結果

問題 No.1116 Cycles of Dense Graph
コンテスト
ユーザー heno239
提出日時 2020-07-19 11:44:34
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 102 ms / 2,000 ms
コード長 5,021 bytes
コンパイル時間 2,002 ms
コンパイル使用メモリ 138,340 KB
実行使用メモリ 7,680 KB
最終ジャッジ日時 2024-12-16 05:40:45
合計ジャッジ時間 4,127 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
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 #
raw source code 

#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<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 998244353;
const ll INF = mod * mod;
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 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++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n,ll m) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 18;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}

struct uf {
private:
	vector<int> par, ran;
public:
	uf(int n) {
		par.resize(n, 0);
		ran.resize(n, 0);
		rep(i, n) {
			par[i] = i;
		}
	}
	int find(int x) {
		if (par[x] == x)return x;
		else return par[x] = find(par[x]);
	}
	void unite(int x, int y) {
		x = find(x), y = find(y);
		if (x == y)return;
		if (ran[x] < ran[y]) {
			par[x] = y;
		}
		else {
			par[y] = x;
			if (ran[x] == ran[y])ran[x]++;
		}
	}
	bool same(int x, int y) {
		return find(x) == find(y);
	}
};

map<P, bool> calced;
map<P, modint> memo;
modint f(int cmp, int rest) {
	if (calced[{cmp, rest}])return memo[{cmp, rest}];
	calced[{cmp, rest}] = true;
	modint res = 0;
	rep(i, rest + 1) {
		res += comb(rest, i) * fact[i + cmp - 1] / fact[cmp - 1];
	}
	return memo[{cmp, rest}] = res;
}

void solve(){
	int n, m; cin >> n >> m;
	vector<int> a(m), b(m);
	rep(i, m) {
		cin >> a[i] >> b[i];
		a[i]--; b[i]--;
	}
	modint ans = 0;
	for (int c = 3; c <= n; c++) {
		ans += comb(n, c) * fact[c - 1] * (modint)((1 + mod) / 2);
	}
	rep1(i, (1 << m) - 1) {
		vector<P> vs;
		vector<int> vx;
		rep(j, m)if (i & (1 << j)) {
			vs.push_back({ a[j],b[j] });
			vx.push_back(a[j]);
			vx.push_back(b[j]);
		}
		sort(all(vx));
		vx.erase(unique(all(vx)), vx.end());
		rep(j, vs.size()) {
			vs[j].first = lower_bound(all(vx), vs[j].first) - vx.begin();
			vs[j].second = lower_bound(all(vx), vs[j].second) - vx.begin();
		}
		vector<int> cnt(vx.size());
		rep(j, vs.size()) {
			cnt[vs[j].first]++;
			cnt[vs[j].second]++;
		}
		bool exi3 = false;
		rep(j, vx.size()) {
			if (cnt[j] >= 3)exi3 = true;
		}
		if (exi3)continue;

		uf u(vx.size()+1);
		bool isc = false;
		rep(j, vs.size()) {
			int l = vs[j].first, r = vs[j].second;
			if (u.same(l, r))isc = true;
			else u.unite(l, r);
		}
		int cmp = 0;
		rep(j, vx.size()) {
			if (!u.same(j, vx.size())) {
				cmp++;
				u.unite(j, vx.size());
			}
		}
		if (isc) {
			if (cmp == 1) {
				if (vs.size() % 2)ans -= 1;
				else ans += 1;
			}
			continue;
		}
		int rest = n - vx.size();
		modint csum = f(cmp, rest);
		if (vs.size() == 1)csum -= 1;
		else {
			rep(tt, cmp - 1)csum *= 2;
			csum *= fact[cmp - 1];
		}
		//cout << i << " ? " << csum << " "<<cmp<<" "<<rest<<"\n";
		if (vs.size() % 2)ans -= csum;
		else ans += csum;
	}
	cout << ans << "\n";
}




signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	init_f();
	//cout << grandy(2, 3, false, false) << "\n";
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}
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