Problem p03168 (C++)

Buggy submission (status: Runtime Error):
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
#include <bits/stdc++.h>
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define ts to_string
#define ub upper_bound
#define lb lower_bound
const char nl = '\n';
using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using str = string;
// The following debugging code was taken from Benjamin Qi's template :)
str ts(char c) { return str(1, c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char *s) { return (str)s; }
str ts(str s) { return s; }
template <class A> str ts(complex<A> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
str ts(vector<bool> v) {
  str res = "{";
  for (int i = 0; i < (int)v.size(); i++)
    res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ> str ts(bitset<SZ> b) {
  str res = "";
  for (int i = 0; i < b.size(); i++)
    res += char('0' + b[i]);
  return res;
}
template <class A, class B> str ts(pair<A, B> p);
template <class T> str ts(T v) {
  bool fst = 1;
  str res = "{";
  for (const auto &x : v) {
    if (!fst)
      res += ", ";
    fst = 0;
    res += ts(x);
  }
  res += "}";
  return res;
}
template <class A, class B> str ts(pair<A, B> p) {
  return "(" + ts(p.f) + ", " + ts(p.s) + ")";
}
void DBG() { cerr << "]" << endl; }
template <class H, class... T> void DBG(H h, T... t) {
  cerr << ts(h);
  if (sizeof...(t))
    cerr << ", ";
  DBG(t...);
}

#ifdef LOCAL
#define dbg(...)                                                               \
  cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [",           \
      DBG(__VA_ARGS__)
#else
#define dbg(...) 0
// freopen(".in", "r", stdin);
// freopen(".out", "w", stdout);
#endif
// CODE STARTS
// HERE-----------------------------------------------------------------------------------------//
const int N = 1e3 + 10;
int n;
double a[N], dp[N][N];
signed main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  dp[1][1] = a[1];
  dp[1][0] = 1 - a[1];
  for (int i = 2; i <= n; i++) {
    for (int j = 0; j <= i; j++) {
      if (j) {
        dp[i][j] += dp[i - 1][j - 1] * a[i];
      }
      dp[i][j] += dp[i - 1][j] * (1 - a[i]);
      dbg(dp[i][j], i, j);
    }
  }
  int m = (n + 2) / 2;
  double ans = 0;
  for (int i = m; i <= n; i++) {
    ans += dp[n][i];
  }
  cout << fixed << setprecision(9) << ans << nl;
}

Fixed submission:
#pragma GCC optimize("O3")
#pragma GCC target("sse4")
#include <bits/stdc++.h>
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define ts to_string
#define ub upper_bound
#define lb lower_bound
const char nl = '\n';
using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using str = string;
// The following debugging code was taken from Benjamin Qi's template :)
str ts(char c) { return str(1, c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char *s) { return (str)s; }
str ts(str s) { return s; }
template <class A> str ts(complex<A> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
str ts(vector<bool> v) {
  str res = "{";
  for (int i = 0; i < (int)v.size(); i++)
    res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ> str ts(bitset<SZ> b) {
  str res = "";
  for (int i = 0; i < b.size(); i++)
    res += char('0' + b[i]);
  return res;
}
template <class A, class B> str ts(pair<A, B> p);
template <class T> str ts(T v) {
  bool fst = 1;
  str res = "{";
  for (const auto &x : v) {
    if (!fst)
      res += ", ";
    fst = 0;
    res += ts(x);
  }
  res += "}";
  return res;
}
template <class A, class B> str ts(pair<A, B> p) {
  return "(" + ts(p.f) + ", " + ts(p.s) + ")";
}
void DBG() { cerr << "]" << endl; }
template <class H, class... T> void DBG(H h, T... t) {
  cerr << ts(h);
  if (sizeof...(t))
    cerr << ", ";
  DBG(t...);
}

#ifdef LOCAL
#define dbg(...)                                                               \
  cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [",           \
      DBG(__VA_ARGS__)
#else
#define dbg(...) 0
// freopen(".in", "r", stdin);
// freopen(".out", "w", stdout);
#endif
// CODE STARTS
// HERE-----------------------------------------------------------------------------------------//
const int N = 3e3 + 10;
int n;
double a[N], dp[N][N];
signed main() {
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  dp[1][1] = a[1];
  dp[1][0] = 1 - a[1];
  for (int i = 2; i <= n; i++) {
    for (int j = 0; j <= i; j++) {
      if (j) {
        dp[i][j] += dp[i - 1][j - 1] * a[i];
      }
      dp[i][j] += dp[i - 1][j] * (1 - a[i]);
      dbg(dp[i][j], i, j);
    }
  }
  int m = (n + 2) / 2;
  double ans = 0;
  for (int i = m; i <= n; i++) {
    ans += dp[n][i];
  }
  cout << fixed << setprecision(9) << ans << nl;
}