#612605 (C++17) No.1116 Cycles of Dense Graph

• 問題: No.1116 Cycles of Dense Graph
• ユーザー: fumofumofuni
• 提出日時: 2021-02-03 14:34:57
• 言語: C++17 (gcc 13.2.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 21 ms / 2,000 ms
• コード長: 4,930 bytes
• コンパイル時間: 2,547 ms
• コンパイル使用メモリ: 222,956 KB
• 実行使用メモリ: 6,236 KB
• 最終ジャッジ日時: 2023-09-12 12:54:37
• 合計ジャッジ時間: 5,501 ms
• ジャッジサーバーID （参考情報）: judge13 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	6 ms; 5,984 KB
testcase_01	AC	16 ms; 6,024 KB
testcase_02	AC	6 ms; 5,984 KB
testcase_03	AC	6 ms; 6,128 KB
testcase_04	AC	6 ms; 6,168 KB
testcase_05	AC	6 ms; 6,108 KB
testcase_06	AC	9 ms; 6,112 KB
testcase_07	AC	6 ms; 6,212 KB
testcase_08	AC	6 ms; 6,104 KB
testcase_09	AC	6 ms; 6,144 KB
testcase_10	AC	6 ms; 6,212 KB
testcase_11	AC	7 ms; 6,236 KB
testcase_12	AC	7 ms; 6,108 KB
testcase_13	AC	6 ms; 6,108 KB
testcase_14	AC	6 ms; 5,960 KB
testcase_15	AC	6 ms; 6,140 KB
testcase_16	AC	7 ms; 5,984 KB
testcase_17	AC	6 ms; 6,160 KB
testcase_18	AC	6 ms; 5,956 KB
testcase_19	AC	7 ms; 6,156 KB
testcase_20	AC	8 ms; 6,160 KB
testcase_21	AC	8 ms; 6,108 KB
testcase_22	AC	10 ms; 5,952 KB
testcase_23	AC	7 ms; 6,220 KB
testcase_24	AC	21 ms; 6,208 KB
testcase_25	AC	6 ms; 6,156 KB
testcase_26	AC	20 ms; 6,144 KB
testcase_27	AC	6 ms; 5,996 KB
testcase_28	AC	9 ms; 5,984 KB
testcase_29	AC	6 ms; 5,956 KB
testcase_30	AC	6 ms; 6,088 KB
testcase_31	AC	5 ms; 5,984 KB
testcase_32	AC	6 ms; 6,160 KB
testcase_33	AC	6 ms; 6,128 KB
testcase_34	AC	6 ms; 6,232 KB
testcase_35	AC	6 ms; 5,956 KB
testcase_36	AC	21 ms; 6,208 KB
testcase_37	AC	19 ms; 6,212 KB
testcase_38	AC	19 ms; 6,156 KB
testcase_39	AC	17 ms; 6,172 KB
testcase_40	AC	18 ms; 6,088 KB

ソースコード

#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=(n)-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define pb push_back
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=1e9+10;
const ll INF=4e18;
//const ll dy[8]={-1,0,1,0,1,1,-1,-1};
//const ll dx[8]={0,-1,0,1,1,-1,1,-1};
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;
}

const int mod = MOD9;
const int max_n = 200005;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x=0):x((x%mod+mod)%mod){}
  mint operator-() const { return mint(-x);}
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod-a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;}
  mint operator+(const mint a) const { return mint(*this) += a;}
  mint operator-(const mint a) const { return mint(*this) -= a;}
  mint operator*(const mint a) const { return mint(*this) *= a;}
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t>>1);
    a *= a;
    if (t&1) a *= *this;
    return a;
  }
  bool operator==(const mint &p) const { return x == p.x; }
  bool operator!=(const mint &p) const { return x != p.x; }
  // for prime mod
  mint inv() const { return pow(mod-2);}
  mint& operator/=(const mint a) { return *this *= a.inv();}
  mint operator/(const mint a) const { return mint(*this) /= a;}
};
istream& operator>>(istream& is, mint& a) { return is >> a.x;}
ostream& operator<<(ostream& os, const mint& a) { return os << a.x;}

struct combination {
  vector<mint> fact, ifact;
  combination(int n):fact(n+1),ifact(n+1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n) return 0;
    return fact[n]*ifact[k]*ifact[n-k];
  }
}comb(max_n);

struct UnionFind {
    vector<int> par;
    
    UnionFind(int n) : par(n, -1) {}

    int root(int x) {
        if (par[x] < 0) return x;
        else return par[x] = root(par[x]);
    }
    
    bool same(int x, int y) {
        return root(x) == root(y);
    }
    
    bool merge(int x, int y) {
        x = root(x); y = root(y);
        if (x == y) return false;
        if (par[x] > par[y]) swap(x, y);
        par[x] += par[y];
        par[y] = x;
        return true;
    }
    
    int size(int x) {
        return -par[root(x)];
    }
};
map<ll,mint> memo[16];
ll n;
mint calc(ll p,ll q){//pはパスの本数、qは残り頂点 辺が1本かつq==n-2の時場合わけ
    if(memo[p].count(q))return memo[p][q];
    mint ret=0;
    for(int i=0;i<=q;i++){
        ret+=comb(q,i)*comb(i+p-1,i)*comb.fact[i];
    }
    ret*=comb.fact[p-1];
    rep(i,p-1)ret*=2;
    if(q==n-2)ret-=1;
    memo[p][q]=ret;
    return ret;
}   
int main(){
    ll m;cin >> n >>m;
    vpl v(m);vl pls(2*m);
    rep(i,m){
        cin >> v[i].fi >> v[i].se;
        pls[i*2]=v[i].fi;
        pls[i*2+1]=v[i].se;
    }
    sort(all(pls));
    pls.erase(unique(all(pls)),pls.end());
    rep(i,m){
        v[i].fi=lower_bound(all(pls),v[i].fi)-pls.begin();
        v[i].se=lower_bound(all(pls),v[i].se)-pls.begin();
    }
    ll k=pls.size();
    mint ans=0;
    for(int i=3;i<=n;i++)ans+=comb(n,i)*comb.fact[i-1]/2;
    repl(bit,1,1<<m){
        UnionFind uf(k);
        vector<ll> deg(k);
        ll cycle=0;
        rep(i,m){
            if(bit>>i&1){
                ll a=v[i].fi,b=v[i].se;
                if(uf.same(a,b))cycle++;
                uf.merge(a,b);
                deg[a]++;deg[b]++;
            }
        }
        bool flag=true;
        mint ret=0;
        rep(i,k)if(deg[i]>=3)flag=false;
        if(cycle>=2)flag=false;
        if(!flag)continue;
        if(cycle==1){
            sort(all(deg));
            if(!binary_search(all(deg),1))ret=1;
        }
        else {
            ll cnt=0,rem=0;
            rep(i,k){
                if(deg[i]==1)cnt++;
                if(deg[i]>=1)rem++;
            }
            cnt/=2;rem=n-rem;
            ret=calc(cnt,rem);
        }
        //cout << ret <<endl;
        if(__builtin_popcount(bit)%2)ret*=-1;
        ans+=ret;
    }
    cout << ans <<endl;
}