Problem p03169 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <vector>

using namespace std;

#define REP(i, m, n) for (int i = (m); i < (int)(n); i++)
#define RREP(i, m, n) for (int i = (int)(n - 1); i >= m; i--)
#define rep(i, n) REP(i, 0, n)
#define rrep(i, n) RREP(i, 0, n)
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define aut(r, v) __typeof(v) r = (v)
#define each(it, o) for (aut(it, (o).begin()); it != (o).end(); ++it)
#define reach(it, o) for (aut(it, (o).rbegin()); it != (o).rend(); ++it)
#define fi first
#define se second
#define debug(...)                                                             \
  {                                                                            \
    cerr << "[L" << __LINE__ << "] ";                                          \
    _debug(__VA_ARGS__);                                                       \
  }

template <typename T1, typename T2>
ostream &operator<<(ostream &o, const pair<T1, T2> &p) {
  return o << "(" << p.first << ", " << p.second << ")";
}
template <typename T> string join(const vector<T> &v, string del = ", ") {
  stringstream s;
  rep(i, v.size()) s << del << v[i];
  return s.str().substr(del.size());
}
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) {
  if (v.size())
    o << "[" << join(v) << "]";
  return o;
}
template <typename T>
ostream &operator<<(ostream &o, const vector<vector<T>> &vv) {
  int l = vv.size();
  if (l) {
    o << endl;
    rep(i, l) {
      o << (i == 0 ? "[ " : ",\n  ") << vv[i] << (i == l - 1 ? " ]" : "");
    }
  }
  return o;
}
template <typename T> ostream &operator<<(ostream &o, const set<T> &st) {
  vector<T> v(st.begin(), st.end());
  o << "{ " << join(v) << " }";
  return o;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &o, const map<T1, T2> &m) {
  each(p, m) {
    o << (p == m.begin() ? "{ " : ",\n  ") << *p
      << (p == --m.end() ? " }" : "");
  }
  return o;
}
inline void _debug() { cerr << endl; }
template <class First, class... Rest>
void _debug(const First &first, const Rest &...rest) {
  cerr << first << " ";
  _debug(rest...);
}

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;

const double PI = (1 * acos(0.0));
const double INF = 0x3f3f3f3f;
const double INFL = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-9;
const double mod = 1e9 + 7;

inline void finput(string filename) { freopen(filename.c_str(), "r", stdin); }

int N;
double dp[310][310][310];

double rec(int c1, int c2, int c3) {
  if (dp[c1][c2][c3] >= 0)
    return dp[c1][c2][c3];
  if (c1 == 0 && c2 == 0 && c3 == 0)
    return 0.0;

  double res = 0.0;
  if (c1 > 0)
    res += rec(c1 - 1, c2, c3) * c1;
  if (c2 > 0)
    res += rec(c1 + 1, c2 - 1, c3) * c2;
  if (c3 > 0)
    res += rec(c1, c2 + 1, c3 - 1) * c3;
  res += N;
  res *= 1.0 / (c1 + c2 + c3);
  return dp[c1][c2][c3] = res;
}

int main() {
  ios_base::sync_with_stdio(0);
  // finput("./input");

  cin >> N;
  int C[4];
  rep(i, N) {
    int a;
    cin >> a;
    C[a]++;
  }
  memset(dp, -1, sizeof(dp));
  cout << fixed << setprecision(10) << rec(C[1], C[2], C[3]) << endl;
  return 0;
}

Fixed submission:
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <fstream>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <vector>

using namespace std;

#define REP(i, m, n) for (int i = (m); i < (int)(n); i++)
#define RREP(i, m, n) for (int i = (int)(n - 1); i >= m; i--)
#define rep(i, n) REP(i, 0, n)
#define rrep(i, n) RREP(i, 0, n)
#define all(a) (a).begin(), (a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define aut(r, v) __typeof(v) r = (v)
#define each(it, o) for (aut(it, (o).begin()); it != (o).end(); ++it)
#define reach(it, o) for (aut(it, (o).rbegin()); it != (o).rend(); ++it)
#define fi first
#define se second
#define debug(...)                                                             \
  {                                                                            \
    cerr << "[L" << __LINE__ << "] ";                                          \
    _debug(__VA_ARGS__);                                                       \
  }

template <typename T1, typename T2>
ostream &operator<<(ostream &o, const pair<T1, T2> &p) {
  return o << "(" << p.first << ", " << p.second << ")";
}
template <typename T> string join(const vector<T> &v, string del = ", ") {
  stringstream s;
  rep(i, v.size()) s << del << v[i];
  return s.str().substr(del.size());
}
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) {
  if (v.size())
    o << "[" << join(v) << "]";
  return o;
}
template <typename T>
ostream &operator<<(ostream &o, const vector<vector<T>> &vv) {
  int l = vv.size();
  if (l) {
    o << endl;
    rep(i, l) {
      o << (i == 0 ? "[ " : ",\n  ") << vv[i] << (i == l - 1 ? " ]" : "");
    }
  }
  return o;
}
template <typename T> ostream &operator<<(ostream &o, const set<T> &st) {
  vector<T> v(st.begin(), st.end());
  o << "{ " << join(v) << " }";
  return o;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &o, const map<T1, T2> &m) {
  each(p, m) {
    o << (p == m.begin() ? "{ " : ",\n  ") << *p
      << (p == --m.end() ? " }" : "");
  }
  return o;
}
inline void _debug() { cerr << endl; }
template <class First, class... Rest>
void _debug(const First &first, const Rest &...rest) {
  cerr << first << " ";
  _debug(rest...);
}

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;

const double PI = (1 * acos(0.0));
const double INF = 0x3f3f3f3f;
const double INFL = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-9;
const double mod = 1e9 + 7;

inline void finput(string filename) { freopen(filename.c_str(), "r", stdin); }

int N;
double dp[310][310][310];

double rec(int c1, int c2, int c3) {
  if (dp[c1][c2][c3] >= 0)
    return dp[c1][c2][c3];
  if (c1 == 0 && c2 == 0 && c3 == 0)
    return 0.0;

  double res = 0.0;
  if (c1 > 0)
    res += rec(c1 - 1, c2, c3) * c1;
  if (c2 > 0)
    res += rec(c1 + 1, c2 - 1, c3) * c2;
  if (c3 > 0)
    res += rec(c1, c2 + 1, c3 - 1) * c3;
  res += N;
  res *= 1.0 / (c1 + c2 + c3);
  return dp[c1][c2][c3] = res;
}

int main() {
  ios_base::sync_with_stdio(0);
  // finput("./input");

  cin >> N;
  int C[4];
  memset(C, 0, sizeof(C));
  rep(i, N) {
    int a;
    cin >> a;
    C[a]++;
  }
  memset(dp, -1, sizeof(dp));
  cout << fixed << setprecision(10) << rec(C[1], C[2], C[3]) << endl;
  return 0;
}