結果
問題 | No.931 Multiplicative Convolution |
ユーザー |
|
提出日時 | 2019-11-23 06:46:47 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 72 ms / 2,000 ms |
コード長 | 4,685 bytes |
コンパイル時間 | 1,989 ms |
コンパイル使用メモリ | 183,816 KB |
実行使用メモリ | 12,080 KB |
最終ジャッジ日時 | 2024-10-11 06:46:34 |
合計ジャッジ時間 | 4,079 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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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
#include <bits/stdc++.h>using namespace std;using ll = long long;#define rep(i, n) for (int i = 0; i < (n); i++)#define repr(i, n) for (int i = (n) - 1; i >= 0; i--)#define repe(i, l, r) for (int i = (l); i < (r); i++)#define reper(i, l, r) for (int i = (r) - 1; i >= (l); i--)#define repi(i, l, r) for (int i = (l); i <= (r); i++)#define repir(i, l, r) for (int i = (r); i >= (l); i--)#define range(a) a.begin(), a.end()void initio() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); }constexpr int MOD = 998244353;constexpr int ROOT = 3;class mint {int n;public:mint(int n_ = 0) : n(n_) {}explicit operator int() { return n; }friend mint operator-(mint a) { return -a.n + MOD * (a.n != 0); }friend mint operator+(mint a, mint b) { int x = a.n + b.n; return x - (x >= MOD) * MOD; }friend mint operator-(mint a, mint b) { int x = a.n - b.n; return x + (x < 0) * MOD; }friend mint operator*(mint a, mint b) { return (long long)a.n * b.n % MOD; }friend mint &operator+=(mint &a, mint b) { return a = a + b; }friend mint &operator-=(mint &a, mint b) { return a = a - b; }friend mint &operator*=(mint &a, mint b) { return a = a * b; }friend bool operator==(mint a, mint b) { return a.n == b.n; }friend bool operator!=(mint a, mint b) { return a.n != b.n; }friend istream &operator>>(istream &i, mint &a) { return i >> a.n; }friend ostream &operator<<(ostream &o, mint a) { return o << a.n; }};mint modpow(mint a, long long b) {mint res = 1;while (b > 0) {if (b & 1) res *= a;a *= a;b >>= 1;}return res;}int modpow2(int a, long long b, int p) {int res = 1;while (b > 0) {if (b & 1) res = (ll)res * a % p;a = (ll)a * a % p;b >>= 1;}return res;}mint modinv(mint n) {int a = (int)n, b = MOD;int s = 1, t = 0;while (b != 0) {int q = a / b;a -= q * b;s -= q * t;swap(a, b);swap(s, t);}return s >= 0 ? s : s + MOD;}template<int N>struct NTT {mint rots[N];NTT() {mint w = modpow(ROOT, (MOD - 1) / N);mint ws = 1;for (int i = 0; i < N / 2; i++) {rots[i + N / 2] = ws;ws *= w;}for (int i = N / 2 - 1; i >= 1; i--) {rots[i] = rots[i * 2];}}void ntt(vector<mint> &a) {const int n = a.size();int i = 0;for (int j = 1; j < n - 1; j++) {for (int k = n >> 1; k > (i ^= k); k >>= 1);if (j < i) swap(a[i], a[j]);}for (int i = 1; i < n; i *= 2) {for (int j = 0; j < n; j += i * 2) {for (int k = 0; k < i; k++) {mint s = a[j + k];mint t = a[j + k + i] * rots[i + k];a[j + k ] = s + t;a[j + k + i] = s - t;}}}}void invntt(vector<mint> &a) {const int n = a.size();ntt(a);reverse(a.begin() + 1, a.end());mint inv_n = modinv(n);for (int i = 0; i < n; i++) {a[i] *= inv_n;}}vector<mint> convolution(vector<mint> a, vector<mint> b) {const int n = a.size() + b.size() - 1;int t = 1;while (t < n) t *= 2;a.resize(t);b.resize(t);ntt(a);ntt(b);for (int i = 0; i < t; i++) {a[i] *= b[i];}invntt(a);a.resize(n);return a;}};NTT<1 << 20> ntt;vector<long long> divisors(long long n) {vector<long long> res;for (long long i = 1; i * i <= n; i++) {if (n % i == 0) {res.push_back(i);if (i * i != n) {res.push_back(n / i);}}}sort(range(res));return res;}int primitive_root(int p) {auto ds = divisors(p - 1);ds.pop_back();for (int i = 1; i <= p - 1; i++) {bool all = true;for (int d : ds) {all &= modpow2(i, d, p) != 1;}if (all) return i;}abort();}int main() { initio();int P; cin >> P;vector<mint> A(P - 1), B(P - 1);rep(i, P - 1) cin >> A[i];rep(i, P - 1) cin >> B[i];int g = primitive_root(P);vector<int> table(P - 1);table[0] = 1;for (int i = 1; i <= P - 2; i++) {table[i] = (ll)table[i - 1] * g % P;}vector<int> inv(P);for (int i = 0; i <= P - 2; i++) {inv[table[i]] = i;}vector<mint> F(P - 1);vector<mint> G(P - 1);for (int i = 0; i <= P - 2; i++) {F[inv[i + 1]] = A[i];G[inv[i + 1]] = B[i];}auto ans = ntt.convolution(F, G);for (int i = P - 1; i < ans.size(); i++) {ans[i % (P - 1)] += ans[i];}vector<mint> true_ans(P);for (int i = 0; i < P - 1; i++) {true_ans[table[i]] = ans[i];}for (int i = 1; i < true_ans.size(); i++) {cout << true_ans[i] << " \n"[i == true_ans.size() - 1];}}