Language: C++

#include <algorithm>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using ll = long long;
using namespace std;
static ll imin = std::numeric_limits<ll>::min() / 10;
static ll imax = std::numeric_limits<ll>::max() / 10;
#define rep(i, n) for (ll i = 0; (i) < (n); ++(i))
#define rep1(i, n) for (ll i = 1; (i) < (n); ++(i))
#define rev_rep(i, n) for (ll i = (n)-1; (i) >= 0; --(i))
#define range(a, i, b) for (ll i = (a); (i) < (b); ++(i))

#ifdef LOCAL
#define dump(x) cout << #x << ":" << x << "\n";
#endif
#ifndef LOCAL
#define dump(x)
#endif

#define all(v) v.begin(), v.end()
#define readl(N)                                                               \
  ll N;                                                                        \
  cin >> N;
#define readlv(N, vec)                                                         \
  vector<ll> vec(N);                                                           \
  rep(i, N) { cin >> vec[i]; }
#define greater_than [](ll l, ll r) { return l > r; }
template <class T1, class T2>
std::ostream &operator<<(std::ostream &os, std::map<T1, T2> &mp);
template <class T1, class T2>
std::ostream &operator<<(std::ostream &os, std::pair<T1, T2> &pair);
template <class T>
std::ostream &operator<<(std::ostream &os, std::vector<T> &vec);
template <class T1, class T2>
std::ostream &operator<<(std::ostream &os, std::pair<T1, T2> &pair) {
  os << '(' << pair.first << ',' << pair.second << ')';
  return os;
}

template <class T>
std::ostream &operator<<(std::ostream &os, std::vector<T> &vec) {
  std::size_t n = vec.size();
  if (n == 0) {
    return os;
  }
  os << " ";
  for (ll i = 0; i < n - 1; ++i) {
    os << vec[i] << " ";
  }
  os << vec[n - 1];
  os << std::endl;
  return os;
}

template <class T1, class T2>
std::ostream &operator<<(std::ostream &os, std::map<T1, T2> &mp) {
  std::size_t n = mp.size();
  if (n == 0) {
    return os;
  }
  os << " ";
  for (auto &&x : mp) {
    os << x << " ";
  }
  os << std::endl;
  return os;
}

template <class T> std::ostream &operator<<(std::ostream &os, std::set<T> &mp) {
  std::size_t n = mp.size();
  if (n == 0) {
    return os;
  }
  os << " ";
  for (auto &&x : mp) {
    os << x << " ";
  }
  os << std::endl;
  return os;
}

template <class T> inline bool chmin(T &a, T const b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T const b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

ll fact(ll n) {
  ll res = 1;
  while (n > 0) {
    res *= n;
    n--;
  }
  return res;
}

ll pow(ll i, ll n) {
  ll res = 1;
  while (n >= 0) {
    res *= i;
    n--;
  }
  return res;
}

ll gcd(ll l, ll r) {
  if (l < r) {
    return gcd(r, l);
  }
  if (r == 0) {
    return l;
  }
  return gcd(r, l % r);
}

template <class T> vector<T> accum_sum(vector<T> const &a) {
  vector<T> b(a.size() + 1);
  b[0] = 0;
  rep(i, a.size()) { b[i + 1] = b[i] + a[i]; }
  return b;
}
constexpr ll mod = 1e9 + 7;

template <class ValueType> auto mkVec(ValueType init, size_t x) {
  return vector<ValueType>(x, init);
};

template <class ValueType, class... Ns>
auto mkVec(ValueType init, size_t n, Ns... ns) {
  return vector<decltype(mkVec(init, ns...))>(n, mkVec(init, ns...));
}

double rec(int i, int j, int k, vector<vector<vector<double>>> &dp, ll N) {
  if (dp[i][j][k] >= 0) {
    return dp[i][j][k];
  }
  if (i == 0 && j == 0 && k == 0) {
    return 0.0;
  }
  double res = 0.0;
  if (i > 0) {
    res += rec(i - 1, j, k, dp, N) * i;
  }
  if (j > 0) {
    res += rec(i + 1, j - 1, k, dp, N) * j;
  }
  if (k > 0) {
    res += rec(i, j + 1, k - 1, dp, N) * k;
  }

  res += N;

  res /= (i + j + k);
  dp[i][j][k] = res;
  return res;
}
int main(int argc, char const *argv[]) {
  ll N;
  cin >> N;
  ll one = 0, two = 0, three = 0;
  static auto dp = mkVec(-1.0, N + 1, N + 1, N + 1);
  for (ll i = 0; i < N; ++i) {
    ll a;
    cin >> a;
    if (a == 1) {
      one++;
    } else if (a == 2) {
      two++;
    } else if (a == 3) {
      three++;
    } else {
      assert("f");
    }
  }

  cout << setprecision(10) << rec(one, two, three, dp, N) << endl;
  dump(dp);
  return 0;
}



Compiler output:
a.cc: In function 'int main(int, const char**)':
a.cc:190:7: error: 'assert' was not declared in this scope
  190 |       assert("f");
      |       ^~~~~~
a.cc:11:1: note: 'assert' is defined in header '<cassert>'; this is probably fixable by adding '#include <cassert>'
   10 | #include <stack>
  +++ |+#include <cassert>
   11 | #include <string>