Problem p03169 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end)                                                     \
  for (int i = (begin), i##_end_ = (end); i < i##_end_; i++)
#define IFOR(i, begin, end)                                                    \
  for (int i = (end)-1, i##_begin_ = (begin); i >= i##_begin_; i--)
#define REP(i, n) FOR(i, 0, n)
#define IREP(i, n) IFOR(i, 0, n)
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (auto &v : vec)
    is >> v;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "[";
  for (auto v : vec)
    os << v << ",";
  os << "]";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) {
  os << "deq[";
  for (auto v : vec)
    os << v << ",";
  os << "]";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) {
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &vec) {
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) {
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) {
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &pa) {
  os << "(" << pa.first << "," << pa.second << ")";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const map<TK, TV> &mp) {
  os << "{";
  for (auto v : mp)
    os << v.first << "=>" << v.second << ",";
  os << "}";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) {
  os << "{";
  for (auto v : mp)
    os << v.first << "=>" << v.second << ",";
  os << "}";
  return os;
}
template <typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template <typename T, typename... Args>
void ndarray(vector<T> &vec, int len, Args... args) {
  vec.resize(len);
  for (auto &v : vec)
    ndarray(v, args...);
}
template <typename T> void Max(T &m, const T q) {
  if (m < q)
    m = q;
}
template <typename T> void Min(T &m, const T q) {
  if (m > q)
    m = q;
}
template <typename T1, typename T2>
pair<T1, T2> operator+(pair<T1, T2> &l, pair<T1, T2> &r) {
  return make_pair(l.first + r.first, l.second + r.second);
}
template <typename T1, typename T2>
pair<T1, T2> operator-(pair<T1, T2> &l, pair<T1, T2> &r) {
  return make_pair(l.first - r.first, l.second - r.second);
}
#define dbg(x)                                                                 \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

int N;
vector<vector<vector<double>>> dp;

int main() {
  cin >> N;
  vector<int> co(4);
  REP(_, N) {
    int a;
    cin >> a;
    co[a]++;
  }
  ndarray(dp, co[1] + co[2] + co[3] + 1, co[2] + co[3] + 1, co[3] + 1);
  REP(k, co[3] + 1)
  REP(j, co[2] + co[3] + 1) REP(i, co[1] + co[2] + co[3] + 1) if (i + j + k) {
    if (i)
      dp[i][j][k] += (dp[i - 1][j][k] + 1) * i / N;
    if (j and i < co[1] + co[2] + co[3])
      dp[i][j][k] += (dp[i + 1][j - 1][k] + 1) * j / N;
    if (k and j < co[2] + co[3])
      dp[i][j][k] += (dp[i][j + 1][k - 1] + 1) * k / N;
    dp[i][j][k] = (dp[i][j][k] + 1) * N / (i + j + k) - 1;
  }
  cout << dp[co[1]][co[2]][co[3]] << endl;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;
using lint = long long int;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios {
  fast_ios() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  };
} fast_ios_;
#define FOR(i, begin, end)                                                     \
  for (int i = (begin), i##_end_ = (end); i < i##_end_; i++)
#define IFOR(i, begin, end)                                                    \
  for (int i = (end)-1, i##_begin_ = (begin); i >= i##_begin_; i--)
#define REP(i, n) FOR(i, 0, n)
#define IREP(i, n) IFOR(i, 0, n)
template <typename T> istream &operator>>(istream &is, vector<T> &vec) {
  for (auto &v : vec)
    is >> v;
  return is;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "[";
  for (auto v : vec)
    os << v << ",";
  os << "]";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) {
  os << "deq[";
  for (auto v : vec)
    os << v << ",";
  os << "]";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) {
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &vec) {
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) {
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) {
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &pa) {
  os << "(" << pa.first << "," << pa.second << ")";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const map<TK, TV> &mp) {
  os << "{";
  for (auto v : mp)
    os << v.first << "=>" << v.second << ",";
  os << "}";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp) {
  os << "{";
  for (auto v : mp)
    os << v.first << "=>" << v.second << ",";
  os << "}";
  return os;
}
template <typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); }
template <typename T, typename... Args>
void ndarray(vector<T> &vec, int len, Args... args) {
  vec.resize(len);
  for (auto &v : vec)
    ndarray(v, args...);
}
template <typename T> void Max(T &m, const T q) {
  if (m < q)
    m = q;
}
template <typename T> void Min(T &m, const T q) {
  if (m > q)
    m = q;
}
template <typename T1, typename T2>
pair<T1, T2> operator+(pair<T1, T2> &l, pair<T1, T2> &r) {
  return make_pair(l.first + r.first, l.second + r.second);
}
template <typename T1, typename T2>
pair<T1, T2> operator-(pair<T1, T2> &l, pair<T1, T2> &r) {
  return make_pair(l.first - r.first, l.second - r.second);
}
#define dbg(x)                                                                 \
  cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

int N;
vector<vector<vector<double>>> dp;

int main() {
  cin >> N;
  vector<int> co(4);
  REP(_, N) {
    int a;
    cin >> a;
    co[a]++;
  }
  ndarray(dp, co[1] + co[2] + co[3] + 1, co[2] + co[3] + 1, co[3] + 1);
  REP(k, co[3] + 1)
  REP(j, co[2] + co[3] - k + 1)
      REP(i, co[1] + co[2] + co[3] - j - k + 1) if (i + j + k) {
    if (i)
      dp[i][j][k] += (dp[i - 1][j][k] + 1) * i / N;
    if (j and i < co[1] + co[2] + co[3])
      dp[i][j][k] += (dp[i + 1][j - 1][k] + 1) * j / N;
    if (k and j < co[2] + co[3])
      dp[i][j][k] += (dp[i][j + 1][k - 1] + 1) * k / N;
    dp[i][j][k] = (dp[i][j][k] + 1) * N / (i + j + k) - 1;
  }
  cout << dp[co[1]][co[2]][co[3]] << endl;
}