結果
| 問題 | No.1116 Cycles of Dense Graph |
| ユーザー |
 Chanyuh
|
| 提出日時 | 2020-07-18 17:29:09 |
| 言語 | C++11 (gcc 13.3.0) |
| 結果 |
AC
|
| 実行時間 | 94 ms / 2,000 ms |
| コード長 | 6,002 bytes |
| コンパイル時間 | 1,314 ms |
| コンパイル使用メモリ | 129,448 KB |
| 実行使用メモリ | 7,296 KB |
| 最終ジャッジ日時 | 2024-11-30 21:42:10 |
| 合計ジャッジ時間 | 3,099 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 38 |
ソースコード
#include<iostream>#include<string>#include<cstdio>#include<vector>#include<cmath>#include<algorithm>#include<functional>#include<iomanip>#include<queue>#include<ciso646>#include<random>#include<map>#include<set>#include<complex>#include<bitset>#include<stack>#include<unordered_map>#include<utility>#include<tuple>using namespace std;typedef long long ll;typedef unsigned int ui;const ll mod = 998244353;const ll INF = (ll)1000000007 * 1000000007;typedef pair<int, int> P;#define stop char nyaa;cin>>nyaa;#define rep(i,n) for(int i=0;i<n;i++)#define per(i,n) for(int i=n-1;i>=0;i--)#define Rep(i,sta,n) for(int i=sta;i<n;i++)#define Per(i,sta,n) for(int i=n-1;i>=sta;i--)#define rep1(i,n) for(int i=1;i<=n;i++)#define per1(i,n) for(int i=n;i>=1;i--)#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)typedef long double ld;const ld eps = 1e-8;const ld pi = acos(-1.0);typedef pair<ll, ll> LP;int dx[4]={1,-1,0,0};int dy[4]={0,0,1,-1};template<int mod>struct ModInt {long long x;ModInt() : x(0) {}ModInt(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}explicit operator int() const {return x;}ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator*=(const ModInt &p) {x = (int)(1LL * x * p.x % mod);return *this;}ModInt &operator/=(const ModInt &p) {*this *= p.inverse();return *this;}ModInt operator-() const { return ModInt(-x); }ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }bool operator==(const ModInt &p) const { return x == p.x; }bool operator!=(const ModInt &p) const { return x != p.x; }ModInt inverse() const{int a = x, b = mod, u = 1, v = 0, t;while(b > 0) {t = a / b;a -= t * b;swap(a, b);u -= t * v;swap(u, v);}return ModInt(u);}ModInt power(long long p) const{int a = x;if (p==0) return 1;if (p==1) return ModInt(a);if (p%2==1) return (ModInt(a)*ModInt(a)).power(p/2)*ModInt(a);else return (ModInt(a)*ModInt(a)).power(p/2);}ModInt power(const ModInt p) const{return ((ModInt)x).power(p.x);}friend ostream &operator<<(ostream &os, const ModInt<mod> &p) {return os << p.x;}friend istream &operator>>(istream &is, ModInt<mod> &a) {long long x;is >> x;a = ModInt<mod>(x);return (is);}};using modint = ModInt<mod>;struct ModFac{public:vector<modint> f,i_f;int n;ModFac(int n_){n=n_;f.resize(n+1,1);i_f.resize(n+1,1);for(int i=0;i<n;i++){f[i+1]=f[i]*(modint)(i+1);}i_f[n]=f[n].power(mod-2);for(int i=n-1;i>=0;i--){i_f[i]=i_f[i+1]*(modint)(i+1);}}ModFac(modint n_){n=(int)n_;f.resize(n+1,1);i_f.resize(n+1,1);for(int i=0;i<n;i++){f[i+1]=f[i]*(modint)(i+1);}i_f[n]=f[n].power(mod-2);for(int i=n-1;i>=0;i--){i_f[i]=i_f[i+1]*(modint)(i+1);}}modint factorial(int x){//cout << f.size() << endl;return f[x];}modint inv_factorial(int x){return i_f[x];}modint comb(int m,int k){if (m<0 or k<0) return 0;if (m<k) return 0;return f[m]*i_f[k]*i_f[m-k];}};int n,m;P E[20];set<int> se;vector<P> G[100010];map<int,bool> visited;map<P,pair<modint,bool>> memo;ModFac MF(110000);void dfs(int s,int edges,int &node,int &edge,int &max_branch){visited[s]=true;int branch=0;node+=1;for(P e:G[s]){if(!(edges&(1 << e.second))) continue;branch+=1;edge+=1;if(visited[e.first]) continue;dfs(e.first,edges,node,edge,max_branch);}max_branch=max(max_branch,branch);}modint f(int M,int K){if(memo[P(M,K)].second) return memo[P(M,K)].first;modint res=0;rep(i,M+1){res+=MF.comb(M,i)*MF.factorial(i+K);}memo[P(M,K)].first=res;memo[P(M,K)].second=true;return res;}void solve(){cin >> n >> m;rep(i,m){int a,b;cin >> a >> b;a--;b--;se.insert(a);se.insert(b);E[i]=P(a,b);G[a].push_back(P(b,i));G[b].push_back(P(a,i));}int U=(1 << m);modint ans=0;rep(S,U){modint res=0;visited.clear();int num_cycle=0,num_pass=0,num_NG=0,others=n;//cout << bitset<15>(S) << endl;for(int a:se){if(visited[a]) continue;int node=0,edge=0,max_branch=0;dfs(a,S,node,edge,max_branch);edge/=2;if(node==1) continue;if(node==edge+1 && max_branch<=2) num_pass+=1;if(node==edge && max_branch==2) num_cycle+=1;if(max_branch>=3) num_NG+=1;others-=node;}//cout << num_pass << " " << num_cycle << " " << num_NG << endl;//cout << others << endl;//if(num_cycle>=2) cout << bitset<15>(S) << endl;if(num_NG) continue;if(num_cycle==1 && num_pass==0) res=1;if(num_cycle==0 && num_pass>=1) {res=((modint)2).power(num_pass-1)*f(others,num_pass-1);if(n-others==2) res-=1;}//cout << res << endl;int cnt=0;rep(i,m){if(S&(1 << i)) cnt+=1;}if(cnt%2==1) ans+=res;else ans-=res;}modint ALL=0;Rep(i,3,n+1){ALL+=MF.factorial(n)/((modint)(2*i)*MF.factorial(n-i));}//cout << ALL << endl;cout << ALL-ans << endl;}int main(){ios::sync_with_stdio(false);cin.tie(0);cout << fixed << setprecision(50);solve();}