Uva_11762 Race to 1

 1 #include <cmath>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <cstdlib>
 5 #include <ctime>
 6 #include <set>
 7 #include <map>
 8 #include <list>
 9 #include <queue>
10 #include <string>
11 #include <vector>
12 #include <fstream>
13 #include <iterator>
14 #include <iostream>
15 #include <algorithm>
16 using namespace std;
17 #define LL long long
18 #define MAXN 1000010
19 #define MOD 1000000007
20 #define eps 1e-6
21 int prime_size;
22 int prime_[MAXN];
23 double f[MAXN];
24 bool prime[MAXN], vis[MAXN];
25 int n;
26 bool is_prime(int x)
27 {
28     if(x <= 1) return false;
29     for(int i = 2; i * i <= x; i ++)
30         if(x % i == 0) return false;
31     return true;
32 }
33 void p_init()
34 {
35     memset(vis, false, sizeof(vis));
36     prime_size = 0;
37     for(int i = 2; i < MAXN; i ++)
38         if(is_prime(i))
39         {
40             prime_[prime_size ++] = i;
41             for(int j = 1; j * i < MAXN; j ++)
42                 prime[j * i] = true;
43         }
44     f[0] = f[1] = 0;
45 }
46 double dp(int x)
47 {
48     if(x == 1) return 0.0;
49     if(vis[x]) return f[x];
50     vis[x] = true;
51     int g = 0;
52     int p = 0;
53     double& ans = f[x];
54     ans = 0;
55     for(int i = 0; i < prime_size  && prime_[i] <= x; i ++)
56     {
57         p ++;
58         if(x % prime_[i] == 0)
59         {
60             g ++;
61             ans += dp(x / prime_[i]);
62         }
63     }
64     ans = (ans + p) / g;
65     return ans;
66 }
67 
68 int main()
69 {
70     int T;
71     int kcase = 0;
72     p_init();
73     scanf("%d", &T);
74     while(T --)
75     {
76         scanf("%d", &n);
77         printf("Case %d: %.7lf\n", ++ kcase, dp(n));
78     }
79     return 0;
80 }