結果

問題 No.2824 Lights Up! (Grid Edition)
コンテスト
ユーザー hitonanode
提出日時 2024-07-26 23:45:32
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 178 ms / 2,000 ms
コード長 13,711 bytes
コンパイル時間 3,044 ms
コンパイル使用メモリ 210,016 KB
実行使用メモリ 12,672 KB
最終ジャッジ日時 2024-07-26 23:45:44
合計ジャッジ時間 11,975 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 100
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif


#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);
}


void No() {
    puts("-1");
    exit(0);
}

constexpr int Wmax = 50 * 50;
void solve_small(const vector<vector<int>> &state) {
    const int N = state.size();
    assert(lint(N) * N <= Wmax);
    vector<bitset<Wmax>> A(N * N);
    vector<bool> b(N * N);

    auto f = [&](int r, int c) { return r * N + c; };
    REP(i, N) REP(j, N) {
        auto op = [&](int r, int c) {
            A[f(r, c)].flip(f(i, j));
            A[f((r + N - 1) % N, c)].flip(f(i, j));
            A[f(r, (c + N - 1) % N)].flip(f(i, j));
            A[f((r + N - 1) % N, (c + N - 1) % N)].flip(f(i, j));
        };

        op(i, j);
        op(0, j);
        op(i, 0);
        b[f(i, j)] = state.at(i).at(j);
    }

    auto [ok, x, _] = f2_system_of_linear_equations<Wmax, decltype(b)>(A, b, N * N);

    if (ok) {
        cout << x.count() << '\n';
        REP(i, N) REP(j, N) {
            if (x[f(i, j)]) cout << i << ' ' << j << '\n';
        }
        exit(0);
    } else {
        No();
    }
}

int main() {
    int N;
    cin >> N;
    vector<string> S(N);
    cin >> S;
    dbg(S);


    // assert(N > 50);

    vector state(N, vector<int>(N));
    REP(i, N) REP(j, N) state.at(i).at(j) = S.at(i).at(j) == '#';

    if (N * N <= Wmax) solve_small(state);

    vector ret(N, vector<int>(N));

    auto sousa = [&](int r, int c) {
        int r1 = (r + N - 1) % N, c1 = (c + N - 1) % N;
        state.at(r).at(c) ^= 1;
        state.at(r1).at(c) ^= 1;
        state.at(r).at(c1) ^= 1;
        state.at(r1).at(c1) ^= 1;
    };

    auto act = [&](int r, int c) {
        ret.at(r).at(c) ^= 1;
        sousa(r, c);
        sousa(r, 0);
        sousa(0, c);
    };

    IFOR(c, 1, N - 1) {
        IFOR(r, 1, N - 1) {
            if (state.at(r).at(c)) act(r, c);
        }
    }


    FOR(r, 1, N - 1) {
        FOR(c, 1, N - 1) assert(state.at(r).at(c) == 0);
    }

    IFOR(r, 1, N) {
        if (state.at(r).front()) {
            FOR(c, 1, N) act(r, c);
        }
    }

    IFOR(c, 1, N) {
        if (state.front().at(c)) {
            FOR(r, 1, N) act(r, c);
        }
    }

    if (state.front().front()) act(0, 0);

    // IFOR(r, 3, N - 1) {
    //     if (state.at(r).front()) {
    //         act(r, 2);
    //         act(r - 1, 2);
    //     }
    // }

    // IFOR(c, 3, N - 1) {
    //     if (state.front().at(c)) {
    //         act(2, c);
    //         act(2, c - 1);
    //     }
    // }

    // if (state.at(2).at(0)) act(2, 2);

    // IFOR(r, 1, N - 1) {
    //     if (state.at(r).front() != state.at(r).back()) act(r, 1);
    // }


    // REP(r, N) {
    //     if (state.at(r).front() != state.at(r).back()) No();
    // }

    // REP(c, N) {
    //     if (state.front().at(c) != state.back().at(c)) No();
    // }

    REP(i, N) REP(j, N) {
        if (state.at(i).at(j)) No();
    }

    // if (state.back().back()) No();

    for (auto s : state) dbg(s);

    int ans = 0;
    for (auto v : ret) ans += accumulate(ALL(v), 0);

    cout << ans << '\n';
    REP(i, N) REP(j, N) {
        if (ret.at(i).at(j)) cout << i << ' ' << j << '\n';
    }
}
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