結果
| 問題 | No.1421 国勢調査 (Hard) |
| ユーザー |
 m_tsubasa
|
| 提出日時 | 2021-03-05 23:13:22 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 8,539 bytes |
| コンパイル時間 | 2,155 ms |
| コンパイル使用メモリ | 207,344 KB |
| 最終ジャッジ日時 | 2025-01-19 11:57:43 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 21 RE * 9 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
template <int mod = (int)(1e9 + 7)>
struct ModInt {
int x;
constexpr ModInt() : x(0) {}
constexpr ModInt(int64_t y)
: x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
constexpr ModInt &operator+=(const ModInt &p) noexcept {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &p) noexcept {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
constexpr ModInt &operator*=(const ModInt &p) noexcept {
x = (int)(1LL * x * p.x % mod);
return *this;
}
constexpr ModInt &operator/=(const ModInt &p) noexcept {
*this *= p.inverse();
return *this;
}
constexpr ModInt operator-() const { return ModInt(-x); }
constexpr ModInt operator+(const ModInt &p) const noexcept {
return ModInt(*this) += p;
}
constexpr ModInt operator-(const ModInt &p) const noexcept {
return ModInt(*this) -= p;
}
constexpr ModInt operator*(const ModInt &p) const noexcept {
return ModInt(*this) *= p;
}
constexpr ModInt operator/(const ModInt &p) const noexcept {
return ModInt(*this) /= p;
}
constexpr bool operator==(const ModInt &p) const noexcept { return x == p.x; }
constexpr bool operator!=(const ModInt &p) const noexcept { return x != p.x; }
constexpr ModInt inverse() const noexcept {
int a = x, b = mod, u = 1, v = 0, t = 0;
while (b > 0) {
t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return ModInt(u);
}
constexpr ModInt pow(int64_t n) const {
ModInt res(1), mul(x);
while (n) {
if (n & 1) res *= mul;
mul *= mul;
n >>= 1;
}
return res;
}
friend constexpr ostream &operator<<(ostream &os, const ModInt &p) noexcept {
return os << p.x;
}
friend constexpr istream &operator>>(istream &is, ModInt &a) noexcept {
int64_t t = 0;
is >> t;
a = ModInt<mod>(t);
return (is);
}
constexpr int get_mod() { return mod; }
};
using mint = ModInt<>;
template <class T>
struct Matrix {
vector<vector<T>> A;
Matrix() {}
Matrix(size_t m, size_t n) : A(m, vector<T>(n, 0)) {}
Matrix(size_t n) : A(n, vector<T>(n, 0)) {}
size_t height() const { return (A.size()); }
size_t width() const { return (A[0].size()); }
inline const vector<T> &operator[](int k) const { return (A.at(k)); }
inline vector<T> &operator[](int k) { return (A.at(k)); }
static Matrix E(size_t n) {
Matrix mat(n);
for (int i = 0; i < n; ++i) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
size_t m = height(), n = width();
assert(m == B.height() && n == B.width());
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) (*this)[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
size_t m = height(), n = width();
assert(m == B.height() && n == B.width());
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) (*this)[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
size_t m = height(), n = B.width(), p = width();
assert(p == B.height());
vector<vector<T>> C(m, vector<T>(n, 0));
for (int i = 0; i < m; ++i)
for (int k = 0; k < p; ++k) {
T tmp = (*this)[i][k];
for (int j = 0; j < n; ++j) C[i][j] += tmp * B[k][j];
}
A.swap(C);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::E(height());
while (k) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
Matrix trans() {
size_t m = height(), n = width();
Matrix res(n, m);
for (int i = 0; i < n; ++i)
for (int j = 0; j < m; ++j) res[i][j] = (*this)[j][i];
return res;
}
Matrix inv() {
assert(height() == width());
size_t n = height();
Matrix B(n, 2 * n);
for (int i = 0; i < n; ++i) {
B[i][i + n] = 1;
for (int j = 0; j < n; ++j) B[i][j] = (*this)[i][j];
}
for (int i = 0; i < n; ++i) {
int piv = i;
for (int j = i; j < n; ++j)
if (abs(B[j][i]) > abs(B[piv][i])) piv = j;
// not exist or unique
assert(abs(B[piv][i]) >= 0);
swap(B[i], B[piv]);
for (int j = i + 1; j < 2 * n; ++j) B[i][j] /= B[i][i];
for (int j = 0; j < n; ++j)
if (i != j)
for (int k = i + 1; k < 2 * n; ++k) B[j][k] -= B[j][i] * B[i][k];
}
Matrix res(n);
for (int i = 0; i < n; ++i)
for (int j = 0; j < n; ++j) res[i][j] = B[i][j + n];
return res;
}
T det() {
int m = height(), n = width();
assert(m == n);
T res = 1;
Matrix B(m);
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) B[i][j] = (*this)[i][j];
for (int i = 0; i < n; ++i) {
int piv = i;
for (int j = i + 1; j < m; ++j)
if (B[j][i] != 0) {
piv = j;
break;
}
// if (abs(B[j][i]) > abs(B[piv][i])) piv = j;
if (B[piv][i] == 0) return (T)0;
// if (abs(B[piv][i]) < EPS) return (T)0; // B[piv][i] < EPS
if (piv != i) swap(B[i], B[piv]), res = -res;
res *= B[i][i];
// for (int j = i + 1; j < m; ++j)
// for (int k = n - 1; k >= i; --k) B[j][k] -= B[i][k] * B[j][i] /
// B[i][i];
{
const T d = (T)1 / B[i][i];
for (int j = i + 1; j < n; ++j) B[i][j] *= d;
for (int j = i + 1; j < m; ++j)
for (int k = i + 1; k < n; ++k) B[j][k] -= B[i][k] * B[j][i];
}
}
return res;
}
friend ostream &operator<<(ostream &os, Matrix &p) {
size_t m = p.height(), n = p.width();
for (int i = 0; i < m; i++) {
os << "[";
for (int j = 0; j < n; j++) {
os << p[i][j] << (j + 1 == n ? "]\n" : ",");
}
}
return (os);
}
};
// use Matrix, ModInt
// MOD ver.
#define MOD (long long)(2)
int gauss_jordan(Matrix<ModInt<MOD>> &A, bool is_extended = false) {
int m = A.height(), n = A.width(), rank = 0;
for (int col = 0; col < n; ++col) {
if (is_extended && col == n - 1) break;
int piv = -1;
for (int row = rank; row < m; ++row)
if (A[row][col] != 0) {
piv = row;
break;
}
if (piv == -1) continue;
swap(A[piv], A[rank]);
ModInt<MOD> inv = A[rank][col];
inv = inv.inverse();
for (int col2 = 0; col2 < n; ++col2) A[rank][col2] = A[rank][col2] * inv;
for (int row = 0; row < m; ++row)
if (row != rank && A[row][col] != 0) {
ModInt<MOD> fac = A[row][col];
for (int col2 = 0; col2 < n; ++col2)
A[row][col2] -= A[rank][col2] * fac;
}
++rank;
}
return rank;
}
int linear_equation(Matrix<ModInt<MOD>> A, vector<ModInt<MOD>> b,
vector<ModInt<MOD>> &ans) {
int m = A.height(), n = A.width();
Matrix<ModInt<MOD>> M(m, n + 1);
assert((int)b.size() == m);
for (int i = 0; i < m; ++i) {
for (int j = 0; j < n; ++j) M[i][j] = A[i][j];
M[i][n] = b[i];
}
int rank = gauss_jordan(M, 1);
ans.assign(n, 0);
for (int i = 0; i < rank; ++i) ans[i] = M[i][n];
// exist?
for (int row = rank; row < m; ++row)
if (M[row][n] != 0) return -1;
return rank;
}
int n, m;
vector<long long> city, bits;
vector<int> solve();
int main() {
cin >> n >> m;
city.assign(m, 0);
bits.assign(m, 0);
for (int i = 0; i < m; ++i) {
int len;
cin >> len;
while (len--) {
int p;
cin >> p;
city[i] |= 1LL << --p;
}
cin >> bits[i];
}
auto res = solve();
if (res.size())
for (auto p : res) cout << p << endl;
else
cout << -1 << endl;
return 0;
}
vector<int> solve() {
vector<int> res(n, 0);
Matrix<ModInt<MOD>> A(m, n);
for (int i = 0; i < m; ++i)
for (int j = 0; j < n; ++j) A[i][j] = city[i] >> j & 1;
for (int i = 0; i < 30; ++i) {
vector<ModInt<MOD>> b(m), ans(n);
for (int j = 0; j < m; ++j) b[j] = bits[j] >> i & 1;
if (linear_equation(A, b, ans) < 0) return vector<int>();
for (int j = 0; j < n; ++j)
if (ans[j] == 1) res[j] |= 1LL << i;
}
for (int i = 0; i < m; ++i) {
long long now = 0;
for (int j = 0; j < n; ++j)
if (city[i] >> j & 1) now ^= res[j];
assert(now == bits[i]);
}
return res;
}