Problem p03169 (C++)

Buggy submission (status: Runtime Error):
#include <algorithm>
#include <bitset>
#include <ciso646>
#include <cmath>
#include <complex>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll mod = 1000000007;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop                                                                   \
  char nyaa;                                                                   \
  cin >> nyaa;
#define rep(i, n) for (int i = 0; i < n; i++)
#define per(i, n) for (int i = n - 1; i >= 0; i--)
#define Rep(i, sta, n) for (int i = sta; i < n; i++)
#define rep1(i, n) for (int i = 1; i <= n; i++)
#define per1(i, n) for (int i = n; i >= 1; i--)
#define Rep1(i, sta, n) for (int i = sta; i <= n; i++)
typedef long double ld;
typedef complex<ld> Point;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;

int n, num[3] = {0};
ld dp[301][301][301] = {0};

void solve() {
  cin >> n;
  rep(i, n) {
    int a;
    cin >> a;
    num[a - 1] += 1;
  }
  // cout << num[0] << " " << num[1] << " " << num[2] << endl;
  rep(a3, n + 1) {
    rep(a2, n + 1) {
      rep(a1, n + 1) {
        if (a1 == 0 && a2 == 0 && a3 == 0)
          continue;
        dp[a1][a2][a3] = (ld)n / (a1 + a2 + a3);
        if (a1 >= 1)
          dp[a1][a2][a3] += ((ld)a1 / (a1 + a2 + a3)) * dp[a1 - 1][a2][a3];
        if (a2 >= 1)
          dp[a1][a2][a3] += ((ld)a2 / (a1 + a2 + a3)) * dp[a1 + 1][a2 - 1][a3];
        if (a3 >= 1)
          dp[a1][a2][a3] += ((ld)a3 / (a1 + a2 + a3)) * dp[a1][a2 + 1][a3 - 1];

        // cout << a1 << " " << a2 << " " << a3 << " " << dp[a1][a2][a3] <<
        // endl;
      }
    }
  }
  cout << dp[num[0]][num[1]][num[2]] << endl;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(10);
  solve();
}

Fixed submission:
#include <algorithm>
#include <bitset>
#include <ciso646>
#include <cmath>
#include <complex>
#include <cstdio>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll mod = 1000000007;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop                                                                   \
  char nyaa;                                                                   \
  cin >> nyaa;
#define rep(i, n) for (int i = 0; i < n; i++)
#define per(i, n) for (int i = n - 1; i >= 0; i--)
#define Rep(i, sta, n) for (int i = sta; i < n; i++)
#define rep1(i, n) for (int i = 1; i <= n; i++)
#define per1(i, n) for (int i = n; i >= 1; i--)
#define Rep1(i, sta, n) for (int i = sta; i <= n; i++)
typedef long double ld;
typedef complex<ld> Point;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;

int n, num[3] = {0};
ld dp[400][400][400] = {0};

void solve() {
  cin >> n;
  rep(i, n) {
    int a;
    cin >> a;
    num[a - 1] += 1;
  }
  // cout << num[0] << " " << num[1] << " " << num[2] << endl;
  rep(a3, n + 1) {
    rep(a2, n + 1) {
      rep(a1, n + 1) {
        if (a1 == 0 && a2 == 0 && a3 == 0)
          continue;
        dp[a1][a2][a3] = (ld)n / (a1 + a2 + a3);
        if (a1 >= 1)
          dp[a1][a2][a3] += ((ld)a1 / (a1 + a2 + a3)) * dp[a1 - 1][a2][a3];
        if (a2 >= 1)
          dp[a1][a2][a3] += ((ld)a2 / (a1 + a2 + a3)) * dp[a1 + 1][a2 - 1][a3];
        if (a3 >= 1)
          dp[a1][a2][a3] += ((ld)a3 / (a1 + a2 + a3)) * dp[a1][a2 + 1][a3 - 1];

        // cout << a1 << " " << a2 << " " << a3 << " " << dp[a1][a2][a3] <<
        // endl;
      }
    }
  }
  cout << dp[num[0]][num[1]][num[2]] << endl;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(10);
  solve();
}