【Uva11762】Race to 1

模拟马尔可夫过程，具体看书。

#include<bits/stdc++.h>
#define N 1000010
using namespace std;
int prime[N],use[N],cnt=;
void calcprime(){
    cnt=;memset(use,,sizeof(use));
    for(int i=;i<=N;i++){
        if(use[i]){prime[++cnt]=i;}
        for(int j=;j<=cnt;j++){
            int t=prime[j]*i;if(t>N)break;
            use[t]=;
            if(i%prime[j]==)break;
        }
    }
}
bool vis[N];double f[N];
double dfs(int x){
    if(x==)return 0.0;if(vis[x])return f[x];
    vis[x]=;double &ans=f[x];
    int g=,p=;ans=;
    for(int j=;j<=cnt;j++){
        if(prime[j]>x)break;++p;
        if(x%prime[j]==){g++;ans+=(dfs(x/prime[j]));}
    }
    ans=(ans+p)/g;return ans;
}
inline int read(){
    int f=,x=;char ch;
    do{ch=getchar();if(ch=='-')f=-;}while(ch<''||ch>'');
    do{x=x*+ch-'';ch=getchar();}while(ch>=''&&ch<='');
    return f*x;
}
int main(){
    calcprime();int T=read();
    for(int t=;t<=T;t++){
        printf("Case %d: %.10lf\n",t,dfs(read()));
    }
    return ;
}#include<bits/stdc++.h>
#define N 1000010
using namespace std;
int prime[N],use[N],cnt=;
void calcprime(){
    cnt=;memset(use,,sizeof(use));
    for(int i=;i<=N;i++){
        if(use[i]){prime[++cnt]=i;}
        for(int j=;j<=cnt;j++){
            int t=prime[j]*i;if(t>N)break;
            use[t]=;
            if(i%prime[j]==)break;
        }
    }
}
bool vis[N];double f[N];
double dfs(int x){
    if(x==)return 0.0;if(vis[x])return f[x];
    vis[x]=;double &ans=f[x];
    int g=,p=;ans=;
    for(int j=;j<=cnt;j++){
        if(prime[j]>x)break;++p;
        if(x%prime[j]==){g++;ans+=(dfs(x/prime[j]));}
    }
    ans=(ans+p)/g;return ans;
}
inline int read(){
    int f=,x=;char ch;
    do{ch=getchar();if(ch=='-')f=-;}while(ch<''||ch>'');
    do{x=x*+ch-'';ch=getchar();}while(ch>=''&&ch<='');
    return f*x;
}
int main(){
    calcprime();int T=read();
    for(int t=;t<=T;t++){
        printf("Case %d: %.10lf\n",t,dfs(read()));
    }
    return ;
}