#1149118 (C++14) No.3449 Mex of Subtree

• 問題: No.3449 Mex of Subtree
• ユーザー: hos.lyric
• 提出日時: 2026-02-23 07:17:18
• 言語: C++14 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 110 ms / 2,000 ms
• コード長: 5,071 bytes
• コンパイル時間: 1,305 ms
• コンパイル使用メモリ: 143,200 KB
• 実行使用メモリ: 102,268 KB
• 最終ジャッジ日時: 2026-02-23 11:41:13
• 合計ジャッジ時間: 6,394 ms
• ジャッジサーバーID （参考情報）: judge2 / judge4

ファイルパターン	結果
sample	AC * 3
other	AC * 59

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>;


/*
  decision (a[u])
    subtree(u)
      fill only [0, a[u])
      k slots left; larger is better
    v[0],...,v[k-1] -> u
      b := max a[v[*]]
      [0, b): filled
      need a[u] >= b
      need/should use (a[u] - b) slots
*/

int N;
vector<int> P;

Mint dp[5010][5010];

int main() {
  for (; ~scanf("%d", &N); ) {
    P.resize(N);
    for (int u = 1; u < N; ++u) {
      scanf("%d", &P[u]);
      --P[u];
    }
    P[0] = -1;
    
    vector<vector<int>> graph(N);
    for (int u = 1; u < N; ++u) graph[P[u]].push_back(u);
    vector<int> sz(N, 1);
    for (int u = N; --u >= 1; ) sz[P[u]] += sz[u];
    
    memset(dp, 0, sizeof(dp));
    for (int u = N; --u >= 0; ) {
      int s = 1;
      dp[u][1] = 1;
      for (const int v : graph[u]) {
        for (int k = s; k >= 0; --k) {
          for (int l = sz[v]; l >= 1; --l) dp[u][k + l] += dp[u][k] * dp[v][l];
          dp[u][k] *= dp[v][0];
        }
        s += sz[v];
      }
      // use slots according to target mex
      for (int k = s; k >= 1; --k) dp[u][k - 1] += dp[u][k];
// cerr<<"dp["<<u<<"] = ";pv(dp[u],dp[u]+(sz[u]+1));
    }
    Mint ans = 0;
    for (int k = 0; k <= N; ++k) ans += dp[0][k];
    printf("%u\n", ans.x);
  }
  return 0;
}