結果
| 問題 | No.1116 Cycles of Dense Graph |
| ユーザー |
👑  emthrm
|
| 提出日時 | 2020-07-18 06:22:32 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 137 ms / 2,000 ms |
| コード長 | 6,675 bytes |
| コンパイル時間 | 4,042 ms |
| コンパイル使用メモリ | 221,980 KB |
| 最終ジャッジ日時 | 2025-01-12 00:01:14 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
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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
#define _USE_MATH_DEFINES#include <bits/stdc++.h>using namespace std;#define FOR(i,m,n) for(int i=(m);i<(n);++i)#define REP(i,n) FOR(i,0,n)#define ALL(v) (v).begin(),(v).end()using ll = long long;const int INF = 0x3f3f3f3f;const ll LINF = 0x3f3f3f3f3f3f3f3fLL;const double EPS = 1e-8;const int MOD = 998244353;const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }struct IOSetup {IOSetup() {cin.tie(nullptr);ios_base::sync_with_stdio(false);cout << fixed << setprecision(20);}} iosetup;int mod = MOD;struct ModInt {unsigned val;ModInt(): val(0) {}ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {}ModInt pow(ll exponent) const {ModInt tmp = *this, res = 1;while (exponent > 0) {if (exponent & 1) res *= tmp;tmp *= tmp;exponent >>= 1;}return res;}ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; }ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; }ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; }ModInt &operator/=(const ModInt &x) {// assert(__gcd(static_cast<int>(x.val), mod) == 1);unsigned a = x.val, b = mod; int u = 1, v = 0;while (b) {unsigned tmp = a / b;swap(a -= tmp * b, b);swap(u -= tmp * v, v);}return *this *= u;}bool operator==(const ModInt &x) const { return val == x.val; }bool operator!=(const ModInt &x) const { return val != x.val; }bool operator<(const ModInt &x) const { return val < x.val; }bool operator<=(const ModInt &x) const { return val <= x.val; }bool operator>(const ModInt &x) const { return val > x.val; }bool operator>=(const ModInt &x) const { return val >= x.val; }ModInt &operator++() { if (++val == mod) val = 0; return *this; }ModInt operator++(int) { ModInt res = *this; ++*this; return res; }ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; }ModInt operator--(int) { ModInt res = *this; --*this; return res; }ModInt operator+() const { return *this; }ModInt operator-() const { return ModInt(val ? mod - val : 0); }ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; }ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; }ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; }ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; }friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; }friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; }};ModInt abs(const ModInt &x) { return x; }struct Combinatorics {int val; // "val!" and "mod" must be disjoint.vector<ModInt> fact, fact_inv, inv;Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) {fact[0] = 1;FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i;fact_inv[val] = ModInt(1) / fact[val];for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i;FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i];}ModInt nCk(int n, int k) const {if (n < 0 || n < k || k < 0) return ModInt(0);// assert(n <= val && k <= val);return fact[n] * fact_inv[k] * fact_inv[n - k];}ModInt nPk(int n, int k) const {if (n < 0 || n < k || k < 0) return ModInt(0);// assert(n <= val);return fact[n] * fact_inv[n - k];}ModInt nHk(int n, int k) const {if (n < 0 || k < 0) return ModInt(0);return k == 0 ? ModInt(1) : nCk(n + k - 1, k);}};struct UnionFind {UnionFind(int n) : data(n, -1) {}int root(int ver) { return data[ver] < 0 ? ver : data[ver] = root(data[ver]); }bool unite(int u, int v) {u = root(u);v = root(v);if (u == v) return false;if (data[u] > data[v]) swap(u, v);data[u] += data[v];data[v] = u;return true;}bool same(int u, int v) { return root(u) == root(v); }int size(int ver) { return -data[root(ver)]; }private:vector<int> data;};int main() {int n, m; cin >> n >> m;if (n < 3) {cout << 0 << '\n';return 0;}Combinatorics com(n);map<pair<int, int>, ModInt> memo;function<ModInt(int, int)> rec = [&](int block, int rem) {if (memo.count({block, rem}) == 1) return memo[{block, rem}];ModInt tmp = 0;FOR(i, block, block + rem + 1) {// cout << block << ' ' << rem << ' ' << com.nCk(rem, i - block) * com.fact[i] << '\n';tmp += com.nCk(rem, i - block) * com.fact[i];}return memo[{block, rem}] = tmp;};vector dp(n + 1, ModInt(0));dp[3] = 1;FOR(i, 4, n + 1) dp[i] = dp[i - 1] * i - dp[i - 2] * (i - 1) + 1LL * (i - 1) * (i - 2) / 2;vector<int> a(m), b(m), comp;REP(i, m) {cin >> a[i] >> b[i], --a[i], --b[i];comp.emplace_back(a[i]);comp.emplace_back(b[i]);}sort(ALL(comp));comp.erase(unique(ALL(comp)), comp.end());int x = comp.size();REP(i, m) {a[i] = lower_bound(ALL(comp), a[i]) - comp.begin();b[i] = lower_bound(ALL(comp), b[i]) - comp.begin();}ModInt ans = dp[n];FOR(i, 1, 1 << m) {UnionFind uf(x);vector cnt(x, 0);REP(j, m) {if (i >> j & 1) {uf.unite(a[j], b[j]);++cnt[a[j]];++cnt[b[j]];}}int united = 0;bool ok = true;REP(i, x) {ok &= cnt[i] <= 2;if (uf.size(i) > 1 && uf.root(i) == i) ++united;}if (!ok) continue;map<int, int> edges;REP(j, m) {if (i >> j & 1) ++edges[uf.root(a[j])];}bool loop = false;for (auto [root, edge] : edges) loop |= uf.size(root) == edge;if (loop) {if (united == 1) {// cout << i << ' ' << 1 << '\n';ans += __builtin_popcount(i) & 1 ? -1 : 1;}continue;}map<int, int> mp;REP(i, x) ++mp[uf.root(i)];int block = 0, sum = 0, mx = 0;for (auto [key, cnt] : mp) {if (cnt >= 2) {++block;sum += cnt;chmax(mx, cnt);}}ModInt tmp = rec(block - 1, n - sum);if (sum == 2) tmp -= 1;// cout << i << ' ' << tmp * ModInt(2).pow(block - 1) << '\n';ans += tmp * (__builtin_popcount(i) & 1 ? -1 : 1) * ModInt(2).pow(block - 1);}cout << ans << '\n';return 0;}