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 uniqueassert(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] < EPSif (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;elsecout << -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;}