Problem p03168 (C++)

Buggy submission (status: Runtime Error):
#pragma warning(disable : 4996)
#pragma comment(linker, "/STACK:336777216")
#pragma GCC optimize("Ofast")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <functional>

using namespace std;
using namespace __gnu_pbds;

typedef long long ll;
#define int long long int
typedef complex<long double> cd;
const long double pi = acos(-1);
typedef double db;
typedef long double ldb;
typedef pair<int, int> pii;
typedef pair<db, db> pdd;
typedef vector<int> vi;
typedef vector<vector<int>> matrix;

#define m1 make_pair
#define pb push_back
#define flush fflush(stdout)
#define IOS                                                                    \
  std::ios::sync_with_stdio(false);                                            \
  cin.tie(NULL);                                                               \
  cout.tie(NULL);
#define reset(x, v) memset(x, v, sizeof(x))

#define fi first
#define se second
#define endl "\n"
#define debug(x) (cerr << #x << ": " << x << "\n")
#define setbits(x) __builtin_popcount(x)
#define setbitsll(x) __builtin_popcountll(x)
#define all(x) x.begin(), x.end()
#define pii pair<int, int>

inline ll gcd(ll a, ll b) {
  if (a == 0)
    return b;
  return gcd(b % a, a);
}
inline ll power(ll a, ll n, ll m) {
  if (n == 0)
    return 1;
  ll p = power(a, n / 2, m);
  p = (p % m * p % m) % m;
  if (n % 2)
    return (p % m * a % m) % m;
  else
    return p;
}
const double EPS = 1e-9;
const ll MOD = 998244353;
const ll hell = 1000000007;
const int INF = 1e18;
const ll LL_INF = 0x3f3f3f3f3f3f3f3f;
template <typename T>
using ordered_set =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

auto seed = chrono::high_resolution_clock::now().time_since_epoch().count();
std::mt19937 rng(seed);

double startTime;
double getCurrentTime() {
  return ((double)clock() - startTime) / CLOCKS_PER_SEC;
}
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};

const int N = 100005;

ldb dp[3000][300];

void solve() {

  int n;
  cin >> n;
  ldb p[n + 1];
  for (int i = 1; i <= n; i++)
    cin >> p[i];
  dp[0][0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j <= i; j++) {
      if (!j)
        dp[i][j] = (1 - p[i]) * dp[i - 1][j];
      else
        dp[i][j] = (1 - p[i]) * dp[i - 1][j] + p[i] * dp[i - 1][j - 1];
    }
  }
  cout << setprecision(20);
  ldb ans = 0;
  for (int i = (n + 1) / 2; i <= n; i++)
    ans = ans + dp[n][i];
  cout << ans << endl;
}

int32_t main() {
  IOS;
  int t;
  t = 1;
  // cin>>t;
  while (t--) {
    solve();
  }
  return 0;
}


Fixed submission:
#pragma warning(disable : 4996)
#pragma comment(linker, "/STACK:336777216")
#pragma GCC optimize("Ofast")

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <functional>

using namespace std;
using namespace __gnu_pbds;

typedef long long ll;
#define int long long int
typedef complex<long double> cd;
const long double pi = acos(-1);
typedef double db;
typedef long double ldb;
typedef pair<int, int> pii;
typedef pair<db, db> pdd;
typedef vector<int> vi;
typedef vector<vector<int>> matrix;

#define m1 make_pair
#define pb push_back
#define flush fflush(stdout)
#define IOS                                                                    \
  std::ios::sync_with_stdio(false);                                            \
  cin.tie(NULL);                                                               \
  cout.tie(NULL);
#define reset(x, v) memset(x, v, sizeof(x))

#define fi first
#define se second
#define endl "\n"
#define debug(x) (cerr << #x << ": " << x << "\n")
#define setbits(x) __builtin_popcount(x)
#define setbitsll(x) __builtin_popcountll(x)
#define all(x) x.begin(), x.end()
#define pii pair<int, int>

inline ll gcd(ll a, ll b) {
  if (a == 0)
    return b;
  return gcd(b % a, a);
}
inline ll power(ll a, ll n, ll m) {
  if (n == 0)
    return 1;
  ll p = power(a, n / 2, m);
  p = (p % m * p % m) % m;
  if (n % 2)
    return (p % m * a % m) % m;
  else
    return p;
}
const double EPS = 1e-9;
const ll MOD = 998244353;
const ll hell = 1000000007;
const int INF = 1e18;
const ll LL_INF = 0x3f3f3f3f3f3f3f3f;
template <typename T>
using ordered_set =
    tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;

auto seed = chrono::high_resolution_clock::now().time_since_epoch().count();
std::mt19937 rng(seed);

double startTime;
double getCurrentTime() {
  return ((double)clock() - startTime) / CLOCKS_PER_SEC;
}
const int dx[] = {-1, 0, 1, 0};
const int dy[] = {0, 1, 0, -1};

const int N = 100005;

ldb dp[3000][3000];

void solve() {

  int n;
  cin >> n;
  ldb p[n + 1];
  for (int i = 1; i <= n; i++)
    cin >> p[i];
  dp[0][0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j <= i; j++) {
      if (!j)
        dp[i][j] = (1 - p[i]) * dp[i - 1][j];
      else
        dp[i][j] = (1 - p[i]) * dp[i - 1][j] + p[i] * dp[i - 1][j - 1];
    }
  }
  cout << setprecision(20);
  ldb ans = 0;
  for (int i = (n + 1) / 2; i <= n; i++)
    ans = ans + dp[n][i];
  cout << ans << endl;
}

int32_t main() {
  IOS;
  int t;
  t = 1;
  // cin>>t;
  while (t--) {
    solve();
  }
  return 0;
}