結果

問題 No.3105 Parallel Connection and Spanning Trees
ユーザー 👑 hos.lyric
提出日時 2025-04-11 22:02:19
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 132 ms / 5,000 ms
コード長 6,120 bytes
コンパイル時間 1,453 ms
コンパイル使用メモリ 125,468 KB
実行使用メモリ 7,844 KB
最終ジャッジ日時 2025-04-11 22:02:23
合計ジャッジ時間 3,960 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 32
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘int main()’:
main.cpp:119:12: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  119 |       scanf("%d%d", &N[k], &M[k]);
      |       ~~~~~^~~~~~~~~~~~~~~~~~~~~~
main.cpp:123:14: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  123 |         scanf("%d%d", &A[k][i], &B[k][i]);
      |         ~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~

ソースコード

diff # 

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <chrono>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;


// det(a)
// O(n^3)
//   Call by value: Modifies a (Watch out when using C-style array!)
template <class T> T det(vector<vector<T>> a) {
  const int n = a.size();
  T prod = 1;
  for (int h = 0; h < n; ++h) {
    for (int i = h; i < n; ++i) if (a[i][h]) {
      if (h != i) {
        prod = -prod;
        swap(a[h], a[i]);
      }
      break;
    }
    if (!a[h][h]) return 0;
    prod *= a[h][h];
    const T s = a[h][h].inv();
    for (int j = h + 1; j < n; ++j) a[h][j] *= s;
    for (int i = h + 1; i < n; ++i) {
      const T t = a[i][h];
      if (t) for (int j = h + 1; j < n; ++j) a[i][j] -= t * a[h][j];
    }
  }
  return prod;
}


int K;
vector<int> N, M;
vector<vector<int>> A, B;

int main() {
  for (; ~scanf("%d", &K); ) {
    N.resize(K);
    M.resize(K);
    A.resize(K);
    B.resize(K);
    for (int k = 0; k < K; ++k) {
      scanf("%d%d", &N[k], &M[k]);
      A[k].resize(M[k]);
      B[k].resize(M[k]);
      for (int i = 0; i < M[k]; ++i) {
        scanf("%d%d", &A[k][i], &B[k][i]);
        --A[k][i];
        --B[k][i];
      }
    }
    
    vector<Mint> dp(K + 1, 0);
    dp[0] += 1;
    for (int k = 0; k < K; ++k) {
      Mint fs[2];
      {
        vector<vector<Mint>> mat(N[k], vector<Mint>(N[k], 0));
        for (int i = 0; i < M[k]; ++i) {
          const int u = A[k][i];
          const int v = B[k][i];
          mat[u][u] += 1;
          mat[u][v] -= 1;
          mat[v][u] -= 1;
          mat[v][v] += 1;
        }
        mat.pop_back();
        for (auto &row : mat) row.pop_back();
        fs[0] = det(mat);
      }
      {
        vector<vector<Mint>> mat(N[k] - 1, vector<Mint>(N[k] - 1, 0));
        for (int i = 0; i < M[k]; ++i) {
          const int u = max(A[k][i] - 1, 0);
          const int v = max(B[k][i] - 1, 0);
          mat[u][u] += 1;
          mat[u][v] -= 1;
          mat[v][u] -= 1;
          mat[v][v] += 1;
        }
        mat.pop_back();
        for (auto &row : mat) row.pop_back();
        fs[1] = det(mat);
      }
cerr<<k<<": ";pv(fs,fs+2);
      for (int l = k; l >= 0; --l) {
        dp[l + 1] += dp[l] * fs[1];
        dp[l] *= fs[0];
      }
    }
cerr<<"dp = "<<dp<<endl;
    
    Mint ans = 0;
    for (int l = 0; l <= K; ++l) {
      const int m = K - l;
      ans += dp[l] * (Mint(m) * Mint(2).pow(m-1));
    }
    printf("%u\n", ans.x);
  }
  return 0;
}
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