結果
問題 | No.1421 国勢調査 (Hard) |
ユーザー |
👑 ![]() |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 30 |
ソースコード
#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;}