I - Coins（dp）

#include<bits/stdc++.h>
#define x first
#define y second
#define PB push_back
#define mst(x,a) memset(x,a,sizeof(x))
#define all(a) begin(a),end(a)
#define rep(x,l,u) for(ll x=l;x<u;x++)
#define rrep(x,l,u) for(ll x=l;x>=u;x--)
#define sz(x) x.size()
#define IOS ios::sync_with_stdio(false);cin.tie(0);
using namespace std;
typedef unsigned long long ull;
typedef pair<int,int> PII;
typedef pair<char,char> PCC;
typedef long long ll;
typedef pair<ll,ll> PLL;
const int N=3005;
const int M=1e5+10;
const int INF=0x3f3f3f3f;
const int MOD=1e9+7;
double a[N],f[N][N];
void solve(){
    int n;cin>>n;
    rep(i,1,n+1) cin>>a[i];
    f[0][0]=1;
    rep(i,1,n+1){
        f[i][0]=f[i-1][0]*(1-a[i]);
        rep(j,1,i+1){
            f[i][j]=f[i-1][j-1]*a[i]+f[i-1][j]*(1-a[i]);
        }
    }
    double ans=0;
    rep(i,0,n+1){
        if(i>n-i) ans+=f[n][i];
    }
    printf("%.9f\n",ans);
}
int main(){
    IOS;
    //freopen("test.txt", "r", stdin);
    //freopen("test.txt", "w", stdout);
    //int t;cin>>t;
    //while(t--)
        solve();
    return 0;
}