Problem p03168 (C++)

Buggy submission (status: Runtime Error):
// Author rahuliitkgp
/*A thing of beauty is a joy forever,
Its loveliness increases,
it will never pass into nothingness.*/
// Men at Work :)
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
typedef long long int ll;

#define ff first
#define ss second
#define SZ(x) ((int)(x).size())
#define pb push_back
#define mp make_pair
#define pii pair<int, int>
#define vi vector<int>
#define mii map<int, int>
#define pqb priority_queue<int>
#define pqs priority_queue<int, vi, greater<int>>
#define setbits(x) __builtin_popcountll(x)
#define mod 1000000007
#define ps(x, y) fixed << setprecision(y) << x
#define mk(arr, n, type) type *arr = new type[n];
#define w(x)                                                                   \
  int x;                                                                       \
  cin >> x;                                                                    \
  while (x--)
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

typedef tree<int, null_type, less<int>, rb_tree_tag,
             tree_order_statistics_node_update>
    pbds;

void cpp() {
  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 main() {
  cpp();
  ll n;
  cin >> n;
  vector<double> v(n);
  for (ll i = 0; i < n; i++)
    cin >> v[i];
  vector<vector<double>> dp(n + 1, vector<double>(n + 1, 0));
  for (ll i = 0; i <= n; i++) {
    dp[i][0] = 1;
  }
  dp[0][0] = 1;
  for (ll i = 1; i <= n; i++) {
    for (ll j = 1; j <= n; j++) {
      dp[i][j] = dp[i - 1][j] * (1 - v[i - 1]) + dp[i - 1][j - 1] * (v[i - 1]);
    }
  }
  cout << ps(dp[n][(n + 1) / 2], 9) << endl;
  return 0;
}


Fixed submission:
// Author rahuliitkgp
/*A thing of beauty is a joy forever,
Its loveliness increases,
it will never pass into nothingness.*/
// Men at Work :)
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
using namespace std;
typedef long long int ll;

#define ff first
#define ss second
#define SZ(x) ((int)(x).size())
#define pb push_back
#define mp make_pair
#define pii pair<int, int>
#define vi vector<int>
#define mii map<int, int>
#define pqb priority_queue<int>
#define pqs priority_queue<int, vi, greater<int>>
#define setbits(x) __builtin_popcountll(x)
#define mod 1000000007
#define ps(x, y) fixed << setprecision(y) << x
#define mk(arr, n, type) type *arr = new type[n];
#define w(x)                                                                   \
  int x;                                                                       \
  cin >> x;                                                                    \
  while (x--)
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

typedef tree<int, null_type, less<int>, rb_tree_tag,
             tree_order_statistics_node_update>
    pbds;

void cpp() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}

int main() {
  cpp();
  ll n;
  cin >> n;
  vector<double> v(n);
  for (ll i = 0; i < n; i++)
    cin >> v[i];
  vector<vector<double>> dp(n + 1, vector<double>(n + 1, 0));
  for (ll i = 0; i <= n; i++) {
    dp[i][0] = 1;
  }
  dp[0][0] = 1;
  for (ll i = 1; i <= n; i++) {
    for (ll j = 1; j <= n; j++) {
      dp[i][j] = dp[i - 1][j] * (1 - v[i - 1]) + dp[i - 1][j - 1] * (v[i - 1]);
    }
  }
  cout << ps(dp[n][(n + 1) / 2], 9) << endl;
  return 0;
}