数学期望/马尔可夫过程
DP/记忆化搜索
刘汝佳老师白书上的例题……
1 //UVA 11762 2 #include<vector> 3 #include<cstdio> 4 #include<cstring> 5 #include<cstdlib> 6 #include<iostream> 7 #include<algorithm> 8 #define rep(i,n) for(int i=0;i<n;++i) 9 #define F(i,j,n) for(int i=j;i<=n;++i) 10 #define D(i,j,n) for(int i=j;i>=n;--i) 11 using namespace std; 12 int getint(){ 13 int v=0,sign=1; char ch=getchar(); 14 while(ch<'0'||ch>'9'){ if (ch=='-') sign=-1; ch=getchar();} 15 while(ch>='0'&&ch<='9'){ v=v*10+ch-'0'; ch=getchar();} 16 return v*=sign; 17 } 18 const int N=1e6+10; 19 #define debug 20 /******************tamplate*********************/ 21 int prime[N],tot; 22 bool check[N]; 23 24 void getpr(int n){ 25 memset(check,0,sizeof check); 26 F(i,2,n){ 27 if (!check[i]) prime[tot++]=i; 28 rep(j,tot){ 29 if (i*prime[j]>n)break; 30 check[i*prime[j]]=1; 31 } 32 } 33 } 34 bool vis[N]; 35 double f[N]; 36 double dp(int x){ 37 if (x==1) return 0.0; 38 if (vis[x]) return f[x]; 39 vis[x]=1; 40 double &ans = f[x]; 41 int g=0,p=0; ans=0; 42 rep(j,tot){ 43 if (prime[j]>x) break; 44 p++; 45 if (x%prime[j]==0){ g++; ans+=dp(x/prime[j]);} 46 } 47 ans=(ans+p)/g; 48 return ans; 49 } 50 int main(){ 51 #ifndef ONLINE_JUDGE 52 freopen("11762Race_to_1.in","r",stdin); 53 freopen("11762Race_to_1.out","w",stdout); 54 #endif 55 getpr(N-2); 56 int T=getint(); 57 F(t,1,T) 58 printf("Case %d: %.10lf ",t,dp(getint())); 59 return 0; 60 }