Problem p03169 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;

#define REP(i, n) for (long long i = 0; i < (n); i++)
#define FOR(i, m, n) for (long long i = (m); i < (n); ++i)
#define ALL(obj) (obj).begin(), (obj).end()
#define SPEED                                                                  \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);

template <class T> using V = vector<T>;
template <class T, class U> using P = pair<T, U>;
template <class T> using PQ = priority_queue<T>;
template <class T> using PQR = priority_queue<T, vector<T>, greater<T>>;

constexpr long long MOD = (long long)1e9 + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433;

template <class T> vector<T> multivector(size_t N, T init) {
  return vector<T>(N, init);
}
template <class... T> auto multivector(size_t N, T... t) {
  return vector<decltype(multivector(t...))>(N, multivector(t...));
}
template <class T> void corner(bool flg, T hoge) {
  if (flg) {
    cout << hoge << endl;
    exit(0);
  }
}
template <class T, class U>
ostream &operator<<(ostream &o, const map<T, U> &obj) {
  o << "{";
  for (auto &x : obj)
    o << " {" << x.first << " : " << x.second << "}"
      << ",";
  o << " }";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const set<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const multiset<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const vector<T> &obj) {
  o << "{";
  for (int i = 0; i < (int)obj.size(); ++i)
    o << (i > 0 ? ", " : "") << obj[i];
  o << "}";
  return o;
}
template <class T, class U>
ostream &operator<<(ostream &o, const pair<T, U> &obj) {
  o << "{" << obj.first << ", " << obj.second << "}";
  return o;
}
template <template <class tmp> class T, class U>
ostream &operator<<(ostream &o, const T<U> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
void print(void) { cout << endl; }
template <class Head> void print(Head &&head) {
  cout << head;
  print();
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
  cout << head << " ";
  print(forward<Tail>(tail)...);
}
template <class T> void chmax(T &a, const T b) { a = max(a, b); }
template <class T> void chmin(T &a, const T b) { a = min(a, b); }
void YN(bool flg) { cout << (flg ? "YES" : "NO") << endl; }
void Yn(bool flg) { cout << (flg ? "Yes" : "No") << endl; }
void yn(bool flg) { cout << (flg ? "yes" : "no") << endl; }

int N;
auto dp = multivector(300, 300, 300, -1.0);

double rec(int i, int j, int k) {
  if (dp[i][j][k] != -1.0)
    return dp[i][j][k];
  double x = i, y = j, z = k, M = N, res = 1.;
  if (i)
    res += x / M * rec(i - 1, j + 1, k);
  if (j)
    res += y / M * rec(i, j - 1, k + 1);
  if (k)
    res += z / M * rec(i, j, k - 1);
  if (N != i + j + k)
    res *= M / (x + y + z);
  return dp[i][j][k] = res;
}

int main() {
  cin >> N;
  dp[0][0][0] = 0.;
  int a = 0, b = 0, c = 0;
  for (int i = 0; i < N; ++i) {
    int d;
    cin >> d;
    if (d == 3)
      a++;
    if (d == 2)
      b++;
    if (d == 1)
      c++;
  }
  printf("%.10f", rec(a, b, c));
}

Fixed submission:
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;

#define REP(i, n) for (long long i = 0; i < (n); i++)
#define FOR(i, m, n) for (long long i = (m); i < (n); ++i)
#define ALL(obj) (obj).begin(), (obj).end()
#define SPEED                                                                  \
  cin.tie(0);                                                                  \
  ios::sync_with_stdio(false);

template <class T> using V = vector<T>;
template <class T, class U> using P = pair<T, U>;
template <class T> using PQ = priority_queue<T>;
template <class T> using PQR = priority_queue<T, vector<T>, greater<T>>;

constexpr long long MOD = (long long)1e9 + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433;

template <class T> vector<T> multivector(size_t N, T init) {
  return vector<T>(N, init);
}
template <class... T> auto multivector(size_t N, T... t) {
  return vector<decltype(multivector(t...))>(N, multivector(t...));
}
template <class T> void corner(bool flg, T hoge) {
  if (flg) {
    cout << hoge << endl;
    exit(0);
  }
}
template <class T, class U>
ostream &operator<<(ostream &o, const map<T, U> &obj) {
  o << "{";
  for (auto &x : obj)
    o << " {" << x.first << " : " << x.second << "}"
      << ",";
  o << " }";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const set<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const multiset<T> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
template <class T> ostream &operator<<(ostream &o, const vector<T> &obj) {
  o << "{";
  for (int i = 0; i < (int)obj.size(); ++i)
    o << (i > 0 ? ", " : "") << obj[i];
  o << "}";
  return o;
}
template <class T, class U>
ostream &operator<<(ostream &o, const pair<T, U> &obj) {
  o << "{" << obj.first << ", " << obj.second << "}";
  return o;
}
template <template <class tmp> class T, class U>
ostream &operator<<(ostream &o, const T<U> &obj) {
  o << "{";
  for (auto itr = obj.begin(); itr != obj.end(); ++itr)
    o << (itr != obj.begin() ? ", " : "") << *itr;
  o << "}";
  return o;
}
void print(void) { cout << endl; }
template <class Head> void print(Head &&head) {
  cout << head;
  print();
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
  cout << head << " ";
  print(forward<Tail>(tail)...);
}
template <class T> void chmax(T &a, const T b) { a = max(a, b); }
template <class T> void chmin(T &a, const T b) { a = min(a, b); }
void YN(bool flg) { cout << (flg ? "YES" : "NO") << endl; }
void Yn(bool flg) { cout << (flg ? "Yes" : "No") << endl; }
void yn(bool flg) { cout << (flg ? "yes" : "no") << endl; }

int N;
auto dp = multivector(301, 301, 301, -1.0);

double rec(int i, int j, int k) {
  if (dp[i][j][k] != -1.0)
    return dp[i][j][k];
  double x = i, y = j, z = k, M = N, res = 1.;
  if (i)
    res += x / M * rec(i - 1, j + 1, k);
  if (j)
    res += y / M * rec(i, j - 1, k + 1);
  if (k)
    res += z / M * rec(i, j, k - 1);
  if (N != i + j + k)
    res *= M / (x + y + z);
  return dp[i][j][k] = res;
}

int main() {
  cin >> N;
  dp[0][0][0] = 0.;
  int a = 0, b = 0, c = 0;
  for (int i = 0; i < N; ++i) {
    int d;
    cin >> d;
    if (d == 3)
      a++;
    if (d == 2)
      b++;
    if (d == 1)
      c++;
  }
  printf("%.10f", rec(a, b, c));
}