結果

問題 No.1421 国勢調査 (Hard)
ユーザー ShengRangShengRang
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
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

#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 matrix
template <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; // singular
if (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 output
std::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;
} else
return 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';
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0