結果
問題 | No.1421 国勢調査 (Hard) |
ユーザー | ShengRang |
提出日時 | 2024-08-13 23:05:37 |
言語 | C++17(clang) (17.0.6 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 21 ms / 2,000 ms |
コード長 | 5,641 bytes |
コンパイル時間 | 1,206 ms |
コンパイル使用メモリ | 129,920 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-08-13 23:05:42 |
合計ジャッジ時間 | 3,423 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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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
#include <bitset>#include <cassert>#include <cstddef>#include <tuple>#include <utility>#include <vector>// Gauss-Jordan elimination of n * m matrix M// Complexity: O(nm + nm rank(M) / 64)// Verified: abc276_h (2000 x 8000)template <std::size_t Wmax>std::vector<std::bitset<Wmax>> f2_gauss_jordan(int W, std::vector<std::bitset<Wmax>> M) {assert(W <= Wmax);int H = M.size(), c = 0;for (int h = 0; h < H and c < W; ++h, ++c) {int piv = -1;for (int j = h; j < H; ++j) {if (M[j][c]) {piv = j;break;}}if (piv == -1) {--h;continue;}std::swap(M[piv], M[h]);for (int hh = 0; hh < H; ++hh) {if (hh != h and M[hh][c]) M[hh] ^= M[h];}}return M;}// Rank of Gauss-Jordan eliminated matrixtemplate <std::size_t Wmax> int f2_rank_gauss_jordan(int W, const std::vector<std::bitset<Wmax>> &M) {assert(W <= Wmax);for (int h = (int)M.size() - 1; h >= 0; h--) {int j = 0;while (j < W and !M[h][j]) ++j;if (j < W) return h + 1;}return 0;}// determinant of F2 matrix.// Return 0 if the matrix is singular, otherwise return 1.// Complexity: O(W^3 / 64)template <std::size_t Wmax> int f2_determinant(const std::vector<std::bitset<Wmax>> &M) {const int H = M.size();if (H > Wmax) return 0;auto tmp = M;for (int h = 0; h < H; ++h) {int piv = -1;for (int j = h; j < H; ++j) {if (tmp.at(j).test(h)) {piv = j;break;}}if (piv == -1) return 0; // singularif (piv != h) std::swap(tmp.at(piv), tmp.at(h));for (int hh = h + 1; hh < H; ++hh) {if (tmp.at(hh).test(h)) tmp.at(hh) ^= tmp.at(h);}}return 1; // nonsingular}template <std::size_t W1, std::size_t W2>std::vector<std::bitset<W2>>f2_matmul(const std::vector<std::bitset<W1>> &A, const std::vector<std::bitset<W2>> &B) {int H = A.size(), K = B.size();std::vector<std::bitset<W2>> C(H);for (int i = 0; i < H; i++) {for (int j = 0; j < K; j++) {if (A.at(i).test(j)) C.at(i) ^= B.at(j);}}return C;}template <std::size_t Wmax>std::vector<std::bitset<Wmax>> f2_matpower(std::vector<std::bitset<Wmax>> X, long long n) {int D = X.size();std::vector<std::bitset<Wmax>> ret(D);for (int i = 0; i < D; i++) ret[i][i] = 1;while (n) {if (n & 1) ret = f2_matmul<Wmax, Wmax>(ret, X);X = f2_matmul<Wmax, Wmax>(X, X), n >>= 1;}return ret;}// Solve Ax = b on F_2// - retval: {true, one of the solutions, {freedoms}} (if solution exists)// {false, {}, {}} (otherwise)// Complexity: O(HW + HW rank(A) / 64 + W^2 len(freedoms))template <std::size_t Wmax, class Vec>std::tuple<bool, std::bitset<Wmax>, std::vector<std::bitset<Wmax>>>f2_system_of_linear_equations(std::vector<std::bitset<Wmax>> A, Vec b, int W) {int H = A.size();assert(W <= Wmax);assert(A.size() == b.size());std::vector<std::bitset<Wmax + 1>> M(H);for (int i = 0; i < H; ++i) {for (int j = 0; j < W; ++j) M[i][j] = A[i][j];M[i][W] = b[i];}M = f2_gauss_jordan<Wmax + 1>(W + 1, M);std::vector<int> ss(W, -1);std::vector<int> ss_nonneg_js;for (int i = 0; i < H; i++) {int j = 0;while (j <= W and !M[i][j]) ++j;if (j == W) return {false, 0, {}};if (j < W) {ss_nonneg_js.push_back(j);ss[j] = i;}}std::bitset<Wmax> x;std::vector<std::bitset<Wmax>> D;for (int j = 0; j < W; ++j) {if (ss[j] == -1) {// This part may require W^2 space complexity in outputstd::bitset<Wmax> d;d[j] = 1;for (int jj : ss_nonneg_js) d[jj] = M[ss[jj]][j];D.emplace_back(d);} else {x[j] = M[ss[j]][W];}}return std::make_tuple(true, x, D);}#include <iostream>#include <utility>#include <vector>using namespace std;template <typename T> bool chmin(T &m, const T q) {if (m > q) {m = q;return true;} elsereturn false;}void bad() {puts("-1");exit(0);}int main() {cin.tie(nullptr), ios::sync_with_stdio(false);int N, M;cin >> N >> M;using ull = unsigned long long;vector<pair<ull, int>> basis;while (M--) {int a;cin >> a;ull mask = 0;while (a--) {int b;cin >> b;b--;mask += 1ULL << b;}int y;cin >> y;for (auto [v, w] : basis) {if (chmin(mask, mask ^ v)) y ^= w;}if (!mask and y) bad();if (mask) basis.emplace_back(mask, y);}vector<int> ret(N);for (int d = 0; d < 30; ++d) {constexpr int Wmax = 320;vector<bitset<Wmax>> A;vector<bool> b;for (int i = 0; i < int(basis.size()); ++i) {b.push_back((basis[i].second >> d) & 1);bitset<Wmax> a;a.reset();for (int j = 0; j < N; ++j) {if ((basis[i].first >> j) & 1) a[j] = 1;}A.emplace_back(a);}auto [ok, solution, freedoms] = f2_system_of_linear_equations(A, b, N);if (!ok) bad();for (int i = 0; i < N; ++i) ret[i] += int(solution[i]) << d;}for (auto x : ret) cout << x << '\n';}