cplib-cpp
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linear_algebra_matrix/test/linalg_bitset.test.cpp
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- Last update: 2024-05-03 14:40:21+09:00
- Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2624
Depends on
Code
#include "../linalg_bitset.hpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2624"
#include <iostream>
#include <numeric>
using namespace std;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
constexpr int Wmax = 320;
int N, T;
cin >> N;
vector<bitset<Wmax>> A(N);
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
int t;
cin >> t;
A[i][j] = t;
}
}
bitset<Wmax> v(N);
for (int i = 0; i < N; i++) {
int t;
cin >> t;
v[i] = t;
}
cin >> T;
A = f2_matpower<Wmax>(A, T);
for (int i = 0; i < N; i++) A[i][N] = v[i];
A = f2_gauss_jordan<Wmax>(N + 1, A);
for (int i = 0; i < N; i++) {
if (A[i].count() == 1 and A[i][N]) {
cout << "none\n";
return 0;
}
}
if (!A[N - 1][N - 1]) {
cout << "ambiguous\n";
return 0;
}
bitset<Wmax> ret;
for (int i = N - 1; i >= 0; i--) {
int a = 0;
for (int j = i + 1; j < N; j++) a ^= ret[j] * A[i][j];
ret[i] = (a != A[i][N]);
}
for (int i = 0; i < N; i++) cout << ret[i] << (i == N - 1 ? '\n' : ' ');
}#line 2 "linear_algebra_matrix/linalg_bitset.hpp"
#include <bitset>
#include <cassert>
#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 <int 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 <int 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 <int 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 <int W1, int 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 <int 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 <int 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);
}
#line 2 "linear_algebra_matrix/test/linalg_bitset.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2624"
#include <iostream>
#include <numeric>
using namespace std;
int main() {
cin.tie(nullptr), ios::sync_with_stdio(false);
constexpr int Wmax = 320;
int N, T;
cin >> N;
vector<bitset<Wmax>> A(N);
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
int t;
cin >> t;
A[i][j] = t;
}
}
bitset<Wmax> v(N);
for (int i = 0; i < N; i++) {
int t;
cin >> t;
v[i] = t;
}
cin >> T;
A = f2_matpower<Wmax>(A, T);
for (int i = 0; i < N; i++) A[i][N] = v[i];
A = f2_gauss_jordan<Wmax>(N + 1, A);
for (int i = 0; i < N; i++) {
if (A[i].count() == 1 and A[i][N]) {
cout << "none\n";
return 0;
}
}
if (!A[N - 1][N - 1]) {
cout << "ambiguous\n";
return 0;
}
bitset<Wmax> ret;
for (int i = N - 1; i >= 0; i--) {
int a = 0;
for (int j = i + 1; j < N; j++) a ^= ret[j] * A[i][j];
ret[i] = (a != A[i][N]);
}
for (int i = 0; i < N; i++) cout << ret[i] << (i == N - 1 ? '\n' : ' ');
}