *= r.x) %= mod(); return *this; }
M operator+(M r) const { return M(*this) += r; }
M operator-(M r) const { return M(*this) -= r; }
M operator*(M r) const { return M(*this) *= r; }
M& operator/=(M r) { return *this *= r.inv(); }
M operator/(M r) const { return *this * r.inv(); }
M pow(ll n) const {
if (n < 0) return inv().pow(-n);
M v = *this, r = 1;
for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
return r;
}
M inv() const {
assert(x != 0);
ll t = 1, v = x, q, r;
while (v != 1) {
q = mod() / v; r = mod() % v;
if (r * 2 < v) {
t *= -q; t %= mod(); v = r;
} else {
t *= q + 1; t %= mod(); v -= r;
}
}
return t;
}
};
ostream& operator<<(ostream& os, runtime_modint r) { return os << r.val(); }
istream& operator>>(istream& is, runtime_modint &r) { ll x; is >> x; r = x; return is; }
using mint = runtime_modint;
// <<<
// https://ei1333.github.io/luzhiled/snippets/math/fast-fourier-transform.html
template< int mod >
struct NumberTheoreticTransform {
vector< int > rev, rts;
int base, max_base, root;
NumberTheoreticTransform() : base(1), rev{0, 1}, rts{0, 1} {
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while(tmp % 2 == 0) tmp >>= 1, max_base++;
root = 2;
while(mod_pow(root, (mod - 1) >> 1) == 1) ++root;
assert(mod_pow(root, mod - 1) == 1);
root = mod_pow(root, (mod - 1) >> max_base);
}
inline int mod_pow(int x, int n) {
int ret = 1;
while(n > 0) {
if(n & 1) ret = mul(ret, x);
x = mul(x, x);
n >>= 1;
}
return ret;
}
inline int inverse(int x) {
return mod_pow(x, mod - 2);
}
inline unsigned add(unsigned x, unsigned y) {
x += y;
if(x >= mod) x -= mod;
return x;
}
inline unsigned mul(unsigned a, unsigned b) {
return 1ull * a * b % (unsigned long long) mod;
}
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) {
int z = mod_pow(root, 1 << (max_base - 1 - base));
for(int i = 1 << (base - 1); i < (1 << base); i++) {
rts[i << 1] = rts[i];
rts[(i << 1) + 1] = mul(rts[i], z);
}
++base;
}
}
void ntt(vector< int > &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++) {
int z = mul(a[i + j + k], rts[j + k]);
a[i + j + k] = add(a[i + j], mod - z);
a[i + j] = add(a[i + j], z);
}
}
}
}
vector< int > multiply(vector< int > a, vector< int > 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);
int inv_sz = inverse(sz);
for(int i = 0; i < sz; i++) {
a[i] = mul(a[i], mul(b[i], inv_sz));
}
reverse(a.begin() + 1, a.end());
ntt(a);
a.resize(need);
return a;
}
};
int32_t main() {
int p; cin >> p;
mint::mod() = p;
int g = generator(p);
vector<int> a(p),b(p);
rep1 (i,p-1) cin >> a[i];
rep1 (i,p-1) cin >> b[i];
vector<int> idx(p-1);
idx[0] = 1;
rep (i,p-2) idx[i+1] = (idx[i]*g) % p;
vector<int> aa(p-1),bb(p-1);
rep (i,p-1) aa[i] = a[idx[i]], bb[i] = b[idx[i]];
NumberTheoreticTransform< 998244353 > ntt;
auto cc = ntt.multiply(aa,bb);
dump(cc);
vector<int> c(p);
rep (i,cc.size()) c[idx[i%(p-1)]] += cc[i];
rep1 (i,p-1) cout << c[i]%998244353 << " ";
cout << endl;
}
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