Light OJ 1038 - Race to 1 Again（概率DP）

    #include<cstdio>
    #include<cstring>
    #include<iostream>
    #include<algorithm>
    #include<cmath>
    #include<queue>
    #include<vector>
    #include<map>
    using namespace std;
    typedef long long LL;
    const int INF = 1e9+7;
    const int MAXN = 100055;
    double dp[MAXN];

    double DFS(int n)
    {
        if(dp[n] != -1) return dp[n];

        dp[n] = 0;
        int len = sqrt(n+1), k = 0;
        for(int i=1; i<=len; i++)
        {
            if(i*i == n)
            {
                k ++;
                dp[n] += DFS(i);
            }
            else if(n%i == 0)
            {
                k += 2;
                dp[n] += DFS(i);
                dp[n] += DFS(n/i);
            }
        }
        dp[n] = 1.0/(k-1) * (dp[n] + k);
        return  dp[n];
    }

    int main()
    {
        int T, cas = 1, n;
        for(int i=0; i<= 100005; i++)
            dp[i] = -1;
        dp[1] = 0;
        scanf("%d", &T);
        while(T --)
        {
            scanf("%d", &n);

            printf("Case %d: %.6lf\n",cas ++, DFS(n) );
        }

        return 0;
    }