Problem p03168 (C++)

Buggy submission (status: Runtime Error):
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<long long> vll;
#define left(x) (x << 1)
#define right(x) (x << 1) + 1
#define mid(l, r) ((l + r) >> 1)
#define mp make_pair
#define pb push_back
#define all(a) a.begin(), a.end()
#define debug(x)                                                               \
  { cerr << #x << " = " << x << "\n"; }
#define debug2(x, y)                                                           \
  { cerr << #x << " = " << x << ", " << #y << " = " << y << "\n"; }
#define debug3(x, y, z)                                                        \
  {                                                                            \
    cerr << #x << " = " << x << ", " << #y << " = " << y << ", " << #z         \
         << " = " << z << "\n";                                                \
  }
#define debug4(x, y, z, w)                                                     \
  {                                                                            \
    cerr << #x << " = " << x << ", " << #y << " = " << y << ", " << #z         \
         << " = " << z << ", " << #w << " = " << w << "\n";                    \
  }
#define ss second
#define ff first
#define m0(x) memset(x, 0, sizeof(x))

template <typename T> T min_(T a, T b) { return a > b ? b : a; }
template <typename T, typename... Ts> T min_(T first, Ts... last) {
  return min_(first, min_(last...));
}
template <typename T> T max_(T a, T b) { return a > b ? a : b; }
template <typename T, typename... Ts> T max_(T first, Ts... last) {
  return max_(first, max_(last...));
}

template <class T, class S>
std::ostream &operator<<(std::ostream &os, const std::pair<T, S> &t) {
  os << "(" << t.first << ", " << t.second << ")";
  return os;
}
template <typename T> ostream &operator<<(ostream &out, const vector<T> &v) {
  out << "[";
  size_t last = v.size() - 1;
  for (size_t i = 0; i < v.size(); ++i) {
    out << v[i];
    if (i != last)
      out << ", ";
  }
  out << "]";
  return out;
}

ll pwr(ll base, ll p, ll mod) {
  ll ans = 1;
  while (p) {
    if (p & 1)
      ans = (ans * base) % mod;
    base = (base * base) % mod;
    p /= 2;
  }
  return ans;
}
ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a % b); }
ll lcm(ll a, ll b) { return a * (b / gcd(a, b)); }

const int day[12] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int digarr[10] = {6, 2, 5, 5, 4, 5, 6, 3, 7, 6};
const int dx[4] = {0, 1, 0, -1};
const int dy[4] = {1, 0, -1, 0};
const int dxo[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
const int dyo[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
const long double PI = (long double)(3.1415926535897932384626433832795);
const ll mx_ll = numeric_limits<ll>::max();
const int mx_int = numeric_limits<int>::max();
const int mod = 1e9 + 7;
const int maxn = 2e5 + 7;
void cppio() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}

double dp[1001][1001];
void solve() {
  int n;
  cin >> n;
  vector<double> p(n + 1);
  for (int i = 0; i < n; i++) {
    cin >> p[i + 1];
  }
  dp[0][0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int h = 0; h <= i; h++) {
      dp[i][h] =
          ((h == 0) ? 0 : dp[i - 1][h - 1] * p[i]) + dp[i - 1][h] * (1 - p[i]);
    }
  }
  double ans = 0;
  for (int h = 0; h <= n; h++) {
    if (h > (n - h))
      ans += dp[n][h];
  }
  cout << setprecision(10) << fixed << ans << "\n";
}

int main() {
  cppio();
#ifdef __APPLE__
  // freopen("test.in", "rb", stdin);
  // freopen("  .out", "wb", stdout);
#endif

  int num_test_cases = 1;
  // cin >> num_test_cases;
  for (int t = 1; t <= num_test_cases; ++t) {
    solve();
  }
  return 0;
}


Fixed submission:
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
#pragma GCC optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <utility>
#include <vector>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<long long> vll;
#define left(x) (x << 1)
#define right(x) (x << 1) + 1
#define mid(l, r) ((l + r) >> 1)
#define mp make_pair
#define pb push_back
#define all(a) a.begin(), a.end()
#define debug(x)                                                               \
  { cerr << #x << " = " << x << "\n"; }
#define debug2(x, y)                                                           \
  { cerr << #x << " = " << x << ", " << #y << " = " << y << "\n"; }
#define debug3(x, y, z)                                                        \
  {                                                                            \
    cerr << #x << " = " << x << ", " << #y << " = " << y << ", " << #z         \
         << " = " << z << "\n";                                                \
  }
#define debug4(x, y, z, w)                                                     \
  {                                                                            \
    cerr << #x << " = " << x << ", " << #y << " = " << y << ", " << #z         \
         << " = " << z << ", " << #w << " = " << w << "\n";                    \
  }
#define ss second
#define ff first
#define m0(x) memset(x, 0, sizeof(x))

template <typename T> T min_(T a, T b) { return a > b ? b : a; }
template <typename T, typename... Ts> T min_(T first, Ts... last) {
  return min_(first, min_(last...));
}
template <typename T> T max_(T a, T b) { return a > b ? a : b; }
template <typename T, typename... Ts> T max_(T first, Ts... last) {
  return max_(first, max_(last...));
}

template <class T, class S>
std::ostream &operator<<(std::ostream &os, const std::pair<T, S> &t) {
  os << "(" << t.first << ", " << t.second << ")";
  return os;
}
template <typename T> ostream &operator<<(ostream &out, const vector<T> &v) {
  out << "[";
  size_t last = v.size() - 1;
  for (size_t i = 0; i < v.size(); ++i) {
    out << v[i];
    if (i != last)
      out << ", ";
  }
  out << "]";
  return out;
}

ll pwr(ll base, ll p, ll mod) {
  ll ans = 1;
  while (p) {
    if (p & 1)
      ans = (ans * base) % mod;
    base = (base * base) % mod;
    p /= 2;
  }
  return ans;
}
ll gcd(ll a, ll b) { return b == 0 ? a : gcd(b, a % b); }
ll lcm(ll a, ll b) { return a * (b / gcd(a, b)); }

const int day[12] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int digarr[10] = {6, 2, 5, 5, 4, 5, 6, 3, 7, 6};
const int dx[4] = {0, 1, 0, -1};
const int dy[4] = {1, 0, -1, 0};
const int dxo[8] = {-1, -1, -1, 0, 1, 1, 1, 0};
const int dyo[8] = {-1, 0, 1, 1, 1, 0, -1, -1};
const long double PI = (long double)(3.1415926535897932384626433832795);
const ll mx_ll = numeric_limits<ll>::max();
const int mx_int = numeric_limits<int>::max();
const int mod = 1e9 + 7;
const int maxn = 2e5 + 7;
void cppio() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}

double dp[5001][5001];
void solve() {
  int n;
  cin >> n;
  vector<double> p(n + 1);
  for (int i = 0; i < n; i++) {
    cin >> p[i + 1];
  }
  dp[0][0] = 1;
  for (int i = 1; i <= n; i++) {
    for (int h = 0; h <= i; h++) {
      dp[i][h] =
          ((h == 0) ? 0 : dp[i - 1][h - 1] * p[i]) + dp[i - 1][h] * (1 - p[i]);
    }
  }
  double ans = 0;
  for (int h = 0; h <= n; h++) {
    if (h > (n - h))
      ans += dp[n][h];
  }
  cout << setprecision(10) << fixed << ans << "\n";
}

int main() {
  cppio();
#ifdef __APPLE__
  // freopen("test.in", "rb", stdin);
  // freopen("  .out", "wb", stdout);
#endif

  int num_test_cases = 1;
  // cin >> num_test_cases;
  for (int t = 1; t <= num_test_cases; ++t) {
    solve();
  }
  return 0;
}