結果

問題 No.1303 Inconvenient Kingdom
ユーザー risujirohrisujiroh
提出日時 2020-11-27 22:44:11
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
RE  
実行時間 -
コード長 7,470 bytes
コンパイル時間 3,275 ms
コンパイル使用メモリ 232,684 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-26 19:04:12
合計ジャッジ時間 6,430 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
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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 2 ms
6,816 KB
testcase_01 AC 2 ms
6,944 KB
testcase_02 RE -
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,944 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 2 ms
6,944 KB
testcase_08 AC 2 ms
6,940 KB
testcase_09 RE -
testcase_10 RE -
testcase_11 RE -
testcase_12 RE -
testcase_13 RE -
testcase_14 RE -
testcase_15 RE -
testcase_16 RE -
testcase_17 RE -
testcase_18 RE -
testcase_19 RE -
testcase_20 RE -
testcase_21 RE -
testcase_22 RE -
testcase_23 RE -
testcase_24 RE -
testcase_25 RE -
testcase_26 AC 2 ms
6,944 KB
testcase_27 AC 2 ms
6,944 KB
testcase_28 AC 2 ms
6,940 KB
testcase_29 AC 2 ms
6,944 KB
testcase_30 AC 2 ms
6,940 KB
testcase_31 AC 2 ms
6,940 KB
testcase_32 AC 2 ms
6,944 KB
testcase_33 AC 2 ms
6,940 KB
testcase_34 AC 2 ms
6,944 KB
testcase_35 RE -
testcase_36 AC 2 ms
6,944 KB
testcase_37 AC 2 ms
6,940 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 # 

#include <bits/stdc++.h>

class Dsu {
 public:
  Dsu() {}
  explicit Dsu(int n) : dat(n, -1), num_ccs_(n) {}

  int size() const { return std::size(dat); }
  int root(int v) {
    assert(0 <= v), assert(v < size());
    return dat[v] < 0 ? v : dat[v] = root(dat[v]);
  }
  std::pair<int, int> unite(int u, int v) {
    assert(0 <= u), assert(u < size());
    assert(0 <= v), assert(v < size());
    u = root(u), v = root(v);
    if (u == v) return {u, -1};
    --num_ccs_;
    if (-dat[u] < -dat[v]) std::swap(u, v);
    dat[u] += dat[v];
    dat[v] = u;
    return {u, v};
  }
  bool same(int u, int v) {
    assert(0 <= u), assert(u < size());
    assert(0 <= v), assert(v < size());
    return root(u) == root(v);
  }
  int size(int v) {
    assert(0 <= v), assert(v < size());
    return -dat[root(v)];
  }
  int num_ccs() const { return num_ccs_; }

 private:
  std::vector<int> dat;
  int num_ccs_;
};

template <uint32_t Modulus>
class ModularInt {
  using M = ModularInt;

 public:
  static_assert(int(Modulus) >= 1, "Modulus must be in the range [1, 2^31)");
  static constexpr int modulus() { return Modulus; }
  static M raw(uint32_t v) { return *reinterpret_cast<M*>(&v); }

  ModularInt() : v_(0) {}
  ModularInt(int64_t v) : v_((v %= Modulus) < 0 ? v + Modulus : v) {}

  template <class T>
  explicit operator T() const {
    return v_;
  }
  M& operator++() { return v_ = ++v_ == Modulus ? 0 : v_, *this; }
  M& operator--() { return --(v_ ? v_ : v_ = Modulus), *this; }
  M operator+() const { return *this; }
  M operator-() const { return raw(v_ ? Modulus - v_ : 0); }
  M& operator*=(M o) { return v_ = uint64_t(v_) * o.v_ % Modulus, *this; }
  M& operator/=(M o) {
    auto [inv, gcd] = extgcd(o.v_, Modulus);
    assert(gcd == 1);
    return *this *= inv;
  }
  M& operator+=(M o) {
    return v_ = int(v_ += o.v_ - Modulus) < 0 ? v_ + Modulus : v_, *this;
  }
  M& operator-=(M o) {
    return v_ = int(v_ -= o.v_) < 0 ? v_ + Modulus : v_, *this;
  }

  friend M operator++(M& a, int) { return std::exchange(a, ++M(a)); }
  friend M operator--(M& a, int) { return std::exchange(a, --M(a)); }
  friend M operator*(M a, M b) { return a *= b; }
  friend M operator/(M a, M b) { return a /= b; }
  friend M operator+(M a, M b) { return a += b; }
  friend M operator-(M a, M b) { return a -= b; }
  friend std::istream& operator>>(std::istream& is, M& x) {
    int64_t v;
    return is >> v, x = v, is;
  }
  friend std::ostream& operator<<(std::ostream& os, M x) { return os << x.v_; }
  friend bool operator==(M a, M b) { return a.v_ == b.v_; }
  friend bool operator!=(M a, M b) { return a.v_ != b.v_; }

 private:
  static std::array<int, 2> extgcd(int a, int b) {
    std::array x{1, 0};
    while (b) std::swap(x[0] -= a / b * x[1], x[1]), std::swap(a %= b, b);
    return {x[0], a};
  }

  uint32_t v_;
};

#pragma region my_template

struct Rep {
  struct I {
    int i;
    void operator++() { ++i; }
    int operator*() const { return i; }
    bool operator!=(I o) const { return i < *o; }
  };
  const int l_, r_;
  Rep(int l, int r) : l_(l), r_(r) {}
  Rep(int n) : Rep(0, n) {}
  I begin() const { return {l_}; }
  I end() const { return {r_}; }
};
struct Per {
  struct I {
    int i;
    void operator++() { --i; }
    int operator*() const { return i; }
    bool operator!=(I o) const { return i > *o; }
  };
  const int l_, r_;
  Per(int l, int r) : l_(l), r_(r) {}
  Per(int n) : Per(0, n) {}
  I begin() const { return {r_ - 1}; }
  I end() const { return {l_ - 1}; }
};

template <class F>
struct Fix : private F {
  Fix(F f) : F(f) {}
  template <class... Args>
  decltype(auto) operator()(Args&&... args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <class T = int>
T scan() {
  T res;
  std::cin >> res;
  return res;
}

template <class T, class U = T>
bool chmin(T& a, U&& b) {
  return b < a ? a = std::forward<U>(b), true : false;
}
template <class T, class U = T>
bool chmax(T& a, U&& b) {
  return a < b ? a = std::forward<U>(b), true : false;
}

#ifndef LOCAL
#define DUMP(...) void(0)
template <int OnlineJudge, int Local>
constexpr int OjLocal = OnlineJudge;
#endif

using namespace std;

#define ALL(c) begin(c), end(c)

#pragma endregion

using Mint = ModularInt<998244353>;

constexpr int N = 1 << 10;

auto fact = [] {
  std::vector<Mint> res(N + 1);
  res[0] = 1;
  for (int i = 1; i <= N; ++i) res[i] = i * res[i - 1];
  return res;
}();
auto ifact = [] {
  std::vector<Mint> res(N + 1);
  res[N] = 1 / fact[N];
  for (int i = N; i--;) res[i] = res[i + 1] * (i + 1);
  return res;
}();
Mint binom(int n, int k) {
  assert(n <= N);
  return 0 <= k and k <= n ? fact[n] * ifact[k] * ifact[n - k] : 0;
}
Mint homo(int n, int k) { return n or k ? binom(n + k - 1, k) : 1; }

auto minv = [] {
  std::vector<Mint> res(N + 1);
  for (int i = 1; i <= N; ++i) res[i] = ifact[i] * fact[i - 1];
  return res;
}();
template <>
Mint& Mint::operator/=(Mint o) {
  assert(o.v_);
  return *this *= o.v_ <= N ? minv[o.v_] : extgcd(o.v_, modulus())[0];
}

template <class T>
T determinant(vector<vector<T>> a) {
  T det = 1;
  for (int j = 0, r = 0, n = a.size(); j < n; ++j, ++r) {
    for (int i = r + 1; i < n; ++i)
      if (!(a[i][j] == 0)) {
        swap(a[r], a[i]), det = -det;
        break;
      }
    if (a[r][j] == 0) return 0;
    det *= a[r][j];
    T inv = 1 / a[r][j];
    for (auto&& e : a[r]) e *= inv;
    for (int i = 0; i < n; ++i)
      if (i != r and !(a[i][j] == 0))
        for (int k = n; k-- > j;) a[i][k] -= a[r][k] * a[i][j];
  }
  return det;
}

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  cout << fixed << setprecision(20);
  int n = scan();
  vector g(n, vector<bool>(n));
  for (int m = scan(); m--;) {
    int i = scan() - 1;
    int j = scan() - 1;
    g[i][j] = true;
    g[j][i] = true;
  }

  Dsu d(n);
  for (int j : Rep(n))
    for (int i : Rep(j))
      if (g[i][j]) d.unite(i, j);

  Mint ans = 1;
  for (int i : Rep(n))
    if (d.root(i) == i) {
      vector<int> idx;
      for (int j : Rep(n))
        if (d.same(i, j)) idx.push_back(j);
      vector mat(size(idx), vector<Mint>(size(idx)));
      for (int y : Rep(size(idx)))
        for (int x : Rep(y)) {
          int u = idx[x];
          int v = idx[y];
          if (g[u][v]) {
            --mat[x][y];
            --mat[y][x];
            ++mat[x][x];
            ++mat[y][y];
          }
        }
      mat.resize(size(idx) - 1);
      for (auto&& e : mat) e.resize(size(idx) - 1);
      ans *= determinant(mat);
    }

  if (d.num_ccs() == 1) {
    cout << "0\n";
    assert(false);
  } else {
    vector<int> a;
    for (int i : Rep(n))
      if (d.root(i) == i) a.push_back(d.size(i));
    sort(ALL(a), greater{});
    while (a[1] != a.back()) a.pop_back();
    Mint coeff;
    if (a[0] == a[1]) {
      for (int x : a) {
        for (int y : a) coeff += x * y;
        coeff -= x * x;
      }
      coeff /= 2;
    } else {
      coeff += a[0] * accumulate(1 + ALL(a), 0);
    }
    ans *= coeff;
    int opt = n * n;
    for (int i : Rep(n))
      if (d.root(i) == i) opt -= d.size(i) * d.size(i);
    opt -= 2 * a[0] * a[1];
    cout << opt << '\n';
  }

  cout << ans << '\n';
}
0