結果

問題 No.1116 Cycles of Dense Graph
ユーザー tokusakurai
提出日時 2020-07-18 09:42:43
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 141 ms / 2,000 ms
コード長 5,476 bytes
コンパイル時間 2,378 ms
コンパイル使用メモリ 210,844 KB
最終ジャッジ日時 2025-01-12 00:10:40
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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 * 3
other AC * 38
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 #
プレゼンテーションモードにする

#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 elif else if
#define sp(x) fixed << setprecision(x)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define sz(x) (int)x.size()
using ll = long long;
using ld = long double;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
//const ll MOD = 1e9+7;
const ll MOD = 998244353;
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
const ld EPS = 1e-10;
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<ll mod>
struct Mod_Int{
    ll x;
    Mod_Int() {}
    Mod_Int(ll y) : x (y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
    Mod_Int &operator += (const Mod_Int &p){
        x = (x + p.x) % mod;
        return *this;
    }
    Mod_Int &operator -= (const Mod_Int &p){
        x = (x + mod - p.x) % mod;
        return *this;
    }
    Mod_Int &operator *= (const Mod_Int &p){
        x = (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 pow(ll n) const{
        Mod_Int now = *this, ret = 1;
        while(n > 0){
            if(n & 1) ret *= now;
            now *= now, n >>= 1;
        }
        return ret;
    }
    Mod_Int inverse() const{
        return pow(mod-2);
    }
    friend ostream &operator << (ostream &os, const Mod_Int &p){
        return os << p.x;
    }
    friend istream &operator >> (istream &is, Mod_Int &p){
        ll a;
        is >> a;
        p = Mod_Int<mod>(a);
        return is;
    }
};
using mint = Mod_Int<MOD>;
const int MAX_N = 1e6;
mint fac[MAX_N+1], ifac[MAX_N+1];
void init(){
    fac[0] = 1;
    rep2(i, 1, MAX_N){
        fac[i] = fac[i-1]*i;
    }
    ifac[MAX_N] = fac[MAX_N].inverse();
    rep3(i, MAX_N, 1){
        ifac[i-1] = ifac[i]*i;
    }
}
mint comb(int n, int k){
    return fac[n]*ifac[n-k]*ifac[k];
}
mint perm(int n, int k){
    return fac[n]*ifac[n-k];
}
struct Union_Find_Tree{
    vector<int> par, rank, num;
    
    Union_Find_Tree(int N){
        par.assign(N, -1);
        rank.assign(N, 0);
        num.assign(N, 1);
    }
    
    int root(int x){
        if(par[x] < 0 || par[x] == x) return x;
        return par[x] = root(par[x]);
    }
    
    void unite(int x, int y){
        x = root(x), y = root(y);
        if(x == y) return;
        elif(rank[x] < rank[y]) par[x] = y, num[y] += num[x];
        else{
            par[y] = x, num[x] += num[y];
            if(rank[x] == rank[y]) rank[x]++;
        }
    }
    
    int size(int x) {return num[root(x)];}
    
    bool same(int x, int y){
        return root(x) == root(y);
    }
    
    void clear(){
        fill(par.begin(), par.end(), -1);
        fill(rank.begin(), rank.end(), 0);
        fill(num.begin(), num.end(), 1);
    }
};
int main(){
    int N, M;
    cin >> N >> M;
    int u[M], v[M];
    rep(i, M) {
        cin >> u[i] >> v[i]; u[i]--, v[i]--;
    }
    mint ans = 0;
    init();
    rep2(i, 3, N) ans += comb(N, i)*fac[i-1]/2;
    mint num[2*M+1][M+1];
    rep(i, 2*M+1){
        int n = N-i;
        if(n < 0) continue;
        rep2(j, 1, M){
            num[i][j] = 0;  
            rep2(k, 0, n){
                num[i][j] += perm(n, k)*comb(k+j-1, k);
            }
            if(i == 2 && j == 1) num[i][j]--;
        }
    }
    map<int, int> mp;
    rep2(i, 1, (1<<M)-1){
        rep(j, M){
            if(i&(1<<j)) mp[u[j]]++, mp[v[j]]++;
        }
        bool flag = false;
        int cnt1 = 0, cnt2 = 0;
        int n = 0;
        for(auto &e: mp){
            if(e.second >= 3) flag = true;
            elif(e.second == 2) cnt2++;
            else cnt1++;
            e.second = n++;
        }
        Union_Find_Tree uft(n);
        int circle = 0;
        rep(j, M){
            if(!(i&(1<<j))) continue;
            if(uft.same(mp[u[j]], mp[v[j]]) && cnt1) flag = true;
            elif(uft.same(mp[u[j]], mp[v[j]])) circle++;
            else uft.unite(mp[u[j]], mp[v[j]]);
        }
        if(circle >= 2) flag = true;
        cnt1 /= 2;
        mp.clear();
        if(flag) continue;
        mint tmp;
        if(cnt1 == 0) tmp = 1;
        else tmp = fac[cnt1-1]*mint(2).pow(cnt1-1)*num[cnt2+cnt1*2][cnt1];
        if(__builtin_popcount(i)%2 == 0) ans += tmp;
        else ans -= tmp;
    }
    cout << ans << endl;
}
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