結果

問題 No.1116 Cycles of Dense Graph
ユーザー hitonanodehitonanode
提出日時 2020-07-17 22:15:14
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,759 ms / 2,000 ms
コード長 10,855 bytes
コンパイル時間 2,868 ms
コンパイル使用メモリ 233,812 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-30 00:38:58
合計ジャッジ時間 14,693 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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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 3 ms
5,248 KB
testcase_01 AC 126 ms
5,248 KB
testcase_02 AC 11 ms
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testcase_03 AC 6 ms
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testcase_04 AC 7 ms
5,248 KB
testcase_05 AC 68 ms
5,248 KB
testcase_06 AC 90 ms
5,248 KB
testcase_07 AC 25 ms
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testcase_08 AC 7 ms
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testcase_09 AC 20 ms
5,248 KB
testcase_10 AC 16 ms
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testcase_11 AC 91 ms
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testcase_12 AC 55 ms
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testcase_13 AC 4 ms
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testcase_14 AC 12 ms
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testcase_15 AC 17 ms
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testcase_16 AC 52 ms
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testcase_17 AC 8 ms
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testcase_18 AC 30 ms
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testcase_19 AC 29 ms
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testcase_20 AC 222 ms
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testcase_21 AC 94 ms
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testcase_22 AC 678 ms
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testcase_23 AC 4 ms
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testcase_24 AC 1,434 ms
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testcase_25 AC 3 ms
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testcase_26 AC 1,615 ms
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testcase_27 AC 8 ms
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testcase_28 AC 190 ms
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testcase_29 AC 4 ms
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testcase_30 AC 2 ms
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testcase_31 AC 2 ms
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testcase_32 AC 2 ms
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testcase_33 AC 2 ms
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testcase_34 AC 2 ms
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testcase_35 AC 2 ms
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testcase_36 AC 1,759 ms
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testcase_37 AC 1,664 ms
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testcase_38 AC 1,663 ms
5,248 KB
testcase_39 AC 301 ms
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testcase_40 AC 296 ms
5,248 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 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> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template <typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }
template <typename V, typename T> void ndfill(V &x, const T &val) { x = val; }
template <typename V, typename T> void ndfill(vector<V> &vec, const T &val) { for (auto &v : vec) ndfill(v, val); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << "(" << pa.first << "," << pa.second << ")"; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

template <int mod>
struct ModInt
{
    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;
    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; }
    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; is >> t; x = ModInt(t); return is; }
    friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val;  return os; }
    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 lint inv() const { return this->power(mod - 2); }
    constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }
    constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }

    inline 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;
        if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();
        else return ModInt(k).fac() * ModInt(2).power(k);
    }

    ModInt nCr(const ModInt &r) const {
        if (this->val < r.val) return ModInt(0);
        return 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));
    }
};

constexpr lint MOD = 998244353;
using mint = ModInt<MOD>;

vector<vector<mint>> dp;

// UnionFind, able to rewind to the previous state by undo()
// Written for Educational Codeforces 62 F, although not verified yet.
struct UndoSizeAwareUnionFind
{
    using pint = std::pair<int, int>;
    std::vector<int> par, cou;
    std::stack<std::pair<int, pint>> history;
    UndoSizeAwareUnionFind(int N) : par(N), cou(N, 1) {
        std::iota(par.begin(), par.end(), 0);
    }
    int find(int x) { return (par[x] == x) ? x :find(par[x]); }
    void unite(int x, int y) {
        x = find(x), y = find(y);
        if (cou[x] < cou[y]) std::swap(x, y);
        history.emplace(y, pint(par[y], cou[x]));
        if (x != y) par[y] = x, cou[x] += cou[y];
    }
    void undo() {
        cou[par[history.top().first]] = history.top().second.second;
        par[history.top().first] = history.top().second.first;
        history.pop();
    }
    void reset() {
        while (!history.empty()) undo();
    }
    int count(int x) { return cou[find(x)]; }
    bool same(int x, int y) { return find(x) == find(y); }
};

int main()
{
    int N, M;
    cin >> N >> M;
    vector<pint> p(M);
    REP(i, M)
    {
        cin >> p[i].first >> p[i].second;
    }

    mint ret = 0;
    FOR(i, 3, N + 1)
    {
        ret += mint(N).fac() / mint(N - i).fac() / i;
    }
    dbg(ret);

    ndarray(dp, M + 1, 2 * M + 1);
    ndfill(dp, 2);
    FOR(e, 1, M + 1) FOR(v, 1, M * 2 + 1) if (N - v >= 0)
    {
        mint tmp = 0;
        REP(nins, N - v + 1)
        {
            if (v + nins < 3) continue;
            tmp += mint(N - v).nCr(nins) * mint(nins).fac() * mint(nins + e - 1).nCr(e - 1);
        }
        dp[e][v] = tmp * mint(e - 1).fac() * mint(2).power(e);
    }

    UndoSizeAwareUnionFind uf(N + 1);
    REP(S, 1 << M) if (S)
    {
        unordered_map<int, int> cnt;
        uf.reset();
        int pc = __builtin_popcount(S);
        int r = -1;
        REP(i, M) if ((S >> i) & 1)
        {
            cnt[p[i].first]++;
            cnt[p[i].second]++;
            r = p[i].first;
            uf.unite(p[i].first, p[i].second);
        }

        bool ok = true;
        int nb1 = 0;
        set<int> vd1;
        for (auto pa : cnt)
        {
            if (pa.second > 2) ok = false;
            nb1 += (pa.second == 1);
            if (pa.second == 1) vd1.insert(pa.first);
        }

        int nok = 0, nbad = 0;
        for (auto pa : cnt)
        {
            int v = pa.first;
            bool flg = false;
            for (auto x : vd1) if (uf.same(v, x)) flg = true;
            if (flg) nok++;
            else nbad++;
        }

        if (nok and nbad) ok = false;
        if (!nok and uf.count(r) != pc) ok = false;
        if (!ok) continue;

        int e = nb1 / 2;
        int v = e + pc;
        ret += dp.at(e).at(v) * (pc % 2 ? -1 : 1);
    }
    cout << ret / 2 << '\n';
}
0