結果

問題 No.1421 国勢調査 (Hard)
ユーザー 👑 emthrmemthrm
提出日時 2021-03-05 22:51:00
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 130 ms / 2,000 ms
コード長 5,790 bytes
コンパイル時間 2,220 ms
コンパイル使用メモリ 204,580 KB
最終ジャッジ日時 2025-01-19 11:44:17
ジャッジサーバーID
(参考情報)
judge4 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 2
other AC * 30
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

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 1000000007;
// constexpr int MOD = 998244353;
constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
IOSetup() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
std::cout << fixed << setprecision(20);
}
} iosetup;
template <int Col = 2500>
struct BinaryMatrix {
int m, n;
BinaryMatrix(int m, int n = Col, bool def = false) : m(m), n(n), dat(m, std::bitset<Col>(0)) {
if (def) {
for (int i = 0; i < m; ++i) for (int j = 0; j < n; ++j) dat[i][j] = 1;
}
}
BinaryMatrix pow(long long exponent) const {
BinaryMatrix tmp = *this, res(n, n);
for (int i = 0; i < n; ++i) res[i][i] = 1;
while (exponent > 0) {
if (exponent & 1) res *= tmp;
tmp *= tmp;
exponent >>= 1;
}
return res;
}
inline const std::bitset<Col> &operator[](const int idx) const { return dat[idx]; }
inline std::bitset<Col> &operator[](const int idx) { return dat[idx]; }
BinaryMatrix &operator=(const BinaryMatrix &x) {
m = x.m;
n = x.n;
dat.resize(m);
for (int i = 0; i < m; ++i) dat[i] = x[i];
return *this;
}
BinaryMatrix &operator+=(const BinaryMatrix &x) {
for (int i = 0; i < m; ++i) dat[i] ^= x[i];
return *this;
}
BinaryMatrix &operator*=(const BinaryMatrix &x) {
int height = m, width = x.n;
BinaryMatrix t_x(x.n, x.m), res(height, width);
for (int i = 0; i < x.n; ++i) for (int j = 0; j < x.m; ++j) t_x[i][j] = x[j][i];
for (int i = 0; i < height; ++i) for (int j = 0; j < width; ++j) res[i][j] = ((dat[i] & t_x[j]).count() & 1);
*this = res;
return *this;
}
BinaryMatrix operator+(const BinaryMatrix &x) const { return BinaryMatrix(*this) += x; }
BinaryMatrix operator*(const BinaryMatrix &x) const { return BinaryMatrix(*this) *= x; }
private:
std::vector<std::bitset<Col>> dat;
};
template <int Col>
int gauss_jordan(BinaryMatrix<Col> &mat, bool is_extended = false) {
int rank = 0;
for (int col = 0; col < mat.n; ++col) {
if (is_extended && col == mat.n - 1) break;
int pivot = -1;
for (int row = rank; row < mat.m; ++row) {
if (mat[row][col]) {
pivot = row;
break;
}
}
if (pivot == -1) continue;
std::swap(mat[rank], mat[pivot]);
for (int row = 0; row < mat.m; ++row) {
if (row != rank && mat[row][col]) mat[row] ^= mat[rank];
}
++rank;
}
return rank;
}
template <int Col>
std::vector<int> linear_equation(const BinaryMatrix<Col> &a, const std::vector<int> &b) {
BinaryMatrix<Col> mat(a.m, a.n + 1);
for (int i = 0; i < a.m; ++i) {
for (int j = 0; j < a.n; ++j) mat[i][j] = a[i][j];
mat[i][a.n] = b[i];
}
int rank = gauss_jordan(mat, true);
std::vector<int> res;
for (int row = rank; row < a.m; ++row) {
if (mat[row][a.n]) return res;
}
res.assign(a.n, 0);
for (int i = 0; i < rank; ++i) {
FOR(j, i, a.n) {
if (mat[i][j]) {
res[j] = mat[i][a.n];
break;
}
}
}
return res;
}
struct Xor128 {
int rand() {
unsigned int t = x ^ (x << 11);
x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
return static_cast<int>(w);
}
int rand(int ub) {
int res = rand() % ub;
return res < 0 ? res + ub : res;
}
int rand(int lb, int ub) { return lb + rand(ub - lb); }
long long randll() {
unsigned long long res = static_cast<unsigned long long>(rand()) << 32;
return static_cast<long long>(res | rand());
}
long long randll(long long ub) {
long long res = randll() % ub;
return res < 0 ? res + ub : res;
}
long long randll(long long lb, long long ub) { return lb + randll(ub - lb); }
private:
unsigned int x = 123456789, y = 362436069, z = 521288629, w = static_cast<unsigned int>(std::time(nullptr));
} xor128;
int main() {
constexpr int N = 50, B = 30;
using binary_matrix = BinaryMatrix<N>;
int n, m; cin >> n >> m;
vector<vector<int>> b(m);
vector<int> y(m);
// vector<int> house(n);
// REP(i, n) house[i] = xor128.rand(0, 1 << B);
REP(i, m) {
int a; cin >> a;
// int a = xor128.rand(1, n + 1);
b[i].resize(a);
REP(j, a) cin >> b[i][j], --b[i][j];
cin >> y[i];
// vector<bool> is_in_b(n, false);
// while (count(ALL(is_in_b), true) < a) is_in_b[xor128.rand(n)] = true;
// REP(j, n) {
// if (is_in_b[j]) {
// b[i].emplace_back(j);
// y[i] ^= house[j];
// }
// }
}
// REP(i, n) cout << house[i] << " \n"[i + 1 == n];
// REP(i, m) {
// REP(j, b[i].size()) cout << b[i][j] << ' ';
// cout << ": " << y[i] << '\n';
// }
vector<int> ans(n, 0);
REP(bit, B) {
binary_matrix a(m, n, 0);
vector<int> v(m);
REP(i, m) {
for (int bij : b[i]) a[i][bij] = 1;
v[i] = y[i] >> bit & 1;
}
vector<int> sol = linear_equation(a, v);
if (sol.empty()) {
cout << "-1\n";
return 0;
}
REP(i, n) ans[i] |= sol[i] << bit;
}
REP(i, n) cout << ans[i] << '\n';
// REP(i, n) cout << ans[i] << " \n"[i + 1 == n];
// REP(i, m) {
// int xo = 0;
// REP(j, b[i].size()) xo ^= ans[b[i][j]];
// cout << xo << " \n"[i + 1 == m];
// }
return 0;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0