#1169386 (C++14) No.3575 Sum of Inversion of Trees

• 問題: No.3575 Sum of Inversion of Trees
• ユーザー: hos.lyric
• 提出日時: 2026-06-19 22:58:36
• 言語: C++14 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 439 ms / 2,000 ms
• コード長: 16,572 bytes
• コンパイル時間: 1,762 ms
• コンパイル使用メモリ: 173,628 KB
• 実行使用メモリ: 38,528 KB
• 最終ジャッジ日時: 2026-06-19 22:58:45
• 合計ジャッジ時間: 4,563 ms
• ジャッジサーバーID （参考情報）: judge1_0 / judge2_0

ファイルパターン	結果
other	AC * 11

ソースコード

#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 T> ostream &operator<<(ostream &os, const vector<T> &as);
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>;

constexpr int LIM_INV = 2'000'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];

void prepare() {
  inv[1] = 1;
  for (int i = 2; i < LIM_INV; ++i) {
    inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
  }
  fac[0] = invFac[0] = 1;
  for (int i = 1; i < LIM_INV; ++i) {
    fac[i] = fac[i - 1] * i;
    invFac[i] = invFac[i - 1] * inv[i];
  }
}
Mint binom(Int n, Int k) {
  if (n < 0) {
    if (k >= 0) {
      return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
    } else if (n - k >= 0) {
      return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
    } else {
      return 0;
    }
  } else {
    if (0 <= k && k <= n) {
      assert(n < LIM_INV);
      return fac[n] * invFac[k] * invFac[n - k];
    } else {
      return 0;
    }
  }
}

////////////////////////////////////////////////////////////////////////////////


// [l, r)^n
template <class F> void doArraysRec(int n, int l, int r, F f, int i, vector<int> &as) {
  if (i == n) {
    f(as);
  } else {
    for (as[i] = l; as[i] < r; ++as[i]) doArraysRec(n, l, r, f, i + 1, as);
  }
}
template <class F> void doArrays(int n, int l, int r, F f) {
  vector<int> as(n);
  doArraysRec(n, l, r, f, 0, as);
}

namespace brute {
int N;
vector<vector<int>> graph;
void ae(int u, int v) {
  graph[u].push_back(v);
  graph[v].push_back(u);
}
int zeit;
vector<int> dis, fin, us;
void dfs(int u, int p) {
  dis[u] = zeit++;
  us.push_back(u);
  for (const int v : graph[u]) if (p != v) {
    dfs(v, u);
    us.push_back(u);
  }
  fin[u] = zeit;
}

vector<Mint> run(int N_) {
  N = N_;
  if (N == 1) return {0};
  vector<Int> ans(N, 0), tateR0(N, 0), tateR1(N, 0), tate0(N, 0), tate1(N, 0), yoko(N, 0);
  doArrays(N - 2, 0, N, [&](const vector<int> &as) -> void {
    vector<int> deg(N, 1);
    for (int i = 0; i < N - 2; ++i) ++deg[as[i]];
    graph.assign(N, {});
    for (int i = 0; i < N - 2; ++i) {
      const int u = find(deg.begin(), deg.end(), 1) - deg.begin();
      const int v = as[i];
      --deg[u];
      --deg[v];
      ae(u, v);
    }
    {
      const int u = find(deg.begin(), deg.end(), 1) - deg.begin();
      --deg[u];
      const int v = find(deg.begin(), deg.end(), 1) - deg.begin();
      --deg[v];
      ae(u, v);
    }
    for (int u = 0; u < N; ++u) sort(graph[u].begin(), graph[u].end());
    for (int r = 0; r < N; ++r) {
      zeit = 0;
      dis.assign(N, -1);
      fin.assign(N, -1);
      us.clear();
      dfs(r, -1);
      for (int i = 0; i < (int)us.size(); ++i) for (int j = i + 1; j < (int)us.size(); ++j) if (us[i] > us[j]) {
        // u > v
        const int u = us[i];
        const int v = us[j];
        ++ans[r];
        if (r == u) {
          ++tateR0[r];
        } else if (r == v) {
          ++tateR1[r];
        } else if (dis[u] <= dis[v] && dis[v] < fin[u]) {
          ++tate0[r];
        } else if (dis[v] <= dis[u] && dis[u] < fin[v]) {
          ++tate1[r];
        } else {
          ++yoko[r];
        }
      }
    }
  });
cerr<<"[brute] N = "<<N<<": tateR0 = "<<tateR0<<endl;
cerr<<"[brute] N = "<<N<<": tateR1 = "<<tateR1<<endl;
cerr<<"[brute] N = "<<N<<": tate0  = "<<tate0 <<endl;
cerr<<"[brute] N = "<<N<<": tate1  = "<<tate1 <<endl;
cerr<<"[brute] N = "<<N<<": yoko   = "<<yoko  <<endl;
cerr<<"[brute] N = "<<N<<": ans    = "<<ans   <<endl;
cerr<<endl;
  return vector<Mint>(ans.begin(), ans.end());
}
}  // brute
/*
[brute] N = 2: tateR0 = [0, 1]
[brute] N = 2: tateR1 = [1, 0]
[brute] N = 2: tate0  = [0, 0]
[brute] N = 2: tate1  = [0, 0]
[brute] N = 2: yoko   = [0, 0]
[brute] N = 2: ans    = [1, 1]

[brute] N = 3: tateR0 = [0, 4, 9]
[brute] N = 3: tateR1 = [9, 4, 0]
[brute] N = 3: tate0  = [1, 1, 1]
[brute] N = 3: tate1  = [1, 1, 1]
[brute] N = 3: yoko   = [0, 0, 0]
[brute] N = 3: ans    = [11, 10, 11]

[brute] N = 4: tateR0 = [0, 25, 54, 87]
[brute] N = 4: tateR1 = [87, 54, 25, 0]
[brute] N = 4: tate0  = [19, 19, 19, 19]
[brute] N = 4: tate1  = [19, 19, 19, 19]
[brute] N = 4: yoko   = [2, 2, 2, 2]
[brute] N = 4: ans    = [127, 119, 119, 127]

[brute] N = 5: tateR0 = [0, 218, 459, 723, 1010]
[brute] N = 5: tateR1 = [1010, 723, 459, 218, 0]
[brute] N = 5: tate0  = [324, 324, 324, 324, 324]
[brute] N = 5: tate1  = [324, 324, 324, 324, 324]
[brute] N = 5: yoko   = [70, 70, 70, 70, 70]
[brute] N = 5: ans    = [1728, 1659, 1636, 1659, 1728]

[brute] N = 6: tateR0 = [0, 2448, 5076, 7884, 10872, 14040]
[brute] N = 6: tateR1 = [14040, 10872, 7884, 5076, 2448, 0]
[brute] N = 6: tate0  = [5880, 5880, 5880, 5880, 5880, 5880]
[brute] N = 6: tate1  = [5880, 5880, 5880, 5880, 5880, 5880]
[brute] N = 6: yoko   = [1900, 1900, 1900, 1900, 1900, 1900]
[brute] N = 6: ans    = [27700, 26980, 26620, 26620, 26980, 27700]

[brute] N = 7: tateR0 = [0, 33712, 69237, 106575, 145726, 186690, 229467]
[brute] N = 7: tateR1 = [229467, 186690, 145726, 106575, 69237, 33712, 0]
[brute] N = 7: tate0  = [117665, 117665, 117665, 117665, 117665, 117665, 117665]
[brute] N = 7: tate1  = [117665, 117665, 117665, 117665, 117665, 117665, 117665]
[brute] N = 7: yoko   = [49930, 49930, 49930, 49930, 49930, 49930, 49930]
[brute] N = 7: ans    = [514727, 505662, 500223, 498410, 500223, 505662, 514727]

[brute] N = 8: tateR0 = [0, 550912, 1124352, 1720320, 2338816, 2979840, 3643392, 4329472]
[brute] N = 8: tateR1 = [4329472, 3643392, 2979840, 2338816, 1720320, 1124352, 550912, 0]
[brute] N = 8: tate0  = [2610888, 2610888, 2610888, 2610888, 2610888, 2610888, 2610888, 2610888]
[brute] N = 8: tate1  = [2610888, 2610888, 2610888, 2610888, 2610888, 2610888, 2610888, 2610888]
[brute] N = 8: yoko   = [1356880, 1356880, 1356880, 1356880, 1356880, 1356880, 1356880, 1356880]
[brute] N = 8: ans    = [10908128, 10772960, 10682848, 10637792, 10637792, 10682848, 10772960, 10908128]
*/

vector<Mint> slow(int N) {
  // [x^N] T^k
  vector<Mint> F(N + 1, 0);
  for (int k = 1; k <= N; ++k) F[k] = fac[N - 1] * k * invFac[N - k] * Mint(N).pow(N-k);
cerr<<"[slow] N = "<<N<<": F = "<<F<<endl;
  // k-vertex skelton, l specified vertex
  auto calc = [&](int k, int l) -> Mint {
    return (0 <= l && l <= k && k <= N) ? (F[k] * invFac[N] * fac[N - l]) : 0;
  };
  
  vector<Mint> hard(N, 0);
  for (int r = 0; r < N; ++r) {
    for (int v = 0; v < r; ++v) {
      // dep[v] = 1
      hard[r] += calc(2, 2);
      hard[r] += calc(3, 2);
      for (int a = 0; a < v; ++a) {
        hard[r] += calc(3, 3);
        hard[r] += calc(4, 3);
      }
      // dep[v] >= 2
      for (int d = 2; d < N; ++d) {
        hard[r] += calc(d + 1, 2);
        hard[r] += calc(d + 2, 2);
        for (int b = 0; b < N; ++b) if (r != b && v != b) {
          for (int a = 0; a < b; ++a) if (r != a && v != a) {
            hard[r] += calc(d + 2, 4);
            hard[r] += calc(d + 3, 4);
          }
        }
      }
    }
  }
  
  Mint tate = 0;
  for (int u = 1; u < N; ++u) for (int v = 1; v < u; ++v) {
    // dep[v] - dep[u] = 1
    for (int du = 1; du < N; ++du) {
      tate += calc(du + 2, 3);
      tate += calc(du + 3, 3);
      for (int a = 1; a < v; ++a) {
        tate += calc(du + 3, 4);
        tate += calc(du + 4, 4);
      }
    }
    // dep[v] - dep[u] >= 2
    for (int du = 1; du < N; ++du) for (int dv = du + 2; dv < N; ++dv) {
      tate += calc(dv + 1, 3);
      tate += calc(dv + 2, 3);
      for (int a = 1; a < N; ++a) if (u != a && v != a) {
        for (int b = a + 1; b < N; ++b) if (u != b && v != b) {
          tate += calc(dv + 2, 5);
          tate += calc(dv + 3, 5);
        }
      }
    }
  }
  
  Mint yoko = 0;
  for (int a = 1; a < N; ++a) for (int b = a + 1; b < N; ++b) {
    // dep[u] - dep[l] = 1 && dep[v] - dep[l] >= 2
    for (int v = 1; v < a; ++v) {
      for (int dl = 0; dl < N; ++dl) for (int dv = dl + 2; dv < N; ++dv) {
        yoko += calc(dv + 2, 4);
        yoko += calc(dv + 3, 4);
        yoko += calc(dv + 3, 4);
        yoko += calc(dv + 4, 4);
      }
    }
    // dep[u] - dep[l] >= 2 && dep[v] - dep[l] = 1
    for (int u = b + 1; u < N; ++u) {
      for (int dl = 0; dl < N; ++dl) for (int du = dl + 2; du < N; ++du) {
        yoko += calc(du + 2, 4);
        yoko += calc(du + 3, 4);
        yoko += calc(du + 3, 4);
        yoko += calc(du + 4, 4);
      }
    }
    // dep[u] - dep[l] >= 2 && dep[v] - dep[l] >= 2
    for (int u = 1; u < N; ++u) if (a != u && b != u) {
      for (int v = 1; v < u; ++v) if (a != v && b != v) {
        for (int dl = 0; dl < N; ++dl) for (int du = dl + 2; du < N; ++du) for (int dv = dl + 2; dv < N; ++dv) {
          yoko += calc(du + dv - dl + 1, 5);
          yoko += calc(du + dv - dl + 2, 5);
          yoko += calc(du + dv - dl + 2, 5);
          yoko += calc(du + dv - dl + 3, 5);
        }
      }
    }
  }
  
  vector<Mint> ans(N, 0);
  for (int r = 0; r < N; ++r) ans[r] = hard[r] + hard[N - 1 - r] + tate + tate + yoko;
cerr<<"[slow] N = "<<N<<": hard = "<<hard<<endl;
cerr<<"[slow] N = "<<N<<": tate = "<<tate<<endl;
cerr<<"[slow] N = "<<N<<": yoko = "<<yoko<<endl;
cerr<<"[slow] N = "<<N<<": ans  = "<<ans <<endl;
cerr<<endl;
  return ans;
}

vector<Mint> fast(int N) {
  // [x^N] T^k
  vector<Mint> F(N + 1, 0);
  for (int k = 1; k <= N; ++k) F[k] = fac[N - 1] * k * invFac[N - k] * Mint(N).pow(N-k);
  // k-vertex skelton, l specified vertex
  auto calc = [&](int k, int l) -> Mint {
    return (0 <= l && l <= k && k <= N) ? (F[k] * invFac[N] * fac[N - l]) : 0;
  };
  
  vector<Mint> hard(N, 0);
  Mint hardSum = 0;
  for (int d = 2; d < N; ++d) {
    hardSum += calc(d + 1, 2);
    hardSum += calc(d + 2, 2);
    hardSum += binom(N - 2, 2) * calc(d + 2, 4);
    hardSum += binom(N - 2, 2) * calc(d + 3, 4);
  }
  for (int r = 0; r < N; ++r) {
    hard[r] += Mint(r) * calc(2, 2);
    hard[r] += Mint(r) * calc(3, 2);
    hard[r] += binom(r, 2) * calc(3, 3);
    hard[r] += binom(r, 2) * calc(4, 3);
    /*
    for (int d = 2; d < N; ++d) {
      hard[r] += Mint(r) * calc(d + 1, 2);
      hard[r] += Mint(r) * calc(d + 2, 2);
      hard[r] += Mint(r) * binom(N - 2, 2) * calc(d + 2, 4);
      hard[r] += Mint(r) * binom(N - 2, 2) * calc(d + 3, 4);
    }
    */
    hard[r] += Mint(r) * hardSum;
  }
  
  Mint tate = 0;
  for (int du = 1; du < N; ++du) {
    tate += binom(N - 1, 2) * calc(du + 2, 3);
    tate += binom(N - 1, 2) * calc(du + 3, 3);
    tate += binom(N - 1, 3) * calc(du + 3, 4);
    tate += binom(N - 1, 3) * calc(du + 4, 4);
  }
  for (int dv = 3; dv < N; ++dv) {
    tate += Mint(dv - 2) * binom(N - 1, 2) * calc(dv + 1, 3);
    tate += Mint(dv - 2) * binom(N - 1, 2) * calc(dv + 2, 3);
    tate += Mint(dv - 2) * binom(N - 1, 2) * binom(N - 3, 2) * calc(dv + 2, 5);
    tate += Mint(dv - 2) * binom(N - 1, 2) * binom(N - 3, 2) * calc(dv + 3, 5);
  }
  
  Mint yoko = 0;
  for (int dv = 2; dv < N; ++dv) {
    yoko += Mint(dv - 1) * binom(N - 1, 3) * calc(dv + 2, 4);
    yoko += Mint(dv - 1) * binom(N - 1, 3) * calc(dv + 3, 4);
    yoko += Mint(dv - 1) * binom(N - 1, 3) * calc(dv + 3, 4);
    yoko += Mint(dv - 1) * binom(N - 1, 3) * calc(dv + 4, 4);
    yoko += Mint(dv - 1) * binom(N - 1, 3) * calc(dv + 2, 4);
    yoko += Mint(dv - 1) * binom(N - 1, 3) * calc(dv + 3, 4);
    yoko += Mint(dv - 1) * binom(N - 1, 3) * calc(dv + 3, 4);
    yoko += Mint(dv - 1) * binom(N - 1, 3) * calc(dv + 4, 4);
  }
  /*
  for (int dl = 0; dl < N; ++dl) for (int du = dl + 2; du < N; ++du) for (int dv = dl + 2; dv < N; ++dv) {
    yoko += binom(N - 1, 2) * binom(N - 3, 2) * calc(du + dv - dl + 1, 5);
    yoko += binom(N - 1, 2) * binom(N - 3, 2) * calc(du + dv - dl + 2, 5);
    yoko += binom(N - 1, 2) * binom(N - 3, 2) * calc(du + dv - dl + 2, 5);
    yoko += binom(N - 1, 2) * binom(N - 3, 2) * calc(du + dv - dl + 3, 5);
  }
  */
  // (>=0) + (>=2) + (>=2) = d
  for (int d = 4; d < N; ++d) {
    yoko += binom(d - 2, 2) * binom(N - 1, 2) * binom(N - 3, 2) * calc(d + 1, 5);
    yoko += binom(d - 2, 2) * binom(N - 1, 2) * binom(N - 3, 2) * calc(d + 2, 5);
    yoko += binom(d - 2, 2) * binom(N - 1, 2) * binom(N - 3, 2) * calc(d + 2, 5);
    yoko += binom(d - 2, 2) * binom(N - 1, 2) * binom(N - 3, 2) * calc(d + 3, 5);
  }
  
  vector<Mint> ans(N, 0);
  for (int r = 0; r < N; ++r) ans[r] = hard[r] + hard[N - 1 - r] + tate + tate + yoko;
// cerr<<"[fast] N = "<<N<<": hard = "<<hard<<endl;
// cerr<<"[fast] N = "<<N<<": tate = "<<tate<<endl;
// cerr<<"[fast] N = "<<N<<": yoko = "<<yoko<<endl;
// cerr<<"[fast] N = "<<N<<": ans  = "<<ans <<endl;
// cerr<<endl;
  return ans;
}

int main() {
  prepare();
  // for (int N = 1; N <= 8; ++N) brute::run(N);
  /*
  for (int N = 1; N <= 8; ++N) {
    const auto brt = brute::run(N);
    const auto slw = slow(N);
    const auto fst = fast(N);
    assert(brt == slw);
    assert(brt == fst);
  }
  */
  
  int N;
  for (; ~scanf("%d", &N); ) {
    const auto ans = fast(N);
    for (int r = 0; r < N; ++r) printf("%u\n", ans[r].x);
  }
  return 0;
}