結果

問題 No.1303 Inconvenient Kingdom
ユーザー hitonanodehitonanode
提出日時 2020-11-28 00:14:19
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 5 ms / 3,000 ms
コード長 10,773 bytes
コンパイル時間 2,944 ms
コンパイル使用メモリ 227,132 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-07-26 21:21:00
合計ジャッジ時間 3,901 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 2 ms
5,376 KB
testcase_06 AC 3 ms
5,376 KB
testcase_07 AC 5 ms
5,376 KB
testcase_08 AC 4 ms
5,376 KB
testcase_09 AC 4 ms
5,376 KB
testcase_10 AC 4 ms
5,376 KB
testcase_11 AC 4 ms
5,376 KB
testcase_12 AC 4 ms
5,376 KB
testcase_13 AC 4 ms
5,376 KB
testcase_14 AC 4 ms
5,376 KB
testcase_15 AC 4 ms
5,376 KB
testcase_16 AC 4 ms
5,376 KB
testcase_17 AC 4 ms
5,376 KB
testcase_18 AC 5 ms
5,376 KB
testcase_19 AC 5 ms
5,376 KB
testcase_20 AC 5 ms
5,376 KB
testcase_21 AC 4 ms
5,376 KB
testcase_22 AC 4 ms
5,376 KB
testcase_23 AC 4 ms
5,376 KB
testcase_24 AC 4 ms
5,376 KB
testcase_25 AC 5 ms
5,376 KB
testcase_26 AC 3 ms
5,376 KB
testcase_27 AC 3 ms
5,376 KB
testcase_28 AC 3 ms
5,376 KB
testcase_29 AC 2 ms
5,376 KB
testcase_30 AC 2 ms
5,376 KB
testcase_31 AC 2 ms
5,376 KB
testcase_32 AC 2 ms
5,376 KB
testcase_33 AC 2 ms
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testcase_34 AC 2 ms
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testcase_35 AC 2 ms
5,376 KB
testcase_36 AC 2 ms
5,376 KB
testcase_37 AC 2 ms
5,376 KB
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 <bits/stdc++.h>
using namespace std;
using pint = pair<int, int>;
#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 <int mod> struct ModInt {
    using lint = long long;
    int val;
    constexpr ModInt() : val(0) {}
    constexpr ModInt &_setval(lint v) {
        val = (v >= mod ? v - mod : v);
        return *this;
    }
    constexpr ModInt(lint v) { _setval(v % mod + mod); }
    explicit operator bool() const { return val != 0; }
    constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }
    constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    constexpr bool operator==(const ModInt &x) const { return val == x.val; }
    constexpr bool operator!=(const ModInt &x) const { return val != x.val; }
    constexpr bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>
    friend std::istream &operator>>(std::istream &is, ModInt &x) {
        lint t;
        return is >> t, x = ModInt(t), is;
    }
    constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
    constexpr lint power(lint n) const {
        lint ans = 1, tmp = this->val;
        while (n) {
            if (n & 1) ans = ans * tmp % mod;
            tmp = tmp * tmp % mod, n /= 2;
        }
        return ans;
    }
    constexpr ModInt pow(lint n) const { return power(n); }
    constexpr lint inv() const { return this->power(mod - 2); }
    ModInt fac() const {
        static std::vector<ModInt> facs;
        int l0 = facs.size();
        if (l0 > this->val) return facs[this->val];

        facs.resize(this->val + 1);
        for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));
        return facs[this->val];
    }
};
using mint = ModInt<998244353>;


template <typename T> struct matrix {
    int H, W;
    std::vector<T> elem;
    typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }
    inline T &at(int i, int j) { return elem[i * W + j]; }
    inline T get(int i, int j) const { return elem[i * W + j]; }
    operator std::vector<std::vector<T>>() const {
        std::vector<std::vector<T>> ret(H);
        for (int i = 0; i < H; i++) std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));
        return ret;
    }

    matrix() = default;
    matrix(int H, int W) : H(H), W(W), elem(H * W) {}
    matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {
        for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));
    }

    static matrix Identity(int N) {
        matrix ret(N, N);
        for (int i = 0; i < N; i++) ret.at(i, i) = 1;
        return ret;
    }

    matrix operator-() const {
        matrix ret(H, W);
        for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];
        return ret;
    }
    matrix operator*(const T &v) const {
        matrix ret = *this;
        for (auto &x : ret.elem) x *= v;
        return ret;
    }
    matrix operator/(const T &v) const {
        matrix ret = *this;
        for (auto &x : ret.elem) x /= v;
        return ret;
    }
    matrix operator+(const matrix &r) const {
        matrix ret = *this;
        for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];
        return ret;
    }
    matrix operator-(const matrix &r) const {
        matrix ret = *this;
        for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];
        return ret;
    }
    matrix operator*(const matrix &r) const {
        matrix ret(H, r.W);
        for (int i = 0; i < H; i++) {
            for (int k = 0; k < W; k++) {
                for (int j = 0; j < r.W; j++) { ret.at(i, j) += this->get(i, k) * r.get(k, j); }
            }
        }
        return ret;
    }
    matrix &operator*=(const T &v) { return *this = *this * v; }
    matrix &operator/=(const T &v) { return *this = *this / v; }
    matrix &operator+=(const matrix &r) { return *this = *this + r; }
    matrix &operator-=(const matrix &r) { return *this = *this - r; }
    matrix &operator*=(const matrix &r) { return *this = *this * r; }
    bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }
    bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }
    bool operator<(const matrix &r) const { return elem < r.elem; }
    matrix pow(int64_t n) const {
        matrix ret = Identity(H);
        if (n == 0) return ret;
        for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {
            ret *= ret;
            if ((n >> i) & 1) ret *= (*this);
        }
        return ret;
    }
    matrix transpose() const {
        matrix ret(W, H);
        for (int i = 0; i < H; i++)
            for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);
        return ret;
    }
    // Gauss-Jordan elimination
    // - Require inverse for every non-zero element
    // - Complexity: O(H^2 W)
    matrix gauss_jordan() const {
        int c = 0;
        matrix mtr(*this);
        for (int h = 0; h < H; h++) {
            if (c == W) break;
            int piv = -1;
            for (int j = h; j < H; j++)
                if (mtr.get(j, c)) {
                    piv = j;
                    break;
                }
            if (piv == -1) {
                c++;
                h--;
                continue;
            }
            if (h != piv) {
                for (int w = 0; w < W; w++) {
                    std::swap(mtr[piv][w], mtr[h][w]);
                    mtr.at(piv, w) *= -1; // To preserve sign of determinant
                }
            }
            for (int hh = 0; hh < H; hh++)
                if (hh != h) {
                    T coeff = mtr.at(hh, c) * mtr.at(h, c).inv();
                    for (int w = W - 1; w >= c; w--) { mtr.at(hh, w) -= mtr.at(h, w) * coeff; }
                }
            c++;
        }
        return mtr;
    }
    T determinant_of_upper_triangle() const {
        T ret = 1;
        for (int i = 0; i < H; i++) ret *= get(i, i);
        return ret;
    }
};


// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind {
    std::vector<int> par, cou;
    UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }
    int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
    bool unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y) return false;
        if (cou[x] < cou[y]) std::swap(x, y);
        par[y] = x, cou[x] += cou[y];
        return true;
    }
    int count(int x) { return cou[find(x)]; }
    bool same(int x, int y) { return find(x) == find(y); }
};


mint gyoretsuki(const vector<int> &vs, const vector<pint> &edges) {
    int D = vs.size();
    matrix<mint> mat(D - 1, D - 1);
    for (auto [u, v] : edges) {
        const int i = lower_bound(vs.begin(), vs.end(), u) - vs.begin();
        const int j = lower_bound(vs.begin(), vs.end(), v) - vs.begin();
        if (i < D - 1) mat[i][i] += 1;
        if (j < D - 1) mat[j][j] += 1;
        if (i + 1 < D and j + 1 < D) {
            mat[i][j] -= 1, mat[j][i] -= 1;
        }
    }
    mat = mat.gauss_jordan();
    return mat.determinant_of_upper_triangle();
}

mint solve1(const int N, const vector<pint> &edges) {
    if (N <= 1) return 1;
    vector d0(N, vector<mint>(N));
    vector d1(N, vector<mint>(N));
    for (auto [u, v] : edges) {
        d0[u][u] += 1;
        d0[v][v] += 1;
        d0[v][u] -= 1;
        d0[u][v] -= 1;
    }
    REP(i, N) REP(j, i) if (d0[i][j] == 0) {
        d1[i][j] -= 1;
        d1[j][i] -= 1;
        d1[i][i] += 1;
        d1[j][j] += 1;
    }

    d0.resize(N - 1);
    d1.resize(N - 1);

    mint r0 = 1, r1 = 0;
    REP(i, N - 1) d0[i].resize(N - 1), d1[i].resize(N - 1);
    REP(i, N - 1) {
        const mint p0 = d0[i][i].inv(), p1 = -d1[i][i] * p0 * p0;
        const mint r0new = r0 * d0[i][i], r1new = r1 * d0[i][i] + r0 * d1[i][i];

        FOR(j, i, N - 1) {
            d1[i][j] = d1[i][j] * p0 + d0[i][j] * p1;
            d0[i][j] = d0[i][j] * p0;
        }
        FOR(l, i + 1, N - 1) {
            IFOR(j, i, N - 1) {
                d1[l][j] -= d1[l][i] * d0[i][j] + d0[l][i] * d1[i][j];
                d0[l][j] -= d0[l][i] * d0[i][j];
            }
        }
        r0 = r0new, r1 = r1new;
    }
    return r0 + r1;
}

int main()
{
    cin.tie(nullptr), ios::sync_with_stdio(false);

    int N, M;
    cin >> N >> M;
    vector<pint> edges;
    UnionFind uf1(N);

    while (M--) {
        int u, v;
        cin >> u >> v;
        u--, v--;
        edges.emplace_back(u, v);
        uf1.unite(u, v);
    }

    if (uf1.count(0) == N) {
        cout << "0\n" << solve1(N, edges) << '\n';
        return 0;
    }

    int max_red_fuben = 0, cntmaxi = 0;

    int fuben = 0;
    REP(i, N) REP(j, N) fuben += !uf1.same(i, j);

    REP(i, N) REP(j, i) if (!uf1.same(i, j)) {
        int s = uf1.count(i) * uf1.count(j);
        if (s > max_red_fuben) max_red_fuben = s, cntmaxi = 1;
        else if (max_red_fuben == s) cntmaxi++;
    }

    mint ret = cntmaxi;

    vector<vector<int>> r2is(N);
    vector<vector<pint>> r2edges(N);
    REP(i, N) r2is[uf1.find(i)].emplace_back(i);
    for (auto [u, v] : edges) r2edges[uf1.find(u)].emplace_back(u, v);

    REP(r, N) if (r2is[r].size()) ret *= gyoretsuki(r2is[r], r2edges[r]);

    cout << fuben - max_red_fuben * 2 << '\n' << ret << '\n';
}
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