Light OJ 1038 / DP - Expected Value

/***
 created: 2022-08-29-01.49.51
***/

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename U> using ordered_set=tree<U, null_type,less<U>,rb_tree_tag,tree_order_statistics_node_update>;
#define ll long long
#define test int tt; cin>>tt; for(int cs=1;cs<=tt;cs++)
#define get_lost_idiot return 0
#define nl '\n'

vector<ll>divs(ll x)
{
    vector<ll>a;

    for(ll i=1;i*i<=x;i++)
    {
        if(x%i==0)
        {
            a.push_back(x/i);
            if(i*i!=x) a.push_back(i);
        }
    }

    return a;
}

double dp[100005];
bool v[100005];

double solve(ll n)
{
    if(n==1) return dp[1]=0.00;
    if(v[n]) return dp[n];

    vector<ll>dv=divs(n);

    v[n]=1;

    double ans=0.00;

    for(ll i=0;i<dv.size();i++)
    {
        ans+=(solve(n/dv[i])*1.00 + 1.00) / (dv.size()-1)*1.00;
    }

    //ans+=(dv.size() * 1.00)/((dv.size()-1)*1.00);

    return dp[n]=ans;
}


int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    test
    {
        ll n,m,i,j,k,l;

        cin>>n;

//        for(i=0;i<100004;i++)
//        {
//            v[i]=0,dp[i]=0.00;
//        }

        cout<<"Case "<<cs<<": "<<fixed<<setprecision(10)<<solve(n)<<nl;
    }



    get_lost_idiot;
}