結果

問題 No.931 Multiplicative Convolution
ユーザー satashun
提出日時 2020-04-20 21:18:40
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 151 ms / 2,000 ms
コード長 6,743 bytes
コンパイル時間 2,589 ms
コンパイル使用メモリ 203,560 KB
最終ジャッジ日時 2025-01-09 22:01:11
ジャッジサーバーID
(参考情報)
judge5 / judge3
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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 ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define ALL(c) (c).begin(), (c).end()
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }
template <class T, class U>
void chmin(T& t, const U& u) {
if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
if (t < u) t = u;
}
template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
os << "(" << p.first << "," << p.second << ")";
return os;
}
template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
os << "{";
rep(i, v.size()) {
if (i) os << ",";
os << v[i];
}
os << "}";
return os;
}
#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << H;
debug_out(T...);
}
#define debug(...) \
cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
template <unsigned int MOD>
struct ModInt {
using uint = unsigned int;
using ull = unsigned long long;
using M = ModInt;
uint v;
ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
M& set_norm(uint _v) { //[0, MOD * 2)->[0, MOD)
v = (_v < MOD) ? _v : _v - MOD;
return *this;
}
explicit operator bool() const { return v != 0; }
M operator+(const M& a) const { return M().set_norm(v + a.v); }
M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
M operator/(const M& a) const { return *this * a.inv(); }
M& operator+=(const M& a) { return *this = *this + a; }
M& operator-=(const M& a) { return *this = *this - a; }
M& operator*=(const M& a) { return *this = *this * a; }
M& operator/=(const M& a) { return *this = *this / a; }
M operator-() const { return M() - *this; }
M& operator++(int) { return *this = *this + 1; }
M& operator--(int) { return *this = *this - 1; }
M pow(ll n) const {
if (n < 0) return inv().pow(-n);
M x = *this, res = 1;
while (n) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
M inv() const {
ll a = v, b = MOD, p = 1, q = 0, t;
while (b != 0) {
t = a / b;
swap(a -= t * b, b);
swap(p -= t * q, q);
}
return M(p);
}
bool operator==(const M& a) const { return v == a.v; }
bool operator!=(const M& a) const { return v != a.v; }
friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
static int get_mod() { return MOD; }
};
using Mint = ModInt<998244353>;
// depend on ModInt, must use NTT friendly mod
template <class D>
struct NumberTheoreticTransform {
D root;
V<D> roots = {0, 1};
V<int> rev = {0, 1};
int base = 1, max_base = -1;
void init() {
int mod = D::get_mod();
int tmp = mod - 1;
max_base = 0;
while (tmp % 2 == 0) {
tmp /= 2;
max_base++;
}
root = 2;
while (true) {
if (root.pow(1 << max_base).v == 1) {
if (root.pow(1 << (max_base - 1)).v != 1) {
break;
}
}
root++;
}
}
void ensure_base(int nbase) {
if (max_base == -1) init();
if (nbase <= base) return;
assert(nbase <= max_base);
rev.resize(1 << nbase);
for (int i = 0; i < (1 << nbase); ++i) {
rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
}
roots.resize(1 << nbase);
while (base < nbase) {
D z = root.pow(1 << (max_base - 1 - base));
for (int i = 1 << (base - 1); i < (1 << base); ++i) {
roots[i << 1] = roots[i];
roots[(i << 1) + 1] = roots[i] * z;
}
++base;
}
}
void ntt(V<D>& a, bool inv = false) {
int n = 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++) {
D x = a[i + j];
D y = a[i + j + k] * roots[j + k];
a[i + j] = x + y;
a[i + j + k] = x - y;
}
}
}
int v = D(n).inv().v;
if (inv) {
reverse(a.begin() + 1, a.end());
for (int i = 0; i < n; i++) {
a[i] *= v;
}
}
}
V<D> mul(V<D> a, V<D> b) {
int s = a.size() + b.size() - 1;
int nbase = 1;
while ((1 << nbase) < s) nbase++;
int sz = 1 << nbase;
a.resize(sz);
b.resize(sz);
ntt(a);
ntt(b);
for (int i = 0; i < sz; i++) {
a[i] *= b[i];
}
ntt(a, true);
a.resize(s);
return a;
}
};
int main() {
NumberTheoreticTransform<Mint> ntt;
ntt.init();
int P;
cin >> P;
V<int> A(P), B(P);
for (int i = 1; i < P; ++i) cin >> A[i];
for (int i = 1; i < P; ++i) cin >> B[i];
int g = 1;
{
while (true) {
ll t = 1;
int ord = 0;
while (true) {
t = t * g % P;
++ord;
if (t == 1) {
break;
}
}
if (ord == P - 1) {
break;
}
++g;
}
}
V<Mint> va(P - 1), vb(P - 1);
int x = 1;
rep(i, P - 1) {
va[i] = A[x];
vb[i] = B[x];
x = (ll)x * g % P;
}
auto vec = ntt.mul(va, vb);
rep(i, vec.size()) if (i >= P - 1) { vec[i - (P - 1)] += vec[i]; }
V<Mint> ans(P);
x = 1;
rep(i, P - 1) {
ans[x] = vec[i];
x = (ll)x * g % P;
}
rep(i, P) if (i) { cout << ans[i] << (i == P - 1 ? '\n' : ' '); }
return 0;
}
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