結果
問題 |
No.1958 Bit Game
|
ユーザー |
![]() |
提出日時 | 2025-08-14 20:37:10 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 100 ms / 2,000 ms |
コード長 | 5,385 bytes |
コンパイル時間 | 3,783 ms |
コンパイル使用メモリ | 292,544 KB |
実行使用メモリ | 6,272 KB |
最終ジャッジ日時 | 2025-08-14 20:37:19 |
合計ジャッジ時間 | 9,232 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
#include <bits/stdc++.h> using namespace std; using ll = long long; bool chmin(auto &a, auto b) { return a > b ? a = b, true : false; } bool chmax(auto &a, auto b) { return a < b ? a = b, true : false; } #include <atcoder/modint> using mint = atcoder::modint998244353; template<typename mint> struct matrix : vector<vector<mint>> { using vector<vector<mint>>::vector; matrix(int h, int w) : vector<vector<mint>>(h, vector<mint>(w)) {} matrix &operator*=(const mint &r) { for (vector<mint> &v : *this) { for (mint &a : v) a *= r; } return *this; } matrix &operator/=(const mint &r) { mint invr = r.inv(); return *this *= invr; } matrix &operator+=(const matrix& a) { assert(this->size() == a.size()); for (int i = 0; i < int(this->size()); i++) { assert((*this)[i].size() == a[i].size()); for (int j = 0; j < int((*this)[i].size()); j++) { (*this)[i][j] += a[i][j]; } } return *this; } matrix &operator-=(const matrix& a) { assert(this->size() == a.size()); for (int i = 0; i < int(this->size()); i++) { assert((*this)[i].size() == a[i].size()); for (int j = 0; j < int((*this)[i].size()); j++) { (*this)[i][j] -= a[i][j]; } } return *this; } matrix &operator*=(const matrix &a) { int n = this->size(), m = a.size(); assert(m >= 1); int l = a[0].size(); matrix res(n, vector<mint>(l)); for (int i = 0; i < n; i++) { assert(int((*this)[i].size()) == m); for (int k = 0; k < m; k++) { for (int j = 0; j < l; j++) { res[i][j] += (*this)[i][k] * a[k][j]; } } } return *this = res; } matrix operator*(const mint &r) const { return matrix(*this) *= r; } matrix operator/(const mint &r) const { return matrix(*this) /= r; } matrix operator+(const matrix &a) const { return matrix(*this) += a; } matrix operator-(const matrix &a) const { return matrix(*this) -= a; } matrix operator*(const matrix &a) const { return matrix(*this) *= a; } static constexpr matrix I(int n) { matrix res(n, n); for (int i = 0; i < n; i++) { res[i][i] = 1; } return res; } static constexpr matrix O(int n) { return matrix(n, n); } matrix pow(long long k) const { matrix res = I(this->size()), a = *this; while (k > 0) { if (k & 1) res *= a; a *= a; k >>= 1; } return res; } mint det() const { int n = this->size(); assert(n >= 1); assert((*this)[0].size() == this->size()); mint res = 1; matrix a = *this; for (int i = 0; i < n; i++) { for (int j = i; j < n; j++) { if (a[j][i] != 0) { if (i != j) res = -res; swap(a[i], a[j]); break; } } if (a[i][i] != 0) { for (int j = i + 1; j < n; j++) { mint inv = a[j][i] * a[i][i].inv(); for (int k = i + 1; k < n; k++) { a[j][k] -= a[i][k] * inv; } } } } for (int i = 0; i < n; i++) { res *= a[i][i]; } return res; } matrix inv() const { int n = this->size(); matrix a = *this, res = I(n); for (int i = 0; i < n; i++) { if (a[i][i] == 0) { for (int j = i + 1; j < n; j++) { if (a[j][i] != 0) { swap(a[i], a[j]); swap(res[i], res[j]); break; } } } assert(a[i][i] != 0); mint cef = a[i][i].inv(); for (int j = 0; j < n; j++) { a[i][j] *= cef; res[i][j] *= cef; } for (int j = 0; j < n; j++) { if (j != i) { cef = a[j][i]; for (int k = 0; k < n; k++) { a[j][k] -= a[i][k] * cef; res[j][k] -= res[i][k] * cef; } } } } return res; } }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int N, X, Y; cin >> N >> X >> Y; vector<int> A(X), B(Y); for (auto &e : A) cin >> e; for (auto &e : B) cin >> e; auto f = [&] (mint a0, mint a1, mint b0, mint b1) -> mint { matrix<mint> M = matrix<mint>::I(2); M *= matrix<mint>{ {1, 0}, {a1 / X, a0 / X} }; M *= matrix<mint>{ {b1 / Y, b0 / Y}, {0, 1} }; M = M.pow(N); return M[1][0]; }; mint ans = 0; for (int i = 0; i < 18; i++) { int a0 = 0, a1 = 0, b0 = 0, b1 = 0; for (int a : A) (a >> i & 1 ? a1 : a0)++; for (int b : B) (b >> i & 1 ? b1 : b0)++; ans += (1 << i) * f(a0, a1, b0, b1); } ans *= (mint(X) * mint(Y)).pow(N); cout << ans.val() << endl; }