Problem p03168 (C++)

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

// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
using namespace std;
#define ll long long
#define endl "\n"
#define ar array
#define pb push_back
#define sz(X) ((int)(X).size())
#define ordered_set                                                            \
  tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>
#define sort_unique(c)                                                         \
  (sort(c.begin(), c.end()),                                                   \
   c.resize(distance(c.begin(), unique(c.begin(), c.end()))))
#define get_pos(c, x) (lower_bound(c.begin(), c.end(), x) - c.begin())
#define all(X) (X).begin(), (X).end()
#define No cout << "NO" << endl;
#define Yes cout << "YES" << endl;
#define nl cout << endl;

template <typename T> ostream &operator+(ostream &out, const vector<T> &vec) {
  for (const auto &x : vec) {
    out << x << " ";
  }
  out << "\n";
  return out;
}

template <typename T> ostream &operator*(ostream &out, const vector<T> &vec) {
  for (const auto &x : vec) {
    out + x;
  }
  return out;
}

template <typename T> istream &operator>>(istream &in, vector<T> &vec) {
  for (auto &x : vec) {
    in >> x;
  }
  return in;
}

// DEBUG
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 _DEBUG // compile with -DLOCAL
#define dbg(...)                                                               \
  cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [",           \
      DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif

template <class T> bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }

template <class T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

const int mod = 1e9 + 7;
const int mod2 = 998244353;
const ll INF = 1e9 + 6;

ll add(ll a, ll b) {
  a += b;
  return a % mod;
}

ll mul(ll a, ll b) {
  a *= b;
  return a % mod;
}

inline ll power(ll x, ll y, ll p) {
  ll res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1)
      res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}

inline ll modInverse(ll x, ll p) { return power(x, p - 2, p); }

int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

const int MXN = 1e3 + 1;
double p[MXN];
double cache[MXN][MXN];
int n;
double dp(int idx, int heads) {
  if (idx > n) {
    if (heads > n / 2)
      return 1;
    else
      return 0;
  }
  double &ans = cache[idx][heads];
  if (ans != -1) {
    return ans;
  }

  ans = dp(idx + 1, heads + 1) * p[idx] + dp(idx + 1, heads) * (1 - p[idx]);
  return ans;
}
void solve() {

  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
  }
  for (int i = 0; i < MXN; i++) {
    for (int j = 0; j < MXN; ++j) {
      cache[i][j] = -1;
    }
  }
  cout << fixed << setprecision(10) << dp(1, 0);
}

int main() {

  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#ifndef ONLINE_JUDGE
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif
  int t = 1;
  // cin >> t;
  while (t--)
    solve();
  // cerr <<endl<< "Time elapsed : " << clock() * 1000.0 / CLOCKS_PER_SEC << "
  // ms" << '\n';
  return 0;
}
// look if it requires ll

Fixed submission:
#include <bits/stdc++.h>

// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
// using namespace __gnu_pbds;
using namespace std;
#define ll long long
#define endl "\n"
#define ar array
#define pb push_back
#define sz(X) ((int)(X).size())
#define ordered_set                                                            \
  tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>
#define sort_unique(c)                                                         \
  (sort(c.begin(), c.end()),                                                   \
   c.resize(distance(c.begin(), unique(c.begin(), c.end()))))
#define get_pos(c, x) (lower_bound(c.begin(), c.end(), x) - c.begin())
#define all(X) (X).begin(), (X).end()
#define No cout << "NO" << endl;
#define Yes cout << "YES" << endl;
#define nl cout << endl;

template <typename T> ostream &operator+(ostream &out, const vector<T> &vec) {
  for (const auto &x : vec) {
    out << x << " ";
  }
  out << "\n";
  return out;
}

template <typename T> ostream &operator*(ostream &out, const vector<T> &vec) {
  for (const auto &x : vec) {
    out + x;
  }
  return out;
}

template <typename T> istream &operator>>(istream &in, vector<T> &vec) {
  for (auto &x : vec) {
    in >> x;
  }
  return in;
}

// DEBUG
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 _DEBUG // compile with -DLOCAL
#define dbg(...)                                                               \
  cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [",           \
      DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif

template <class T> bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; }

template <class T> bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }

const int mod = 1e9 + 7;
const int mod2 = 998244353;
const ll INF = 1e9 + 6;

ll add(ll a, ll b) {
  a += b;
  return a % mod;
}

ll mul(ll a, ll b) {
  a *= b;
  return a % mod;
}

inline ll power(ll x, ll y, ll p) {
  ll res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1)
      res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}

inline ll modInverse(ll x, ll p) { return power(x, p - 2, p); }

int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

const int MXN = 3e3 + 1;
double p[MXN];
double cache[MXN][MXN];
int n;
double dp(int idx, int heads) {
  if (idx > n) {
    if (heads > n / 2)
      return 1;
    else
      return 0;
  }
  double &ans = cache[idx][heads];
  if (ans != -1) {
    return ans;
  }

  ans = dp(idx + 1, heads + 1) * p[idx] + dp(idx + 1, heads) * (1 - p[idx]);
  return ans;
}
void solve() {

  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> p[i];
  }
  for (int i = 0; i < MXN; i++) {
    for (int j = 0; j < MXN; ++j) {
      cache[i][j] = -1;
    }
  }
  cout << fixed << setprecision(10) << dp(1, 0);
}

int main() {

  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
#ifndef ONLINE_JUDGE
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif
  int t = 1;
  // cin >> t;
  while (t--)
    solve();
  // cerr <<endl<< "Time elapsed : " << clock() * 1000.0 / CLOCKS_PER_SEC << "
  // ms" << '\n';
  return 0;
}
// look if it requires ll