結果
問題 | No.2413 Multiple of 99 |
ユーザー |
![]() |
提出日時 | 2023-08-11 22:30:10 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 6,756 ms / 8,000 ms |
コード長 | 3,426 bytes |
コンパイル時間 | 2,903 ms |
コンパイル使用メモリ | 111,780 KB |
最終ジャッジ日時 | 2025-02-16 01:46:04 |
ジャッジサーバーID (参考情報) |
judge5 / judge4 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 21 |
ソースコード
#ifndef CLASS_MODINT #define CLASS_MODINT #include <cstdint> template <std::uint32_t mod> class modint { private: std::uint32_t n; public: modint() : n(0) {}; modint(std::int64_t n_) : n((n_ >= 0 ? n_ : mod - (-n_) % mod) % mod) {}; static constexpr std::uint32_t get_mod() { return mod; } std::uint32_t get() const { return n; } bool operator==(const modint& m) const { return n == m.n; } bool operator!=(const modint& m) const { return n != m.n; } modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; } modint operator+(const modint& m) const { return modint(*this) += m; } modint operator-(const modint& m) const { return modint(*this) -= m; } modint operator*(const modint& m) const { return modint(*this) *= m; } modint inv() const { return (*this).pow(mod - 2); } modint pow(std::uint64_t b) const { modint ans = 1, m = modint(*this); while (b) { if (b & 1) ans *= m; m *= m; b >>= 1; } return ans; } }; #endif // CLASS_MODINT #include <vector> #include <iostream> #include <algorithm> using namespace std; using mint = modint<998244353>; vector<mint> fft(int n, const vector<mint>& v, bool inv) { if (n == 1) { return v; } vector<mint> v0(n / 2), v1(n / 2); for (int i = 0; i < n / 2; i++) { v0[i] = v[i * 2 + 0]; v1[i] = v[i * 2 + 1]; } v0 = fft(n / 2, v0, inv); v1 = fft(n / 2, v1, inv); mint p = mint(3).pow((mint::get_mod() - 1) / n); if (inv) { p = p.inv(); } mint mult = 1; vector<mint> res(n); for (int i = 0; i < n / 2; i++) { res[i] = v0[i] + v1[i] * mult; res[i + n / 2] = v0[i] - v1[i] * mult; mult *= p; } return res; } vector<mint> convolve(const vector<mint>& v1, const vector<mint>& v2) { if (v1.empty() || v2.empty()) { return vector<mint>(); } int s = v1.size() + v2.size() - 1; int n = 1; while (n < s) { n *= 2; } vector<mint> c1 = v1, c2 = v2; c1.resize(n); c2.resize(n); c1 = fft(n, c1, false); c2 = fft(n, c2, false); for (int i = 0; i < n; i++) { c1[i] *= c2[i]; } c1 = fft(n, c1, true); c1.resize(s); mint mult = mint(n).inv(); for (int i = 0; i < s; i++) { c1[i] *= mult; } return c1; } vector<mint> power(vector<mint> poly, int n) { vector<mint> res = { mint(1) }; while (n >= 1) { if (n % 2 == 1) { res = convolve(res, poly); } poly = convolve(poly, poly); n /= 2; } return res; } int main() { int N, K; cin >> N >> K; vector<mint> pbase(10, mint(1)); vector<mint> p1 = power(pbase, (N + 1) / 2); vector<mint> p2 = power(pbase, N / 2); vector<mint> answer(N * 9 + 1, mint(0)); for (int i = 0; i < 99; i++) { int target = (99 - i) * 10 % 99; vector<mint> subp1((p1.size() + 98) / 99); vector<mint> subp2((p2.size() + 98) / 99); for (int j = i; j < p1.size(); j += 99) { subp1[j / 99] = p1[j]; } for (int j = target; j < p2.size(); j += 99) { subp2[j / 99] = p2[j]; } vector<mint> res = convolve(subp1, subp2); for (int j = 0; j < res.size(); j++) { if (res[j] != mint(0)) { answer[j * 99 + i + target] += res[j]; } } } mint final_answer = 0; for (int i = 0; i <= N * 9; i++) { if (answer[i] != mint(0)) { final_answer += answer[i] * mint(i).pow(K); } } cout << final_answer.get() << endl; return 0; }