Problem p03169 (C++)

Buggy submission (status: Runtime Error):

/*****/

#define TRUE true

/**/
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
/**/

#include <bits/stdc++.h>

// #define int long long

using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using vec = vector<T>;
template <class T> using grapth = vec<vec<T>>;

#define rep(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define rep1(i, n) for (ll i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define rrep1(i, n) for (ll i = (n); i > 0; --i)
#define step(i, a, n) for (ll i = (a), i##_len = (a) + (n); i < i##_len; ++i)
#define rstep(i, a, n)                                                         \
  for (ll i = (a) + (n)-1, i##_len = (a); i >= i##_len; --i)
#define range(i, a, b) for (ll i = (a), i##_len = (b); i < i##_len; ++i)
#define rrange(i, a, b) for (ll i = (b)-1, i##_len = (a); i >= i##_len; --i)

constexpr int INF = numeric_limits<int>::max();
constexpr ll INFL = numeric_limits<ll>::max();

std::string strMulti(const char c, const int n) {
  std::string out = "";
  for (int i = 0; i < n; i++) {
    out += c;
  }
  return out;
}
std::string strMulti(const std::string t, const int n) {
  std::string out = "";
  for (int i = 0; i < n; i++) {
    out += t;
  }
  return out;
}
std::string tab(const int n) { return strMulti('\t', n); }
std::string join(const vector<string> &v, const char *delim = 0) {
  std::string s;
  if (!v.empty()) {
    s += v[0];
    for (decltype(v.size()) i = 1, c = v.size(); i < c; ++i) {
      if (delim)
        s += delim;
      s += v[i];
    }
  }
  return s;
}

string to_string(string s) { return '"' + s + '"'; }
string to_string(char c) { return string({'\'', c, '\''}); }
template <size_t N> string to_string(bitset<N> bs) { return bs.to_string(); }
template <class T1, class T2> string to_string(pair<T1, T2> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class Tuple, size_t... I>
string _to_string_tuple(Tuple &&t, std::index_sequence<I...>) {
  vector<string> texts = {to_string(std::get<I>(t))...};
  return "(" + join(texts, ", ") + ")";
}
template <class... Args> string to_string(tuple<Args...> t) {
  using Tuple = tuple<Args...>;
  return _to_string_tuple(
      std::forward<Tuple>(t),
      std::make_index_sequence<std::tuple_size<std::decay_t<Tuple>>::value>{});
}
template <class T> string to_string(vector<T> ar) {
  vector<string> texts(ar.size());
  for (size_t i = 0; i < ar.size(); ++i) {
    texts[i] = to_string(ar[i]);
  }
  return "{" + join(texts, ", ") + "}";
}
template <class T> string to_string(initializer_list<T> il) {
  vector<string> texts(il.size());
  size_t i = 0;
  for (T v : il) {
    texts[i] = to_string(v);
    i++;
  }
  return "{" + join(texts, ", ") + "}";
}

#ifdef DEBUG_BUILD
#define debugvar(x) debugln(#x, (x))
#define debugvartab(x, t) debugln(tab(t) + #x, (x))
void debug(string name) { std::cerr << name; }
void debugln(string name) { std::cerr << name << '\n'; }
template <class T> void debug(string name, T v) {
  std::cerr << name << " = " << to_string(v);
}
template <class T> void debugln(string name, T v) {
  std::cerr << name << " = " << to_string(v) << '\n';
}
template <class T> void debug(string name, initializer_list<T> il) {
  std::cerr << name << " = " << to_string(il);
}
template <class T> void debugln(string name, initializer_list<T> il) {
  std::cerr << name << " = " << to_string(il) << '\n';
}
template <class... Args> void debug(string name, Args... args) {
  std::cerr << name << " = " << to_string(tuple<Args...>(args...));
}
template <class... Args> void debugln(string name, Args... args) {
  std::cerr << name << " = " << to_string(tuple<Args...>(args...)) << '\n';
}
#else
#define debugvar(x)
#define debugvartab(x, t)
void debug(string name) {}
void debugln(string name) {}
template <class T> void debug(string name, T v) {}
template <class T> void debugln(string name, T v) {}
template <class T> void debug(string name, initializer_list<T> il) {}
template <class T> void debugln(string name, initializer_list<T> il) {}
template <class... Args> void debug(string name, Args... args) {}
template <class... Args> void debugln(string name, Args... args) {}
#endif

#define all(x) (x).begin(), (x).end()
#define pair(a, b) make_pair(a, b)

template <class T> bool chmax(T &a, const T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, const T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> T divup(const T a, const T b) {
  if (a % b == 0) {
    return a / b;
  }
  return a / b + 1;
}
template <class T> bool cmp_2nd(pair<T, T> a, pair<T, T> b) {
  if (a.second != b.second) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
ll modpow(ll x, ll n, const ll &p) {
  ll ret = 1;
  while (n > 0) {
    if (n & 1) {
      (ret *= x) %= p;
    }
    (x *= x) %= p;
    n >>= 1;
  }
  return ret;
}
template <class T> T modinv(T a, const T &p) {
  T b = p, u = 1, v = 0;
  while (b) {
    T t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= p;
  if (u < 0) {
    u += p;
  }
  return u;
}
template <class T> T math_P(T m, T n) {
  T ret = 1;
  for (T i = m; i > m - n; i--) {
    ret *= i;
  }
  return ret;
}
template <class T> T math_C(T m, T n) {
  T ret = math_P(m, n);
  for (T i = 2; i <= n; i++) {
    ret /= i;
  }
  return ret;
}
ll extended_euclidean(ll u, ll v) {
  ll r0 = u;
  ll r1 = v;
  ll s0 = 1;
  ll s1 = 0;
  ll t0 = 0;
  ll t1 = 1;
  while (r1 != 0) {
    ll q = r0 / r1;
    ll r = r0 - q * r1;
    ll s = s0 - q * s1;
    ll t = t0 - q * t1;
    r0 = r1;
    s0 = s1;
    t0 = t1;
    r1 = r;
    s1 = s;
    t1 = t;
  }
  if (t0 < 0) {
    return t0 + u;
  } else {
    return t0;
  }
}
ll math_C_mod(ll n, ll c, const ll &p) {
  ll upe = 1;
  ll dow = 1;
  for (ll i = 1; i < c + 1; ++i) {
    upe = upe * n % p;
    dow = dow * i % p;
    n -= 1;
  }
  return (upe * extended_euclidean(p, dow)) % p;
}
template <class T> T math_gcd(T a, T b) {
  if (b == 0) {
    return a;
  } else {
    return math_gcd(b, a % b);
  }
}
template <class T> T math_lcm(T a, T b) { return a / math_gcd(a, b) * b; }
template <class T> T SumStep(T a, T n, T d) {
  return n * (2 * a + (n - 1) * d) / 2;
}
template <class T> T SumRange(T a, T b, T d) {
  return SumStep(a, (b - a) / d, d);
}

constexpr ll MOD = 1000000007; // 10^9+7
// constexpr ll MOD = 998244353;

/*****/

vec<vec<vec<ld>>> dp;
int N;

ld rec(int i, int j, int k) {
  if (dp[i][j][k] >= 0)
    return dp[i][j][k];

  if (i == 0 && j == 0 && k == 0)
    return 0.0;

  ld res = 0.0;
  if (i > 0)
    res += rec(i - 1, j, k) * i;
  if (j > 0)
    res += rec(i + 1, j - 1, k) * j;
  if (k > 0)
    res += rec(i, j + 1, k - 1) * k;

  res += N;
  res *= 1.0 / (i + j + k);

  return dp[i][j][k] = res;
}

void Main() {
  cin >> N;
  vec<int> ac(4);
  rep(i, N) {
    int a;
    cin >> a;
    ac[a]++;
  }

  dp.resize(ac[1] + 100, vec<vec<ld>>(ac[2] + 100, vec<ld>(ac[3] + 100, -1)));

  cout << rec(ac[1], ac[2], ac[3]) << endl;
}

/*****/

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);

  std::cout << std::fixed << std::setprecision(10);

#ifdef TRUE
  Main();
#endif
  std::cerr << flush;
  std::cout << flush;

  return 0;
}


Fixed submission:

/*****/

#define TRUE true

/**/
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
/**/

#include <bits/stdc++.h>

// #define int long long

using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pint = pair<int, int>;
using pll = pair<long long, long long>;
template <class T> using vec = vector<T>;
template <class T> using grapth = vec<vec<T>>;

#define rep(i, n) for (ll i = 0, i##_len = (n); i < i##_len; ++i)
#define rep1(i, n) for (ll i = 1, i##_len = (n); i <= i##_len; ++i)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; --i)
#define rrep1(i, n) for (ll i = (n); i > 0; --i)
#define step(i, a, n) for (ll i = (a), i##_len = (a) + (n); i < i##_len; ++i)
#define rstep(i, a, n)                                                         \
  for (ll i = (a) + (n)-1, i##_len = (a); i >= i##_len; --i)
#define range(i, a, b) for (ll i = (a), i##_len = (b); i < i##_len; ++i)
#define rrange(i, a, b) for (ll i = (b)-1, i##_len = (a); i >= i##_len; --i)

constexpr int INF = numeric_limits<int>::max();
constexpr ll INFL = numeric_limits<ll>::max();

std::string strMulti(const char c, const int n) {
  std::string out = "";
  for (int i = 0; i < n; i++) {
    out += c;
  }
  return out;
}
std::string strMulti(const std::string t, const int n) {
  std::string out = "";
  for (int i = 0; i < n; i++) {
    out += t;
  }
  return out;
}
std::string tab(const int n) { return strMulti('\t', n); }
std::string join(const vector<string> &v, const char *delim = 0) {
  std::string s;
  if (!v.empty()) {
    s += v[0];
    for (decltype(v.size()) i = 1, c = v.size(); i < c; ++i) {
      if (delim)
        s += delim;
      s += v[i];
    }
  }
  return s;
}

string to_string(string s) { return '"' + s + '"'; }
string to_string(char c) { return string({'\'', c, '\''}); }
template <size_t N> string to_string(bitset<N> bs) { return bs.to_string(); }
template <class T1, class T2> string to_string(pair<T1, T2> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class Tuple, size_t... I>
string _to_string_tuple(Tuple &&t, std::index_sequence<I...>) {
  vector<string> texts = {to_string(std::get<I>(t))...};
  return "(" + join(texts, ", ") + ")";
}
template <class... Args> string to_string(tuple<Args...> t) {
  using Tuple = tuple<Args...>;
  return _to_string_tuple(
      std::forward<Tuple>(t),
      std::make_index_sequence<std::tuple_size<std::decay_t<Tuple>>::value>{});
}
template <class T> string to_string(vector<T> ar) {
  vector<string> texts(ar.size());
  for (size_t i = 0; i < ar.size(); ++i) {
    texts[i] = to_string(ar[i]);
  }
  return "{" + join(texts, ", ") + "}";
}
template <class T> string to_string(initializer_list<T> il) {
  vector<string> texts(il.size());
  size_t i = 0;
  for (T v : il) {
    texts[i] = to_string(v);
    i++;
  }
  return "{" + join(texts, ", ") + "}";
}

#ifdef DEBUG_BUILD
#define debugvar(x) debugln(#x, (x))
#define debugvartab(x, t) debugln(tab(t) + #x, (x))
void debug(string name) { std::cerr << name; }
void debugln(string name) { std::cerr << name << '\n'; }
template <class T> void debug(string name, T v) {
  std::cerr << name << " = " << to_string(v);
}
template <class T> void debugln(string name, T v) {
  std::cerr << name << " = " << to_string(v) << '\n';
}
template <class T> void debug(string name, initializer_list<T> il) {
  std::cerr << name << " = " << to_string(il);
}
template <class T> void debugln(string name, initializer_list<T> il) {
  std::cerr << name << " = " << to_string(il) << '\n';
}
template <class... Args> void debug(string name, Args... args) {
  std::cerr << name << " = " << to_string(tuple<Args...>(args...));
}
template <class... Args> void debugln(string name, Args... args) {
  std::cerr << name << " = " << to_string(tuple<Args...>(args...)) << '\n';
}
#else
#define debugvar(x)
#define debugvartab(x, t)
void debug(string name) {}
void debugln(string name) {}
template <class T> void debug(string name, T v) {}
template <class T> void debugln(string name, T v) {}
template <class T> void debug(string name, initializer_list<T> il) {}
template <class T> void debugln(string name, initializer_list<T> il) {}
template <class... Args> void debug(string name, Args... args) {}
template <class... Args> void debugln(string name, Args... args) {}
#endif

#define all(x) (x).begin(), (x).end()
#define pair(a, b) make_pair(a, b)

template <class T> bool chmax(T &a, const T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, const T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> T divup(const T a, const T b) {
  if (a % b == 0) {
    return a / b;
  }
  return a / b + 1;
}
template <class T> bool cmp_2nd(pair<T, T> a, pair<T, T> b) {
  if (a.second != b.second) {
    return a.second < b.second;
  }
  return a.first < b.first;
}
ll modpow(ll x, ll n, const ll &p) {
  ll ret = 1;
  while (n > 0) {
    if (n & 1) {
      (ret *= x) %= p;
    }
    (x *= x) %= p;
    n >>= 1;
  }
  return ret;
}
template <class T> T modinv(T a, const T &p) {
  T b = p, u = 1, v = 0;
  while (b) {
    T t = a / b;
    a -= t * b;
    swap(a, b);
    u -= t * v;
    swap(u, v);
  }
  u %= p;
  if (u < 0) {
    u += p;
  }
  return u;
}
template <class T> T math_P(T m, T n) {
  T ret = 1;
  for (T i = m; i > m - n; i--) {
    ret *= i;
  }
  return ret;
}
template <class T> T math_C(T m, T n) {
  T ret = math_P(m, n);
  for (T i = 2; i <= n; i++) {
    ret /= i;
  }
  return ret;
}
ll extended_euclidean(ll u, ll v) {
  ll r0 = u;
  ll r1 = v;
  ll s0 = 1;
  ll s1 = 0;
  ll t0 = 0;
  ll t1 = 1;
  while (r1 != 0) {
    ll q = r0 / r1;
    ll r = r0 - q * r1;
    ll s = s0 - q * s1;
    ll t = t0 - q * t1;
    r0 = r1;
    s0 = s1;
    t0 = t1;
    r1 = r;
    s1 = s;
    t1 = t;
  }
  if (t0 < 0) {
    return t0 + u;
  } else {
    return t0;
  }
}
ll math_C_mod(ll n, ll c, const ll &p) {
  ll upe = 1;
  ll dow = 1;
  for (ll i = 1; i < c + 1; ++i) {
    upe = upe * n % p;
    dow = dow * i % p;
    n -= 1;
  }
  return (upe * extended_euclidean(p, dow)) % p;
}
template <class T> T math_gcd(T a, T b) {
  if (b == 0) {
    return a;
  } else {
    return math_gcd(b, a % b);
  }
}
template <class T> T math_lcm(T a, T b) { return a / math_gcd(a, b) * b; }
template <class T> T SumStep(T a, T n, T d) {
  return n * (2 * a + (n - 1) * d) / 2;
}
template <class T> T SumRange(T a, T b, T d) {
  return SumStep(a, (b - a) / d, d);
}

constexpr ll MOD = 1000000007; // 10^9+7
// constexpr ll MOD = 998244353;

/*****/

vec<vec<vec<ld>>> dp;
int N;

ld rec(int i, int j, int k) {
  if (dp[i][j][k] >= 0)
    return dp[i][j][k];

  if (i == 0 && j == 0 && k == 0)
    return 0.0;

  ld res = 0.0;
  if (i > 0)
    res += rec(i - 1, j, k) * i;
  if (j > 0)
    res += rec(i + 1, j - 1, k) * j;
  if (k > 0)
    res += rec(i, j + 1, k - 1) * k;

  res += N;
  res *= 1.0 / (i + j + k);

  return dp[i][j][k] = res;
}

void Main() {
  cin >> N;
  vec<int> ac(4);
  rep(i, N) {
    int a;
    cin >> a;
    ac[a]++;
  }

  dp.resize(301, vec<vec<ld>>(301, vec<ld>(301, -1)));

  cout << rec(ac[1], ac[2], ac[3]) << endl;
}

/*****/

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(0);

  std::cout << std::fixed << std::setprecision(10);

#ifdef TRUE
  Main();
#endif
  std::cerr << flush;
  std::cout << flush;

  return 0;
}