結果

問題 No.1116 Cycles of Dense Graph
ユーザー 👑 emthrmemthrm
提出日時 2020-07-18 06:22:32
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 86 ms / 2,000 ms
コード長 6,675 bytes
コンパイル時間 2,707 ms
コンパイル使用メモリ 230,700 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-08-20 16:38:58
合計ジャッジ時間 4,301 ms
ジャッジサーバーID
（参考情報） 		judge11 / judge12
このコードへのチャレンジ（β）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
4,376 KB
testcase_01 AC 51 ms
4,376 KB
testcase_02 AC 3 ms
4,376 KB
testcase_03 AC 1 ms
4,376 KB
testcase_04 AC 1 ms
4,376 KB
testcase_05 AC 3 ms
4,380 KB
testcase_06 AC 18 ms
4,376 KB
testcase_07 AC 2 ms
4,376 KB
testcase_08 AC 1 ms
4,380 KB
testcase_09 AC 2 ms
4,376 KB
testcase_10 AC 2 ms
4,376 KB
testcase_11 AC 10 ms
4,376 KB
testcase_12 AC 3 ms
4,376 KB
testcase_13 AC 1 ms
4,376 KB
testcase_14 AC 2 ms
4,376 KB
testcase_15 AC 2 ms
4,380 KB
testcase_16 AC 3 ms
4,376 KB
testcase_17 AC 2 ms
4,376 KB
testcase_18 AC 2 ms
4,380 KB
testcase_19 AC 5 ms
4,380 KB
testcase_20 AC 3 ms
4,380 KB
testcase_21 AC 3 ms
4,376 KB
testcase_22 AC 11 ms
4,380 KB
testcase_23 AC 2 ms
4,380 KB
testcase_24 AC 86 ms
4,376 KB
testcase_25 AC 1 ms
4,380 KB
testcase_26 AC 82 ms
4,380 KB
testcase_27 AC 1 ms
4,376 KB
testcase_28 AC 3 ms
4,380 KB
testcase_29 AC 1 ms
4,380 KB
testcase_30 AC 1 ms
4,376 KB
testcase_31 AC 1 ms
4,380 KB
testcase_32 AC 1 ms
4,376 KB
testcase_33 AC 1 ms
4,376 KB
testcase_34 AC 1 ms
4,380 KB
testcase_35 AC 1 ms
4,376 KB
testcase_36 AC 86 ms
4,380 KB
testcase_37 AC 20 ms
4,376 KB
testcase_38 AC 22 ms
4,380 KB
testcase_39 AC 79 ms
4,376 KB
testcase_40 AC 79 ms
4,380 KB
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 # 

#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;
}
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