Problem p03168 (C++)

Buggy submission (status: Runtime Error):
#include <bits/stdc++.h>
using namespace std;

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define ll long long

template <class T> using v = std::vector<T>;
template <class T> using vv = v<v<T>>;

const int mod = 1000000007;
const int INF = 1001001001;
const ll LINF = 1001002003004005006ll;
// const int mod = 998244353;

struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
}

ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};
double dp[2999][2999];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  dp[0][0] = 1;
  rep(i, n) {
    double p;
    cin >> p;
    for (int j = 0; j <= i; ++j) {
      dp[j + 1][i + 1] += dp[j][i] * p;
      dp[j][i + 1] += dp[j][i] * (1 - p);
    }
  }

  //    rep(i,n+1) {
  //        rep(j,n+1) {
  //            printf("%.5f ",dp[i][j]);
  //        }
  //        printf("\n");
  //    }

  double ans = 0;
  for (int i = n; i > n / 2; --i) {
    //        cout << dp[i][n] << endl;
    ans += dp[i][n];
  }
  cout << fixed << setprecision(10) << ans << endl;
  return 0;
}


Fixed submission:
#include <bits/stdc++.h>
using namespace std;

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define ll long long

template <class T> using v = std::vector<T>;
template <class T> using vv = v<v<T>>;

const int mod = 1000000007;
const int INF = 1001001001;
const ll LINF = 1001002003004005006ll;
// const int mod = 998244353;

struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }

template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return 1;
  }
}
template <class T> bool chmin(T &a, const T &b) {
  if (b < a) {
    a = b;
    return 1;
  }
}

ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }

// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};
double dp[3002][3002];
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  dp[0][0] = 1;
  rep(i, n) {
    double p;
    cin >> p;
    for (int j = 0; j <= i; ++j) {
      dp[j + 1][i + 1] += dp[j][i] * p;
      dp[j][i + 1] += dp[j][i] * (1 - p);
    }
  }

  //    rep(i,n+1) {
  //        rep(j,n+1) {
  //            printf("%.5f ",dp[i][j]);
  //        }
  //        printf("\n");
  //    }

  double ans = 0;
  for (int i = n; i > n / 2; --i) {
    //        cout << dp[i][n] << endl;
    ans += dp[i][n];
  }
  cout << fixed << setprecision(10) << ans << endl;
  return 0;
}