結果
| 問題 | No.1116 Cycles of Dense Graph |
| ユーザー |
 haruki_K
|
| 提出日時 | 2020-07-18 17:02:42 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 113 ms / 2,000 ms |
| コード長 | 9,857 bytes |
| コンパイル時間 | 2,325 ms |
| コンパイル使用メモリ | 209,652 KB |
| 最終ジャッジ日時 | 2025-01-12 00:19:24 |
|
ジャッジサーバーID （参考情報） |
judge5 / 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
// >>> TEMPLATES#include <bits/stdc++.h>using namespace std;using ll = long long;using ld = long double;using i32 = int32_t;using i64 = int64_t;using u32 = uint32_t;using u64 = uint64_t;#define int ll#define double ld#define rep(i,n) for (int i = 0; i < (int)(n); i++)#define rep1(i,n) for (int i = 1; i <= (int)(n); i++)#define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--)#define rep1R(i,n) for (int i = (int)(n); i >= 1; i--)#define loop(i,a,B) for (int i = a; i B; i++)#define loopR(i,a,B) for (int i = a; i B; i--)#define all(x) (x).begin(), (x).end()#define allR(x) (x).rbegin(), (x).rend()#define pb push_back#define eb emplace_back#define mp make_pair#define fst first#define snd secondtemplate <class Int> auto constexpr inf = numeric_limits<Int>::max()/2-1;auto constexpr INF32 = inf<int32_t>;auto constexpr INF64 = inf<int64_t>;auto constexpr INF = inf<int>;#ifdef LOCAL#include "debug.hpp"#else#define dump(...) (void)(0)#define say(x) (void)(0)#define debug if (0)#endiftemplate <class T> using pque_max = priority_queue<T>;template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; }template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; }template <class T, class S> ostream& operator<<(ostream& os, pair<T,S> const& p) { return os << "(" << p.first << ", " << p.second << ")"; }template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; }struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;template <class F> struct FixPoint : private F {constexpr FixPoint(F&& f) : F(forward<F>(f)) {}template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }};struct MakeFixPoint {template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); }};#define MFP MakeFixPoint()|#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)template <class T, size_t d> struct vec_impl {using type = vector<typename vec_impl<T,d-1>::type>;template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); }};template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } };template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type;template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); }template <class T> void quit(T const& x) { cout << x << endl; exit(0); }template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; }template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; }template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); }template <class T> int sz(T const& x) { return x.size(); }template <class C, class T> int lbd(C const& v, T const& x) {return lower_bound(v.begin(), v.end(), x)-v.begin();}template <class C, class T> int ubd(C const& v, T const& x) {return upper_bound(v.begin(), v.end(), x)-v.begin();}const int dx[] = { 1,0,-1,0 };const int dy[] = { 0,1,0,-1 };constexpr int popcnt(ll x) { return __builtin_popcountll(x); }template <class Int> struct Random {mt19937_64 mt{random_device{}()};//mt19937_64 mt{(unsigned)time(0)};Int a,b; // [a,b]Random(Int a, Int b) : a(a), b(b) {}Int operator()() { return uniform_int_distribution<Int>(a,b)(mt); }};template <class Int> Int rand(Int a, Int b) { // [a,b]static mt19937_64 mt{random_device{}()};return uniform_int_distribution<Int>(a,b)(mt);}// <<<// >>> modinttemplate <uint32_t md>class modint {static_assert(md < (1u<<31), "");using M = modint;using i64 = int64_t;uint32_t x;public:static constexpr uint32_t mod = md;constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { }constexpr i64 val() const { return x; }constexpr explicit operator i64() const { return x; }constexpr bool operator==(M r) const { return x == r.x; }constexpr bool operator!=(M r) const { return x != r.x; }constexpr M operator+() const { return *this; }constexpr M operator-() const { return M()-*this; }constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; }constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; }constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; }constexpr M& operator/=(M r) { return *this *= r.inv(); }constexpr M operator+(M r) const { return M(*this) += r; }constexpr M operator-(M r) const { return M(*this) -= r; }constexpr M operator*(M r) const { return M(*this) *= r; }constexpr M operator/(M r) const { return M(*this) /= r; }friend constexpr M operator+(i64 x, M y) { return M(x)+y; }friend constexpr M operator-(i64 x, M y) { return M(x)-y; }friend constexpr M operator*(i64 x, M y) { return M(x)*y; }friend constexpr M operator/(i64 x, M y) { return M(x)/y; }constexpr M inv() const { assert(x > 0); return pow(md-2); }constexpr M pow(i64 n) const {assert(not (x == 0 && n == 0));if (n < 0) return inv().pow(-n);M v = *this, r = 1;for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;return r;}#ifdef LOCALfriend string to_s(M r) { return to_s(r.val(), mod); }#endiffriend ostream& operator<<(ostream& os, M r) { return os << r.val(); }friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }};// <<<constexpr int64_t MOD = 998244353;//constexpr int64_t MOD = 1e9+7;using mint = modint<MOD>;mint sgn(int n) { return n%2 == 0 ? +1 : -1; }// >>> mod tabletemplate <int32_t mod>struct ModTable {static constexpr int32_t Size = 1e6 + 10;static_assert(Size <= mod, "");using ll = int64_t;int32_t fact[Size], finv[Size], inv[Size];ModTable() {fact[0] = fact[1] = finv[0] = finv[1] = inv[1] = 1;for (int i = 2; i < Size; i++) {fact[i] = ll(fact[i-1])*i % mod;inv[i] = mod - ll(inv[mod%i])*(mod/i) % mod;finv[i] = ll(finv[i-1])*inv[i] % mod;}}};const ModTable<MOD> mod_tab;modint<MOD> fact(int n) {assert(0 <= n); assert(n < ModTable<MOD>::Size);return mod_tab.fact[n];}modint<MOD> finv(int n) {assert(0 <= n); assert(n < ModTable<MOD>::Size);return mod_tab.finv[n];}modint<MOD> C(int n, int k) {if (n < 0 || k < 0 || n < k) return 0;return fact(n)*finv(k)*finv(n-k);}modint<MOD> P(int n, int k) {assert(k >= 0);return fact(n)*finv(n-k);}// <<<// >>> union findstruct UnionFind {int n, sz; // id : 0...n-1vector<int> par;UnionFind(int n = 0) : n(n), sz(n), par(n,-1) { }int root(int x) {assert(0 <= x); assert(x < n);return par[x] < 0 ? x : par[x] = root(par[x]);}bool unite(int x, int y) {x = root(x), y = root(y);if (x == y) return false;sz--;if (par[x] < par[y]) swap(x,y);par[y] += par[x];par[x] = y;return true;}bool same(int x, int y) { return root(x) == root(y); }int size(int x) { return -par[root(x)]; }int size() const { return sz; }struct groups_t {vector<vector<int> > grp;vector<pair<int,int> > id;};groups_t groups() {vector<vector<int> > g(n);rep (i,n) if (par[i] < 0) g[i].reserve(-par[i]);rep (i,n) g[root(i)].push_back(i);vector<vector<int> > grp; grp.reserve(size());rep (i,n) if (g[i].size()) grp.emplace_back(move(g[i]));vector<pair<int,int> > id(n);rep (i,grp.size()) rep (j,grp[i].size()) {id[grp[i][j]] = make_pair(i,j);}return { grp, id };}};// <<<int32_t main() {int n,m; cin >> n >> m;vector<int> a(m),b(m);rep (i,m) cin >> a[i] >> b[i], --a[i],--b[i];auto memo = make_v<mint,2>(2*m+1,m+1);rep (k,2*m+1) rep (r,m+1) {if (k == 0 || r == 0) continue;auto &res = memo[k][r];rep (i,n-k+1) if (k+i >= 3) res += C(n-k,i) * fact(r+i-1);res *= mint(2).pow(r-1);}rep (i,n+1) if (i >= 3) memo[0][0] += C(n,i) * fact(i-1) / 2;vector<int> deg(n);mint ans = 0;UnionFind uf(n);rep (s,1LL<<m) {bool ok = true;int k = 0, r = 0;rep (i,m) if (s>>i&1) {uf.unite(a[i],b[i]);r++;if (deg[a[i]] == 0) k++;if (deg[b[i]] == 0) k++;if (deg[a[i]] == 1) r--;if (deg[b[i]] == 1) r--;if (++deg[a[i]] > 2) ok = false;if (++deg[b[i]] > 2) ok = false;}if (ok) {int loop = uf.size() - (n-k) - r;if (loop == 1 && r == 0) {ans += sgn(popcnt(s));} else if (loop == 0) {ans += sgn(popcnt(s)) * memo[k][r];}}rep (i,m) if (s>>i&1) {--deg[a[i]],--deg[b[i]];uf.par[a[i]] = -1;uf.par[b[i]] = -1;}uf.sz = n;}cout << ans << endl;}