結果
問題 | No.1116 Cycles of Dense Graph |
ユーザー |
![]() |
提出日時 | 2020-07-17 22:15:14 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
TLE
(最新)
AC
(最初)
|
実行時間 | - |
コード長 | 10,855 bytes |
コンパイル時間 | 14,758 ms |
コンパイル使用メモリ | 283,724 KB |
最終ジャッジ日時 | 2025-01-11 22:49:45 |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 33 TLE * 5 |
ソースコード
#include <bits/stdc++.h>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }template <typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); }template <typename V, typename T> void ndfill(V &x, const T &val) { x = val; }template <typename V, typename T> void ndfill(vector<V> &vec, const T &val) { for (auto &v : vec) ndfill(v, val); }template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }template <typename T> vector<T> srtunq(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); returnvec; }template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; }template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os;}template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; }template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; returnos; }template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os;}template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << "{"; for (auto v : vec) os << v << ","; os << "}";return os; }template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << "(" << pa.first << "," << pa.second << ")";return os; }template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; }template <typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) { os << "{"; for (auto v : mp) os << v.first <<"=>" << v.second << ","; os << "}"; return os; }#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;template <int mod>struct ModInt{using lint = long long;static int get_mod() { return mod; }static int get_primitive_root() {static int primitive_root = 0;if (!primitive_root) {primitive_root = [&](){std::set<int> fac;int v = mod - 1;for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < mod; g++) {bool ok = true;for (auto i : fac) if (ModInt(g).power((mod - 1) / i) == 1) { ok = false; break; }if (ok) return g;}return -1;}();}return primitive_root;}int val;constexpr ModInt() : val(0) {}constexpr ModInt &_setval(lint v) { val = (v >= mod ? v - mod : v); return *this; }constexpr ModInt(lint v) { _setval(v % mod + mod); }explicit operator bool() const { return val != 0; }constexpr ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); }constexpr ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); }constexpr ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); }constexpr ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); }constexpr ModInt operator-() const { return ModInt()._setval(mod - val); }constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); }friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); }friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); }friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); }constexpr bool operator==(const ModInt &x) const { return val == x.val; }constexpr bool operator!=(const ModInt &x) const { return val != x.val; }bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T>friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; is >> t; x = ModInt(t); return is; }friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { os << x.val; return os; }constexpr lint power(lint n) const {lint ans = 1, tmp = this->val;while (n) {if (n & 1) ans = ans * tmp % mod;tmp = tmp * tmp % mod;n /= 2;}return ans;}constexpr lint inv() const { return this->power(mod - 2); }constexpr ModInt operator^(lint n) const { return ModInt(this->power(n)); }constexpr ModInt &operator^=(lint n) { return *this = *this ^ n; }inline ModInt fac() const {static std::vector<ModInt> facs;int l0 = facs.size();if (l0 > this->val) return facs[this->val];facs.resize(this->val + 1);for (int i = l0; i <= this->val; i++) facs[i] = (i == 0 ? ModInt(1) : facs[i - 1] * ModInt(i));return facs[this->val];}ModInt doublefac() const {lint k = (this->val + 1) / 2;if (this->val & 1) return ModInt(k * 2).fac() / ModInt(2).power(k) / ModInt(k).fac();else return ModInt(k).fac() * ModInt(2).power(k);}ModInt nCr(const ModInt &r) const {if (this->val < r.val) return ModInt(0);return this->fac() / ((*this - r).fac() * r.fac());}ModInt sqrt() const {if (val == 0) return 0;if (mod == 2) return val;if (power((mod - 1) / 2) != 1) return 0;ModInt b = 1;while (b.power((mod - 1) / 2) == 1) b += 1;int e = 0, m = mod - 1;while (m % 2 == 0) m >>= 1, e++;ModInt x = power((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModInt z = b.power(m);while (y != 1) {int j = 0;ModInt t = y;while (t != 1) j++, t *= t;z = z.power(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModInt(std::min(x.val, mod - x.val));}};constexpr lint MOD = 998244353;using mint = ModInt<MOD>;vector<vector<mint>> dp;// UnionFind, able to rewind to the previous state by undo()// Written for Educational Codeforces 62 F, although not verified yet.struct UndoSizeAwareUnionFind{using pint = std::pair<int, int>;std::vector<int> par, cou;std::stack<std::pair<int, pint>> history;UndoSizeAwareUnionFind(int N) : par(N), cou(N, 1) {std::iota(par.begin(), par.end(), 0);}int find(int x) { return (par[x] == x) ? x :find(par[x]); }void unite(int x, int y) {x = find(x), y = find(y);if (cou[x] < cou[y]) std::swap(x, y);history.emplace(y, pint(par[y], cou[x]));if (x != y) par[y] = x, cou[x] += cou[y];}void undo() {cou[par[history.top().first]] = history.top().second.second;par[history.top().first] = history.top().second.first;history.pop();}void reset() {while (!history.empty()) undo();}int count(int x) { return cou[find(x)]; }bool same(int x, int y) { return find(x) == find(y); }};int main(){int N, M;cin >> N >> M;vector<pint> p(M);REP(i, M){cin >> p[i].first >> p[i].second;}mint ret = 0;FOR(i, 3, N + 1){ret += mint(N).fac() / mint(N - i).fac() / i;}dbg(ret);ndarray(dp, M + 1, 2 * M + 1);ndfill(dp, 2);FOR(e, 1, M + 1) FOR(v, 1, M * 2 + 1) if (N - v >= 0){mint tmp = 0;REP(nins, N - v + 1){if (v + nins < 3) continue;tmp += mint(N - v).nCr(nins) * mint(nins).fac() * mint(nins + e - 1).nCr(e - 1);}dp[e][v] = tmp * mint(e - 1).fac() * mint(2).power(e);}UndoSizeAwareUnionFind uf(N + 1);REP(S, 1 << M) if (S){unordered_map<int, int> cnt;uf.reset();int pc = __builtin_popcount(S);int r = -1;REP(i, M) if ((S >> i) & 1){cnt[p[i].first]++;cnt[p[i].second]++;r = p[i].first;uf.unite(p[i].first, p[i].second);}bool ok = true;int nb1 = 0;set<int> vd1;for (auto pa : cnt){if (pa.second > 2) ok = false;nb1 += (pa.second == 1);if (pa.second == 1) vd1.insert(pa.first);}int nok = 0, nbad = 0;for (auto pa : cnt){int v = pa.first;bool flg = false;for (auto x : vd1) if (uf.same(v, x)) flg = true;if (flg) nok++;else nbad++;}if (nok and nbad) ok = false;if (!nok and uf.count(r) != pc) ok = false;if (!ok) continue;int e = nb1 / 2;int v = e + pc;ret += dp.at(e).at(v) * (pc % 2 ? -1 : 1);}cout << ret / 2 << '\n';}