#585925 (C++17) No.1303 Inconvenient Kingdom

提出ソース

結果

問題	No.1303 Inconvenient Kingdom
ユーザー	hitonanode
提出日時	2020-11-27 23:18:43
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	4 ms / 3,000 ms
コード長	15,211 bytes
コンパイル時間	2,633 ms
コンパイル使用メモリ	230,652 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-07-26 19:36:11
合計ジャッジ時間	3,718 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

このコードへのチャレンジ
（要ログイン）

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 6,812 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,940 KB
testcase_06	AC	3 ms 6,940 KB
testcase_07	AC	4 ms 6,944 KB
testcase_08	AC	4 ms 6,940 KB
testcase_09	AC	4 ms 6,944 KB
testcase_10	AC	4 ms 6,940 KB
testcase_11	AC	4 ms 6,940 KB
testcase_12	AC	4 ms 6,940 KB
testcase_13	AC	4 ms 6,944 KB
testcase_14	AC	4 ms 6,944 KB
testcase_15	AC	4 ms 6,944 KB
testcase_16	AC	3 ms 6,940 KB
testcase_17	AC	4 ms 6,944 KB
testcase_18	AC	4 ms 6,940 KB
testcase_19	AC	4 ms 6,944 KB
testcase_20	AC	4 ms 6,944 KB
testcase_21	AC	3 ms 6,944 KB
testcase_22	AC	4 ms 6,940 KB
testcase_23	AC	4 ms 6,940 KB
testcase_24	AC	4 ms 6,940 KB
testcase_25	AC	4 ms 6,944 KB
testcase_26	AC	3 ms 6,944 KB
testcase_27	AC	3 ms 6,940 KB
testcase_28	AC	2 ms 6,940 KB
testcase_29	AC	1 ms 6,944 KB
testcase_30	AC	2 ms 6,944 KB
testcase_31	AC	2 ms 6,940 KB
testcase_32	AC	2 ms 6,944 KB
testcase_33	AC	2 ms 6,944 KB
testcase_34	AC	2 ms 6,940 KB
testcase_35	AC	2 ms 6,944 KB
testcase_36	AC	1 ms 6,944 KB
testcase_37	AC	2 ms 6,940 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

raw source code

#include <bits/stdc++.h>
using namespace std;
using pint = pair<int, int>;
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> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }

template <int mod> struct ModInt {
#if __cplusplus >= 201402L
#define MDCONST constexpr
#else
#define MDCONST
#endif
    using lint = long long;
    static int get_mod() { return mod; }
    static int get_primitive_root() {
        static int primitive_root = 0;
        if (!primitive_root) {
            primitive_root = [&]() {
                std::set<int> fac;
                int v = mod - 1;
                for (lint i = 2; i * i <= v; i++)
                    while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (int g = 1; g < mod; g++) {
                    bool ok = true;
                    for (auto i : fac)
                        if (ModInt(g).power((mod - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return -1;
            }();
        }
        return primitive_root;
    }
    int val;
    MDCONST ModInt() : val(0) {}
    MDCONST ModInt &_setval(lint v) {
        val = (v >= mod ? v - mod : v);
        return *this;
    }
    MDCONST ModInt(lint v) { _setval(v % mod + mod); }
    explicit operator bool() const { return val != 0; }
    MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }
    MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }
    MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }
    MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }
    MDCONST ModInt operator-() const { return ModInt()._setval(mod - val); }
    MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
    MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
    MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
    MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
    friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }
    friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }
    friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }
    friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }
    MDCONST bool operator==(const ModInt &x) const { return val == x.val; }
    MDCONST bool operator!=(const ModInt &x) const { return val != x.val; }
    MDCONST 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;
    }
    MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; }
    MDCONST 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;
    }
    MDCONST ModInt pow(lint n) const { return power(n); }
    MDCONST 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];
    }

    ModInt doublefac() const {
        lint k = (this->val + 1) / 2;
        return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k);
    }
    ModInt nCr(const ModInt &r) const { return (this->val < r.val) ? 0 : this->fac() / ((*this - r).fac() * r.fac()); }

    ModInt sqrt() const {
        if (val == 0) return 0;
        if (mod == 2) return val;
        if (power((mod - 1) / 2) != 1) return 0;
        ModInt b = 1;
        while (b.power((mod - 1) / 2) == 1) b += 1;
        int e = 0, m = mod - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModInt x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModInt z = b.power(m);
        while (y != 1) {
            int j = 0;
            ModInt t = y;
            while (t != 1) j++, t *= t;
            z = z.power(1LL << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModInt(std::min(x.val, mod - x.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;
    }
    int rank_of_gauss_jordan() const {
        for (int i = H * W - 1; i >= 0; i--)
            if (elem[i]) return i / W + 1;
        return 0;
    }
    T determinant_of_upper_triangle() const {
        T ret = 1;
        for (int i = 0; i < H; i++) ret *= get(i, i);
        return ret;
    }
    int inverse() {
        assert(H == W);
        std::vector<std::vector<T>> ret = Identity(H), tmp = *this;
        int rank = 0;
        for (int i = 0; i < H; i++) {
            int ti = i;
            while (ti < H and tmp[ti][i] == 0) ti++;
            if (ti == H)
                continue;
            else
                rank++;
            ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);
            T inv = tmp[i][i].inv();
            for (int j = 0; j < W; j++) { ret[i][j] *= inv; }
            for (int j = i + 1; j < W; j++) { tmp[i][j] *= inv; }
            for (int h = 0; h < H; h++) {
                if (i == h) continue;
                const T c = -tmp[h][i];
                for (int j = 0; j < W; j++) { ret[h][j] += ret[i][j] * c; }
                for (int j = i + 1; j < W; j++) { tmp[h][j] += tmp[i][j] * c; }
            }
        }
        *this = ret;
        return rank;
    }
    friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {
        assert(m.W == int(v.size()));
        std::vector<T> ret(m.H);
        for (int i = 0; i < m.H; i++) {
            for (int j = 0; j < m.W; j++) { ret[i] += m.get(i, j) * v[j]; }
        }
        return ret;
    }
    friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {
        assert(int(v.size()) == m.H);
        std::vector<T> ret(m.W);
        for (int i = 0; i < m.H; i++) {
            for (int j = 0; j < m.W; j++) { ret[j] += v[i] * m.get(i, j); }
        }
        return ret;
    }
    friend std::ostream &operator<<(std::ostream &os, const matrix &x) {
        os << "[(" << x.H << " * " << x.W << " matrix)";
        os << "\n[column sums: ";
        for (int j = 0; j < x.W; j++) {
            T s = 0;
            for (int i = 0; i < x.H; i++) s += x.get(i, j);
            os << s << ",";
        }
        os << "]";
        for (int i = 0; i < x.H; i++) {
            os << "\n[";
            for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";
            os << "]";
        }
        os << "]\n";
        return os;
    }
    friend std::istream &operator>>(std::istream &is, matrix &x) {
        for (auto &v : x.elem) is >> v;
        return is;
    }
};


// 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(ALL(vs), u) - vs.begin();
        const int j = lower_bound(ALL(vs), 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) {
        mint p = d0[i][i].inv(), q = -d1[i][i] * p * p;
        mint r0new = r0 * d0[i][i];
        mint r1new = r1 * d0[i][i] + r0 * d1[i][i];

        FOR(j, i, N - 1) {
            d1[i][j] = d1[i][j] * p + d0[i][j] * q;
            d0[i][j] = d0[i][j] * p;
        }
        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()
{
    int N, M;
    cin >> N >> M;
    vector<pint> edges;
    UnionFind uf1(N);

    REP(e, 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 maxi = 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 > maxi) maxi = s, cntmaxi = 1;
        else if (maxi == 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 - maxi * 2 << '\n' << ret << '\n';
}

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結果

テストケース

ソースコード