competitive-programming/solved-lightOj/1038.cpp at master · the-redback/competitive-programming · GitHub

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/**
 *                                   ____
 *       ____ ___  ____ ________  __/ __/
 *      / __ `__ \/ __ `/ ___/ / / / /_
 *     / / / / / / /_/ / /  / /_/ / __/
 *    /_/ /_/ /_/\__,_/_/   \__,_/_/
 *
 *    @link : https://the-redback.com
 */

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef unsigned long long llu;

#define ft        first
#define sd        second
#define mp        make_pair
#define pb(x)     push_back(x)
#define all(x)    x.begin(), x.end()
#define allr(x)   x.rbegin(), x.rend()
#define mem(a, b) memset(a, b, sizeof(a))
#define inf       1e9
#define eps       1e-9
#define mod       1000000007
#define NN        100001

#define read(a) scanf("%lld", &a)

bool dc[NN + 7];
double dp[NN + 7];
vector<ll> Div[NN];

void prework(ll N) {
    ll i, j, k;
    for (i = 2; i <= N; i++) {
        for (j = i; j <= N; j += i) Div[j].pb(i);
    }
    return;
}

double rec(ll num) {
    if (num <= 1) return 0;

    double& tc = dp[num];
    if (dc[num]) return tc;

    ll m = (ll)Div[num].size();
    m++;

    double res = 1;
    for (ll i = 0; i < Div[num].size(); i++) {
        res += rec(num / Div[num][i]) + 1;
    }
    tc = res / (m - 1);
    dc[num] = 1;
    return tc;
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
#ifdef redback
    freopen("C:\\Users\\Maruf\\Desktop\\in.txt", "r", stdin);
#endif
    prework(NN);

    ll t = 1, tc;
    cin >> tc;
    ll i, j, k, l, m, n;
    while (tc--) {
        cin >> n;
        memset(dc, 0, sizeof(bool) * (n + 2));
        double res = rec(n);
        printf("Case %lld: %.8lf\n", t++, res);
    }
    return 0;
}