#925651 (C++23) No.2531 Coloring Vertices on Namori

• 問題: No.2531 Coloring Vertices on Namori
• ユーザー: emthrm
• 提出日時: 2023-11-03 22:01:29
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 212 ms / 2,000 ms
• コード長: 7,877 bytes
• コンパイル時間: 3,611 ms
• コンパイル使用メモリ: 266,528 KB
• 実行使用メモリ: 43,132 KB
• 最終ジャッジ日時: 2024-09-25 20:19:35
• 合計ジャッジ時間: 8,526 ms
• ジャッジサーバーID （参考情報）: judge1 / judge5

ファイルパターン	結果
sample	AC * 3
other	AC * 31

ソースコード

#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)
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int 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() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <unsigned int M>
struct MInt {
  unsigned int v;

  constexpr MInt() : v(0) {}
  constexpr MInt(const long long x) : v(x >= 0 ? x % M : x % M + M) {}
  static constexpr MInt raw(const int x) {
    MInt x_;
    x_.v = x;
    return x_;
  }

  static constexpr int get_mod() { return M; }
  static constexpr void set_mod(const int divisor) {
    assert(std::cmp_equal(divisor, M));
  }

  static void init(const int x) {
    inv<true>(x);
    fact(x);
    fact_inv(x);
  }

  template <bool MEMOIZES = false>
  static MInt inv(const int n) {
    // assert(0 <= n && n < M && std::gcd(n, M) == 1);
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) return inverse[n];
    if constexpr (MEMOIZES) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[M % i] * raw(M / i);
      }
      return inverse[n];
    }
    int u = 1, v = 0;
    for (unsigned int a = n, b = M; b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }

  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    if (const int prev = factorial.size(); n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }

  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    if (const int prev = f_inv.size(); n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }

  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? MInt() : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? MInt() : (k == 0 ? 1 : nCk(n + k - 1, k));
  }

  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) [[unlikely]] return MInt();
    inv<true>(k);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }

  constexpr MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  constexpr MInt& operator+=(const MInt& x) {
    if ((v += x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator-=(const MInt& x) {
    if ((v += M - x.v) >= M) v -= M;
    return *this;
  }
  constexpr MInt& operator*=(const MInt& x) {
    v = (unsigned long long){v} * x.v % M;
    return *this;
  }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }

  constexpr auto operator<=>(const MInt& x) const = default;

  constexpr MInt& operator++() {
    if (++v == M) [[unlikely]] v = 0;
    return *this;
  }
  constexpr MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  constexpr MInt& operator--() {
    v = (v == 0 ? M - 1 : v - 1);
    return *this;
  }
  constexpr MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }

  constexpr MInt operator+() const { return *this; }
  constexpr MInt operator-() const { return raw(v ? M - v : 0); }

  constexpr MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  constexpr MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  constexpr MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt& x) const { return MInt(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
    return os << x.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }
};
using ModInt = MInt<MOD>;

struct UnicyclicGraph {
  std::vector<bool> is_in_loop;
  std::vector<int> belong, mapping, loop;
  std::vector<std::vector<int>> invs;
  std::vector<std::vector<std::vector<int>>> forest;

  explicit UnicyclicGraph(const int n)
      : is_in_loop(n, false), belong(n, -1), mapping(n, -1), n(n), graph(n) {}

  void add_edge(const int src, const int dst) {
    const int id = srcs.size();
    srcs.emplace_back(src);
    dsts.emplace_back(dst);
    graph[src].emplace_back(id);
    if (dst != src) [[likely]] graph[dst].emplace_back(id);
  }

  void build() {
    dfs(-1, 0);
    std::queue<int> que;
    for (const int root : loop) {
      const int forest_id = forest.size();
      belong[root] = forest_id;
      mapping[root] = 0;
      std::vector<int> inv{root};
      std::vector<std::vector<int>> tree(1);
      que.emplace(root);
      while (!que.empty()) {
        const int ver = que.front();
        que.pop();
        for (const int id : graph[ver]) {
          const int dst = destination(id, ver);
          if (belong[dst] == -1 && !is_in_loop[dst]) {
            const int idx = tree.size();
            belong[dst] = forest_id;
            mapping[dst] = idx;
            inv.emplace_back(dst);
            tree[mapping[ver]].emplace_back(idx);
            tree.emplace_back(std::vector<int>{mapping[ver]});
            que.emplace(dst);
          }
        }
      }
      if (inv.size() == 1) {
        belong[root] = mapping[root] = -1;
      } else {
        invs.emplace_back(inv);
        forest.emplace_back(tree);
      }
    }
  }

 private:
  const int n;
  std::vector<int> srcs, dsts;
  std::vector<std::vector<int>> graph;

  int destination(const int id, const int s) const {
    return (srcs[id] == s ? dsts : srcs)[id];
  }

  bool dfs(const int prev_id, const int ver) {
    is_in_loop[ver] = true;
    loop.emplace_back(ver);
    for (const int id : graph[ver]) {
      if (id == prev_id) continue;
      const int dst = destination(id, ver);
      if (is_in_loop[dst]) {
        for (int i = loop.size() - 1; i >= 0; --i) {
          if (loop[i] == dst) {
            for (int j = 0; j < i; ++j) {
              is_in_loop[loop[j]] = false;
            }
            loop.erase(loop.begin(), std::next(loop.begin(), i));
            return true;
          }
        }
        assert(false);
      }
      if (dfs(id, dst)) return true;
    }
    loop.pop_back();
    is_in_loop[ver] = false;
    return false;
  }
};

int main() {
  int n, k; cin >> n >> k;
  UnicyclicGraph graph(n);
  REP(_, n) {
    int u, v; cin >> u >> v; --u; --v;
    graph.add_edge(u, v);
  }
  graph.build();
  const int l = graph.loop.size();
  array<ModInt, 2> dp{0, k};
  FOR(i, 1, l) {
    array<ModInt, 2> nxt{dp[false] * (k - 2) + dp[true] * (k - 1), dp[false]};
    dp.swap(nxt);
  }
  cout << dp[false] * ModInt::raw(k - 1).pow(n - l) << '\n';
  return 0;
}