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// @brief Inverse Matrix (Mod 2)
#define PROBLEM "https://judge.yosupo.jp/problem/inverse_matrix_mod_2"
#pragma GCC optimize("Ofast,unroll-loops")
#include "cp-algo/data_structures/bitpack.hpp"
#include <bits/stdc++.h>
using namespace std;
using namespace cp_algo::data_structures;
const int maxn = 1 << 13;
bitpack<maxn> a[maxn];
void solve() {
int n;
cin >> n;
string row;
vector<int> lead(n);
for(int i = 0; i < n; i++) {
cin >> row;
a[i] = row;
a[i].set(n + i);
for(int j = 0; j < i; j++) {
if(a[i][lead[j]]) {
a[i].xor_hint(a[j], lead[j]);
}
}
lead[i] = a[i].ctz();
if(lead[i] >= n) {
cout << -1 << "\n";
return;
}
for(int j = 0; j < i; j++) {
if(a[j][lead[i]]) {
a[j].xor_hint(a[i], lead[i]);
}
}
}
for(int i = 0; i < n; i++) {
while(lead[i] != i) {
swap(a[i], a[lead[i]]);
swap(lead[i], lead[lead[i]]);
}
cout << a[i].to_string().substr(n, n) << "\n";
}
}
signed main() {
//freopen("input.txt", "r", stdin);
ios::sync_with_stdio(0);
cin.tie(0);
int t = 1;
while(t--) {
solve();
}
}
#line 1 "verify/data_structures/bitpack/inv_mod_2.test.cpp"
// @brief Inverse Matrix (Mod 2)
#define PROBLEM "https://judge.yosupo.jp/problem/inverse_matrix_mod_2"
#pragma GCC optimize("Ofast,unroll-loops")
#line 1 "cp-algo/data_structures/bitpack.hpp"
#include <cstdint>
#include <cstddef>
#include <string>
#include <array>
#include <bit>
namespace cp_algo::data_structures {
template<size_t n, typename Int = uint64_t>
struct bitpack {
static constexpr uint8_t bits_per_block = 8 * sizeof(Int);
static constexpr uint32_t blocks = (n + bits_per_block - 1) / bits_per_block;
std::array<Int, blocks> data;
auto operator <=> (bitpack const& t) const = default;
bitpack(): data{} {}
bitpack(std::string bits): data{} {
size_t rem = size(bits) % bits_per_block;
if(rem) {
bits += std::string(bits_per_block - rem, '0');
}
for(size_t i = 0, pos = 0; pos < size(bits); i++, pos += bits_per_block) {
for(size_t j = bits_per_block; j; j--) {
data[i] *= 2;
data[i] ^= bits[pos + j - 1] == '1';
}
}
}
bitpack& xor_hint(bitpack const& t, size_t hint) {
for(size_t i = hint / bits_per_block; i < blocks; i++) {
data[i] ^= t.data[i];
}
return *this;
}
bitpack& operator ^= (bitpack const& t) {
return xor_hint(t, 0);
}
bitpack operator ^ (bitpack const& t) const {
return bitpack(*this) ^= t;
}
int operator[](size_t i) const {
return (data[i / bits_per_block] >> (i % bits_per_block)) & 1;
}
void set(size_t i) {
data[i / bits_per_block] |= 1ULL << (i % bits_per_block);
}
std::string to_string() const {
std::string res(blocks * bits_per_block, '0');
for(size_t i = 0, pos = 0; i < blocks; i++, pos += bits_per_block) {
Int block = data[i];
for(size_t j = 0; j < bits_per_block; j++) {
res[pos + j] = '0' + block % 2;
block /= 2;
}
}
res.resize(n);
return res;
}
size_t ctz() const {
size_t res = 0;
size_t i = 0;
while(i < blocks && data[i] == 0) {
res += bits_per_block;
i++;
}
if(i < blocks) {
res += std::countr_zero(data[i]);
}
return std::min(res, n);
}
};
}
#line 5 "verify/data_structures/bitpack/inv_mod_2.test.cpp"
#include <bits/stdc++.h>
using namespace std;
using namespace cp_algo::data_structures;
const int maxn = 1 << 13;
bitpack<maxn> a[maxn];
void solve() {
int n;
cin >> n;
string row;
vector<int> lead(n);
for(int i = 0; i < n; i++) {
cin >> row;
a[i] = row;
a[i].set(n + i);
for(int j = 0; j < i; j++) {
if(a[i][lead[j]]) {
a[i].xor_hint(a[j], lead[j]);
}
}
lead[i] = a[i].ctz();
if(lead[i] >= n) {
cout << -1 << "\n";
return;
}
for(int j = 0; j < i; j++) {
if(a[j][lead[i]]) {
a[j].xor_hint(a[i], lead[i]);
}
}
}
for(int i = 0; i < n; i++) {
while(lead[i] != i) {
swap(a[i], a[lead[i]]);
swap(lead[i], lead[lead[i]]);
}
cout << a[i].to_string().substr(n, n) << "\n";
}
}
signed main() {
//freopen("input.txt", "r", stdin);
ios::sync_with_stdio(0);
cin.tie(0);
int t = 1;
while(t--) {
solve();
}
}
Env | Name | Status | Elapsed | Memory |
---|---|---|---|---|
g++ | example_00 | AC | 6 ms | 12 MB |
g++ | example_01 | AC | 6 ms | 12 MB |
g++ | example_02 | AC | 6 ms | 12 MB |
g++ | lowrank_max_random_00 | AC | 6 ms | 12 MB |
g++ | lowrank_max_random_01 | AC | 6 ms | 12 MB |
g++ | lowrank_max_random_02 | AC | 6 ms | 12 MB |
g++ | lowrank_max_random_03 | AC | 270 ms | 12 MB |
g++ | lowrank_max_random_04 | AC | 276 ms | 12 MB |
g++ | lowrank_max_random_05 | AC | 248 ms | 12 MB |
g++ | lowrank_max_random_06 | AC | 83 ms | 12 MB |
g++ | lowrank_max_random_07 | AC | 182 ms | 12 MB |
g++ | max_fullrank_00 | AC | 307 ms | 12 MB |
g++ | max_fullrank_01 | AC | 294 ms | 12 MB |
g++ | max_fullrank_02 | AC | 305 ms | 12 MB |
g++ | max_fullrank_03 | AC | 312 ms | 12 MB |
g++ | max_random_00 | AC | 271 ms | 12 MB |
g++ | max_random_01 | AC | 295 ms | 12 MB |
g++ | max_random_02 | AC | 273 ms | 12 MB |
g++ | max_random_03 | AC | 273 ms | 12 MB |
g++ | perm_max_random_00 | AC | 6 ms | 12 MB |
g++ | perm_max_random_01 | AC | 6 ms | 12 MB |
g++ | random_00 | AC | 13 ms | 12 MB |
g++ | random_01 | AC | 7 ms | 12 MB |
g++ | random_02 | AC | 6 ms | 12 MB |
g++ | random_03 | AC | 171 ms | 12 MB |
g++ | random_fullrank_00 | AC | 16 ms | 12 MB |
g++ | random_fullrank_01 | AC | 7 ms | 12 MB |
g++ | random_fullrank_02 | AC | 6 ms | 12 MB |
g++ | random_fullrank_03 | AC | 195 ms | 12 MB |
g++ | small_random_00 | AC | 6 ms | 12 MB |
g++ | small_random_01 | AC | 6 ms | 12 MB |
g++ | small_random_02 | AC | 6 ms | 12 MB |
g++ | small_random_03 | AC | 6 ms | 12 MB |
g++ | small_random_04 | AC | 6 ms | 12 MB |
g++ | small_random_05 | AC | 6 ms | 12 MB |
g++ | small_random_06 | AC | 6 ms | 12 MB |
g++ | small_random_07 | AC | 6 ms | 12 MB |