Inverse Matrix (Mod 2) (verify/structures/bitpack/inv_mod_2.test.cpp)

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Last update: 2024-11-15 00:01:35+01:00
Problem: https://judge.yosupo.jp/problem/inverse_matrix_mod_2

Depends on

Code

// @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/structures/bitpack.hpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo::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/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/structures/bitpack.hpp"



#line 1 "cp-algo/structures/bit_array.hpp"


#line 1 "cp-algo/util/bit.hpp"


#include <immintrin.h>
#include <cstdint>
#include <array>
#include <bit>
namespace cp_algo {
    template<typename Uint>
    constexpr size_t bit_width = sizeof(Uint) * 8;

    size_t order_of_bit(auto x, size_t k) {
        return k ? std::popcount(x << (bit_width<decltype(x)> - k)) : 0;
    }
    [[gnu::target("bmi2")]]
    size_t kth_set_bit(uint64_t x, size_t k) {
        return std::countr_zero(_pdep_u64(1ULL << k, x));
    }
    template<int fl = 0>
    void with_bit_floor(size_t n, auto &&callback) {
        if constexpr (fl >= 63) {
            return;
        } else if (n >> (fl + 1)) {
            with_bit_floor<fl + 1>(n, callback);
        } else {
            callback.template operator()<1ULL << fl>();
        }
    }
}

#line 4 "cp-algo/structures/bit_array.hpp"
namespace cp_algo::structures {
    template<size_t N, typename Uint = uint64_t>
    struct bit_array {
        static constexpr size_t width = bit_width<Uint>;
        static constexpr size_t blocks = N / width + 1;
        std::array<Uint, blocks> data = {};

        uint64_t word(size_t x) const {
            return data[x];
        }
        void set(size_t x) {
            data[x / width] |= 1ULL << (x % width);
        }
        void flip(size_t x) {
            data[x / width] ^= 1ULL << (x % width);
        }
        bool test(size_t x) const {
            return (data[x / width] >> (x % width)) & 1;
        }
        bool operator[](size_t x) const {
            return test(x);
        }
    };
}

#line 6 "cp-algo/structures/bitpack.hpp"
#include <cstddef>
#include <string>
#line 9 "cp-algo/structures/bitpack.hpp"
namespace cp_algo::structures {
    template<size_t n, typename Int = uint64_t>
    struct bitpack: bit_array<n, Int> {
        using Base = bit_array<n, Int>;
        using Base::width, Base::blocks, Base::data;
        auto operator <=> (bitpack const& t) const = default;

        bitpack() {}
        bitpack(std::string bits) {
            size_t rem = size(bits) % width;
            if(rem) {
                bits += std::string(width - rem, '0');
            }
            for(size_t i = 0, pos = 0; pos < size(bits); i++, pos += width) {
                for(size_t j = width; 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 / width; 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;
        }

        std::string to_string() const {
            std::string res(blocks * width, '0');
            for(size_t i = 0, pos = 0; i < blocks; i++, pos += width) {
                Int block = data[i];
                for(size_t j = 0; j < width; 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 += width;
                i++;
            }
            if(i < blocks) {
                res += std::countr_zero(data[i]);
            }
            return std::min(res, n);
        }
    };
}

#line 5 "verify/structures/bitpack/inv_mod_2.test.cpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo::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();
    }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	7 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	305 ms	12 MB
g++	lowrank_max_random_04	AC	281 ms	12 MB
g++	lowrank_max_random_05	AC	266 ms	12 MB
g++	lowrank_max_random_06	AC	87 ms	12 MB
g++	lowrank_max_random_07	AC	201 ms	12 MB
g++	max_fullrank_00	AC	325 ms	12 MB
g++	max_fullrank_01	AC	325 ms	12 MB
g++	max_fullrank_02	AC	326 ms	12 MB
g++	max_fullrank_03	AC	327 ms	12 MB
g++	max_random_00	AC	285 ms	12 MB
g++	max_random_01	AC	325 ms	12 MB
g++	max_random_02	AC	284 ms	12 MB
g++	max_random_03	AC	285 ms	12 MB
g++	perm_max_random_00	AC	7 ms	12 MB
g++	perm_max_random_01	AC	6 ms	12 MB
g++	random_00	AC	15 ms	12 MB
g++	random_01	AC	7 ms	12 MB
g++	random_02	AC	6 ms	12 MB
g++	random_03	AC	185 ms	12 MB
g++	random_fullrank_00	AC	18 ms	12 MB
g++	random_fullrank_01	AC	8 ms	12 MB
g++	random_fullrank_02	AC	6 ms	12 MB
g++	random_fullrank_03	AC	215 ms	12 MB
g++	small_random_00	AC	7 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	7 ms	12 MB