#754558 (C++17) No.1907 DETERMINATION

• 問題: No.1907 DETERMINATION
• ユーザー: tokusakurai
• 提出日時: 2022-04-16 10:57:31
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 1,353 ms / 4,000 ms
• コード長: 7,585 bytes
• コンパイル時間: 2,610 ms
• コンパイル使用メモリ: 208,224 KB
• 最終ジャッジ日時: 2025-01-28 18:52:26
• ジャッジサーバーID （参考情報）: judge5 / judge5

ファイルパターン	結果
sample	AC * 4
other	AC * 63

ソースコード

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep2(i, x, n) for (int i = x; i <= n; i++)
#define rep3(i, x, n) for (int i = x; i >= n; i--)
#define each(e, v) for (auto &e : v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
bool chmax(T &x, const T &y) {
    return (x < y) ? (x = y, true) : false;
}

template <typename T>
bool chmin(T &x, const T &y) {
    return (x > y) ? (x = y, true) : false;
}

template <typename T>
int flg(T x, int i) {
    return (x >> i) & 1;
}

template <typename T>
void print(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
    if (v.empty()) cout << '\n';
}

template <typename T>
void printn(const vector<T> &v, T x = 0) {
    int n = v.size();
    for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}

template <typename T>
int lb(const vector<T> &v, T x) {
    return lower_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
int ub(const vector<T> &v, T x) {
    return upper_bound(begin(v), end(v), x) - begin(v);
}

template <typename T>
void rearrange(vector<T> &v) {
    sort(begin(v), end(v));
    v.erase(unique(begin(v), end(v)), end(v));
}

template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
    int n = v.size();
    vector<int> ret(n);
    iota(begin(ret), end(ret), 0);
    sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
    return ret;
}

template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first + q.first, p.second + q.second);
}

template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
    return make_pair(p.first - q.first, p.second - q.second);
}

template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
    S a;
    T b;
    is >> a >> b;
    p = make_pair(a, b);
    return is;
}

template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
    return os << p.first << ' ' << p.second;
}

struct io_setup {
    io_setup() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

const int inf = (1 << 30) - 1;
const ll INF = (1LL << 60) - 1;
// const int MOD = 1000000007;
const int MOD = 998244353;

template <int mod>
struct Mod_Int {
    int x;

    Mod_Int() : x(0) {}

    Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

    static int get_mod() { return mod; }

    Mod_Int &operator+=(const Mod_Int &p) {
        if ((x += p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator-=(const Mod_Int &p) {
        if ((x += mod - p.x) >= mod) x -= mod;
        return *this;
    }

    Mod_Int &operator*=(const Mod_Int &p) {
        x = (int)(1LL * x * p.x % mod);
        return *this;
    }

    Mod_Int &operator/=(const Mod_Int &p) {
        *this *= p.inverse();
        return *this;
    }

    Mod_Int &operator++() { return *this += Mod_Int(1); }

    Mod_Int operator++(int) {
        Mod_Int tmp = *this;
        ++*this;
        return tmp;
    }

    Mod_Int &operator--() { return *this -= Mod_Int(1); }

    Mod_Int operator--(int) {
        Mod_Int tmp = *this;
        --*this;
        return tmp;
    }

    Mod_Int operator-() const { return Mod_Int(-x); }

    Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }

    Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }

    Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }

    Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }

    bool operator==(const Mod_Int &p) const { return x == p.x; }

    bool operator!=(const Mod_Int &p) const { return x != p.x; }

    Mod_Int inverse() const {
        assert(*this != Mod_Int(0));
        return pow(mod - 2);
    }

    Mod_Int pow(long long k) const {
        Mod_Int now = *this, ret = 1;
        for (; k > 0; k >>= 1, now *= now) {
            if (k & 1) ret *= now;
        }
        return ret;
    }

    friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }

    friend istream &operator>>(istream &is, Mod_Int &p) {
        long long a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};

using mint = Mod_Int<MOD>;

template <typename T>
vector<T> characteristic_polynomial(vector<vector<T>> A) {
    int n = A.size();
    for (int j = 0; j < n - 2; j++) {
        for (int i = j + 2; i < n; i++) {
            if (A[i][j] != 0) {
                swap(A[j + 1], A[i]);
                for (int k = 0; k < n; k++) swap(A[k][j + 1], A[k][i]);
                break;
            }
        }
        if (A[j + 1][j] != 0) {
            T inv = A[j + 1][j].inverse();
            for (int i = j + 2; i < n; i++) {
                T c = A[i][j] * inv;
                for (int k = j; k < n; k++) A[i][k] -= A[j + 1][k] * c;
                for (int k = 0; k < n; k++) A[k][j + 1] += A[k][i] * c;
            }
        }
    }
    vector<vector<T>> p(n + 1);
    p[0] = {1};
    for (int i = 0; i < n; i++) {
        p[i + 1].assign(i + 2, 0);
        for (int j = 0; j <= i; j++) {
            p[i + 1][j + 1] += p[i][j];
            p[i + 1][j] -= p[i][j] * A[i][i];
        }
        T c = 1;
        for (int k = 1; k <= i; k++) {
            c *= -A[i + 1 - k][i - k];
            T x = c * (k & 1 ? A[i - k][i] : -A[i - k][i]);
            for (int j = 0; j <= i - k; j++) p[i + 1][j] += p[i - k][j] * x;
        }
    }
    return p[n];
}

int main() {
    int N;
    cin >> N;

    vector<vector<mint>> a(N, vector<mint>(N)), b(N, vector<mint>(N));
    rep(i, N) rep(j, N) cin >> a[i][j];
    rep(i, N) rep(j, N) cin >> b[i][j];

    mint tmp = 1;
    int deg = 0;

    rep(j, N) {
        while (deg <= N) {
            rep3(i, j - 1, 0) {
                mint y = b[i][j];
                rep(k, N) {
                    a[k][j] -= a[k][i] * y;
                    b[k][j] -= b[k][i] * y;
                }
            }
            rep2(i, j + 1, N - 1) {
                if (b[i][j] != 0) {
                    swap(a[j], a[i]);
                    swap(b[j], b[i]);
                    tmp *= -1;
                    break;
                }
            }
            if (b[j][j] != 0) break;
            deg++;
            rep(i, N) {
                b[i][j] = a[i][j];
                a[i][j] = 0;
            }
        }

        if (deg > N) {
            rep(i, N + 1) cout << 0 << '\n';
            return 0;
        }

        mint x = b[j][j].inverse();
        tmp *= b[j][j];
        rep(k, N) {
            a[j][k] *= x;
            b[j][k] *= x;
        }
        rep(i, N) {
            if (i != j) {
                mint y = b[i][j];
                rep(k, N) {
                    a[i][k] -= y * a[j][k];
                    b[i][k] -= y * b[j][k];
                }
            }
        }
    }

    // rep(i, N) print(a[i]);
    // rep(i, N) print(b[i]);
    // cout << tmp << '\n';

    rep(i, N) rep(j, N) a[i][j] *= -1;
    auto f = characteristic_polynomial(a);

    vector<mint> p(N + 1, 0);
    rep2(i, deg, N) p[i - deg] += f[i] * tmp;
    printn(p);
}