結果

問題 No.1303 Inconvenient Kingdom
ユーザー nok0
提出日時 2020-10-15 15:22:49
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,475 ms / 3,000 ms
コード長 15,093 bytes
コンパイル時間 3,664 ms
コンパイル使用メモリ 245,672 KB
最終ジャッジ日時 2025-01-15 07:27:33
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 34
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘void scan(char*)’:
main.cpp:59:28: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   59 | void scan(char a[]) { scanf("%s", a); }
      |                       ~~~~~^~~~~~~~~

ソースコード

diff #
プレゼンテーションモードにする

/**
 *  author: nok0
 *  created: 2020.10.05 18:09:46
**/
#ifdef LOCAL
#define _GLIBCXX_DEBUG
#endif
#include <bits/stdc++.h>
using namespace std;
#pragma region Macros
#define FOR(i, l, r) for(int i = (l); i < (r); ++i)
#define REP(i, n) FOR(i, 0, n)
#define REPS(i, n) FOR(i, 1, n + 1)
#define RFOR(i, l, r) for(int i = (l); i >= (r); --i)
#define RREP(i, n) RFOR(i, n - 1, 0)
#define RREPS(i, n) RFOR(i, n, 1)
#define pb push_back
#define eb emplace_back
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
template <class T = int>
using V = vector<T>;
template <class T = int>
using VV = V<V<T>>;
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#define VEC(type, name, size) \
    V<type> name(size);       \
    IN(name)
#define VVEC(type, name, h, w)    \
    VV<type> name(h, V<type>(w)); \
    IN(name)
#define INT(...)     \
    int __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LL(...)     \
    ll __VA_ARGS__; \
    IN(__VA_ARGS__)
#define STR(...)        \
    string __VA_ARGS__; \
    IN(__VA_ARGS__)
#define CHAR(...)     \
    char __VA_ARGS__; \
    IN(__VA_ARGS__)
#define DOUBLE(...)     \
    DOUBLE __VA_ARGS__; \
    IN(__VA_ARGS__)
#define LD(...)     \
    LD __VA_ARGS__; \
    IN(__VA_ARGS__)
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(long double &a) { cin >> a; }
void scan(char a[]) { scanf("%s", a); }
void scan(string &a) { cin >> a; }
template <class T>
void scan(V<T> &);
template <class T, class L>
void scan(pair<T, L> &);
template <class T>
void scan(V<T> &a) {
    for(auto &i : a) scan(i);
}
template <class T, class L>
void scan(pair<T, L> &p) {
    scan(p.first);
    scan(p.second);
}
template <class T>
void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail>
void IN(Head &head, Tail &... tail) {
    scan(head);
    IN(tail...);
}
template <class T>
inline void print(T x) { cout << x << '\n'; }
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
    is >> p.first >> p.second;
    return is;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
    os << p.first << " " << p.second;
    return os;
}
template <class T>
ostream &operator<<(ostream &os, const V<T> &v) {
    REP(i, SZ(v)) {
        if(i) os << " ";
        os << v[i];
    }
    return os;
}
//debug
template <typename T>
void view(const V<T> &v) {
    cerr << "{ ";
    for(const auto &e : v) {
        cerr << e << ", ";
    }
    cerr << "\b\b }";
}
template <typename T>
void view(const VV<T> &vv) {
    cerr << "{\n";
    for(const auto &v : vv) {
        cerr << "\t";
        view(v);
        cerr << "\n";
    }
    cerr << "}";
}
template <typename T, typename U>
void view(const V<pair<T, U>> &v) {
    cerr << "{\n";
    for(const auto &c : v) cerr << "\t(" << c.first << ", " << c.second << ")\n";
    cerr << "}";
}
template <typename T, typename U>
void view(const map<T, U> &m) {
    cerr << "{\n";
    for(auto &t : m) cerr << "\t[" << t.first << "] : " << t.second << "\n";
    cerr << "}";
}
template <typename T, typename U>
void view(const pair<T, U> &p) { cerr << "(" << p.first << ", " << p.second << ")"; }
template <typename T>
void view(const set<T> &s) {
    cerr << "{ ";
    for(auto &t : s) {
        view(t);
        cerr << ", ";
    }
    cerr << "\b\b }";
}
template <typename T>
void view(T e) { cerr << e; }
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    view(H);
    cerr << ", ";
    debug_out(T...);
}
#define debug(...)                                           \
    do {                                                     \
        cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
        debug_out(__VA_ARGS__);                              \
        cerr << "\b\b]\n";                                   \
    } while(0)
#else
#define debug(...) (void(0))
#endif
template <class T>
V<T> press(V<T> &x) {
    V<T> res = x;
    sort(all(res));
    res.erase(unique(all(res)), res.end());
    REP(i, SZ(x)) {
        x[i] = lower_bound(all(res), x[i]) - res.begin();
    }
    return res;
}
template <class T>
inline bool chmin(T &a, T b) {
    if(a > b) {
        a = b;
        return true;
    }
    return false;
}
template <class T>
inline bool chmax(T &a, T b) {
    if(a < b) {
        a = b;
        return true;
    }
    return false;
}
inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; }
inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; }
inline void err(bool b = true) {
    if(b) {
        cout << -1 << '\n';
        exit(0);
    }
}
template <class T>
inline void fin(bool b = true, T e = 0) {
    if(b) {
        cout << e << '\n';
        exit(0);
    }
}
template <class T>
T divup(T x, T y) { return (x + (y - 1)) / y; }
template <typename T>
T pow(T a, long long n, T e = 1) {
    T ret = e;
    while(n) {
        if(n & 1) ret *= a;
        a *= a;
        n >>= 1;
    }
    return ret;
}
struct iofast {
    iofast() {
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
        cout << fixed << setprecision(15);
    }
} iofast_;
const int inf = 1e9;
const ll INF = 1e18;
#pragma endregion
struct UnionFind {
private:
    std::vector<int> par;
public:
    UnionFind() = default;
    UnionFind(size_t n)
      : par(n, -1) {}
    int root(int x) {
        if(par[x] < 0) return x;
        return par[x] = root(par[x]);
    }
    bool same(int x, int y) { return root(x) == root(y); }
    bool unite(int x, int y) {
        x = root(x);
        y = root(y);
        if(x == y) return false;
        if(par[x] > par[y]) std::swap(x, y);
        par[x] += par[y];
        par[y] = x;
        return true;
    }
    size_t size(int x) { return -par[root(x)]; }
    size_t size() const { return par.size(); }
};
template <class T>
struct Matrix {
private:
    std::vector<std::vector<T>> A;
    static Matrix I(size_t n) {
        Matrix mat(n);
        for(int i = 0; i < n; i++) mat[i][i] = 1;
        return mat;
    }
public:
    Matrix() = default;
    Matrix(std::vector<std::vector<T>> &vvec) { A = vvec; }
    Matrix(size_t n, size_t m) : A(n, std::vector<T>(m, 0)) {}
    Matrix(size_t n, size_t m, T init) : A(n, std::vector<T>(m, init)) {}
    Matrix(size_t n, std::vector<T> &vec) : A(n, vec) {}
    Matrix(size_t n) : A(n, std::vector<T>(n, 0)) {}
    size_t height() const { return A.size(); }
    size_t width() const { return A[0].size(); }
    inline const std::vector<T> &operator[](int k) const {
        return A[k];
    }
    inline std::vector<T> &operator[](int k) {
        return A[k];
    }
    Matrix &operator+=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() and m == B.width());
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                (*this)[i][j] += B[i][j];
        return *this;
    }
    Matrix &operator-=(const Matrix &B) {
        size_t n = height(), m = width();
        assert(n == B.height() and m == B.width());
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                (*this)[i][j] -= B[i][j];
        return *this;
    }
    Matrix &operator*=(const Matrix &B) {
        size_t n = height(), m = B.width(), p = width();
        assert(p == B.height());
        std::vector<std::vector<T>> C(n, std::vector<T>(m, 0));
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                for(int k = 0; k < p; k++)
                    C[i][j] += (*this)[i][k] * B[k][j];
        A.swap(C);
        return *this;
    }
    Matrix &operator^=(long long k) {
        Matrix B = Matrix::I(height());
        while(k > 0) {
            if(k & 1) B *= (*this);
            *this *= *this;
            k >>= 1ll;
        }
        A.swap(B.A);
        return *this;
    }
    bool operator==(const Matrix &B) {
        size_t n = height(), m = width();
        if(n != B.height() or m != B.width()) return false;
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                if((*this)[i][j] != B[i][j]) return false;
        return true;
    }
    Matrix operator+(const Matrix &B) const {
        return (Matrix(*this) += B);
    }
    Matrix operator-(const Matrix &B) const {
        return (Matrix(*this) -= B);
    }
    Matrix operator*(const Matrix &B) const {
        return (Matrix(*this) *= B);
    }
    Matrix operator^(const long long &k) const {
        return (Matrix(*this) ^= k);
    }
    Matrix &operator+=(const T &t) {
        int n = height(), m = width();
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                (*this)[i][j] += t;
        return *this;
    }
    Matrix &operator-=(const T &t) {
        int n = height(), m = width();
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                (*this)[i][j] -= t;
        return *this;
    }
    Matrix &operator*=(const T &t) {
        int n = height(), m = width();
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                (*this)[i][j] *= t;
        return *this;
    }
    Matrix &operator/=(const T &t) {
        int n = height(), m = width();
        for(int i = 0; i < n; i++)
            for(int j = 0; j < m; j++)
                (*this)[i][j] /= t;
        return *this;
    }
    Matrix operator+(const T &t) const {
        return (Matrix(*this) += t);
    }
    Matrix operator-(const T &t) const {
        return (Matrix(*this) -= t);
    }
    Matrix operator*(const T &t) const {
        return (Matrix(*this) *= t);
    }
    Matrix operator/(const T &t) const {
        return (Matrix(*this) /= t);
    }
    friend std::ostream &operator<<(std::ostream &os, Matrix &p) {
        size_t n = p.height(), m = p.width();
        for(int i = 0; i < n; i++) {
            os << '[';
            for(int j = 0; j < m; j++)
                os << p[i][j] << (j == m - 1 ? "]\n" : ",");
        }
        return (os);
    }
    T determinant() {
        Matrix B(*this);
        size_t n = height(), m = width();
        assert(n == m);
        T ret = 1;
        for(int i = 0; i < n; i++) {
            int idx = -1;
            for(int j = i; j < n; j++)
                if(B[j][i] != 0) idx = j;
            if(idx == -1) return 0;
            if(i != idx) {
                ret *= -1;
                swap(B[i], B[idx]);
            }
            ret *= B[i][i];
            T vv = B[i][i];
            for(int j = 0; j < n; j++) B[i][j] /= vv;
            for(int j = i + 1; j < n; j++) {
                T a = B[j][i];
                for(int k = 0; k < n; k++) {
                    B[j][k] -= B[i][k] * a;
                }
            }
        }
        return ret;
    }
    Matrix inv() {
        int n = height();
        if(determinant() == T(0)) return Matrix(0);
        Matrix a(*(this)), l = I(n), u(n);
        for(int j = 0; j < n; j++) u[0][j] = a[0][j];
        for(int j = 1; j < n; j++) l[j][0] = a[j][0] / u[0][0];
        for(int k = 1; k < n; k++) {
            for(int j = k; j < n; j++)
                for(int i = 0; i < k; i++) a[j][k] -= l[j][i] * u[i][k];
            u[k][k] = a[k][k];
            for(int j = k + 1; j < n; j++) {
                u[k][j] = a[k][j];
                for(int i = 0; i < k; i++)
                    u[k][j] -= l[k][i] * u[i][j];
            }
            for(int j = k + 1; j < n; j++) l[j][k] = a[j][k] / u[k][k];
        }
        Matrix x(n), y = I(n);
        for(int i = 0; i < n; i++)
            for(int j = 0; j < n; j++) {
                for(int k = 0; k < j; k++) y[j][i] -= l[j][k] * y[k][i];
            }
        T sigma;
        for(int h = 0; h < n; h++)
            for(int i = n - 1; i >= 0; i--) {
                sigma = y[i][h];
                for(int j = i + 1; j < n; j++) {
                    sigma -= u[i][j] * x[j][h];
                }
                x[i][h] = sigma / u[i][i];
            }
        return x;
    }
};
//ModInt
template <const int &mod>
struct ModInt {
private:
    long long x;
    long long ext_gcd(long long a, long long b, long long &x, long long &y) {
        if(b == 0) {
            x = 1, y = 0;
            return a;
        }
        long long q = a / b;
        long long g = ext_gcd(b, a - q * b, x, y);
        long long z = x - q * y;
        x = y, y = z;
        return g;
    }
public:
    ModInt() : x(0) {}
    ModInt(long long x_) {
        if((x = x_ % mod + mod) >= mod) x -= mod;
    }
    constexpr ModInt &operator+=(ModInt rhs) {
        if((x += rhs.x) >= mod) x -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(ModInt rhs) {
        if((x -= rhs.x) < 0) x += mod;
        return *this;
    }
    constexpr ModInt &operator*=(ModInt rhs) {
        x = (unsigned long long)x * rhs.x % mod;
        return *this;
    }
    constexpr ModInt &operator/=(ModInt rhs) {
        x = (unsigned long long)x * rhs.inv().x % mod;
        return *this;
    }
    constexpr ModInt operator-() const noexcept { return -x < 0 ? mod - x : -x; }
    constexpr ModInt operator+(ModInt rhs) const noexcept { return ModInt(*this) += rhs; }
    constexpr ModInt operator-(ModInt rhs) const noexcept { return ModInt(*this) -= rhs; }
    constexpr ModInt operator*(ModInt rhs) const noexcept { return ModInt(*this) *= rhs; }
    constexpr ModInt operator/(ModInt rhs) const noexcept { return ModInt(*this) /= rhs; }
    constexpr ModInt &operator++() {
        *this += 1;
        return *this;
    }
    constexpr ModInt operator++(int) {
        *this += 1;
        return *this - 1;
    }
    constexpr ModInt &operator--() {
        *this -= 1;
        return *this;
    }
    constexpr ModInt operator--(int) {
        *this -= 1;
        return *this + 1;
    }
    bool operator==(ModInt rhs) const { return x == rhs.x; }
    bool operator!=(ModInt rhs) const { return x != rhs.x; }
    bool operator<=(ModInt rhs) const { return x <= rhs.x; }
    bool operator>=(ModInt rhs) const { return x >= rhs.x; }
    bool operator<(ModInt rhs) const { return x < rhs.x; }
    bool operator>(ModInt rhs) const { return x > rhs.x; }
    ModInt inv() {
        long long x, y;
        ext_gcd(this->x, mod, x, y);
        return (ModInt)x;
    }
    friend std::ostream &operator<<(std::ostream &s, ModInt<mod> a) {
        s << a.x;
        return s;
    }
    friend std::istream &operator>>(std::istream &s, ModInt<mod> &a) {
        s >> a.x;
        return s;
    }
};
//Modulo Calculation
static int MOD = 998244353;
using mint = ModInt<MOD>;
int main() {
    INT(n, m);
    int connect = n, inconv = 0;
    mint pat = 1;
    UnionFind uf(n);
    V<> a(m), b(m);
    V<> h(n, 0);
    REP(i, m) {
        INT(x, y);
        x--, y--;
        if(x > y) swap(x, y);
        a[i] = x, b[i] = y;
        h[x]++, h[y]++;
        if(!uf.same(x, y)) connect--;
        uf.unite(x, y);
    }
    V<bool> used(n, 0);
    V<int> siz;
    REP(i, n) {
        if(used[uf.root(i)]) continue;
        used[uf.root(i)] = 1;
        siz.pb(uf.size(i));
    }
    if(connect == 1) {
        inconv = 0;
        Matrix<mint> mat(n), nm(n - 1);
        REP(i, n)
        mat[i][i] = h[i];
        REP(i, m) {
            mat[a[i]][b[i]]--;
            mat[b[i]][a[i]]--;
        }
        REP(i, n - 1)
        REP(j, n - 1)
        nm[i][j] = mat[i][j];
        pat = nm.determinant();
        V<Matrix<mint>> vec(n);
        REP(k, n) {
            Matrix<mint> nmat(n - 1);
            int icnt = -1;
            REP(i, n) {
                if(i == k) continue;
                icnt++;
                int jcnt = -1;
                REP(j, n) {
                    if(j == k) continue;
                    jcnt++;
                    nmat[icnt][jcnt] = mat[i][j];
                }
            }
            vec[k] = nmat.inv() * nmat.determinant();
        }
        REP(i, n)
        debug(vec[i]);
        for(int i = 0; i < n - 1; i++)
            for(int j = i + 1; j < n; j++) {
                if(mat[i][j] != 0) continue;
                pat += vec[i][j - 1][j - 1];
            }
    } else {
        sort(rall(siz));
        int fircount = 0, seccount = 0;
        int fir = siz[0], sec = siz[1];
        inconv += (n - (siz[0] + siz[1])) * (siz[0] + siz[1]);
        for(int i = 2; i < siz.size(); i++) {
            inconv += (n - siz[i]) * siz[i];
        }
        REP(i, SZ(siz)) {
            if(siz[i] == fir) fircount++;
            if(siz[i] == sec) seccount++;
        }
        map<int, pair<V<>, V<pii>>> mp;
        REP(i, m) {
            int r = uf.root(a[i]);
            mp[r].first.pb(a[i]);
            mp[r].first.pb(b[i]);
            mp[r].second.eb(a[i], b[i]);
        }
        for(auto v : mp) {
            auto &tyo = v.second.first;
            auto &hen = v.second.second;
            V<> res = press(tyo);
            int sz = SZ(res);
            map<int, int> changer;
            REP(i, sz)
            changer[res[i]] = i;
            Matrix<mint> mat(sz), nmat(sz - 1);
            REP(i, SZ(hen)) {
                auto [a, b] = hen[i];
                a = changer[a], b = changer[b];
                mat[a][a]++, mat[b][b]++, mat[a][b]--, mat[b][a]--;
            }
            REP(i, sz - 1)
            REP(j, sz - 1)
            nmat[i][j] = mat[i][j];
            mint nowp = nmat.determinant();
            pat *= nowp;
        }
        if(fir != sec) {
            pat *= fir * sec * seccount;
        } else {
            pat *= fir * fir * fircount * (fircount - 1) / 2;
        }
    }
    print(inconv);
    print(pat);
}
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