HDU 5013 City Tour

小鱼儿 2022-03-28 01:58 171阅读 0赞

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5013

题意：

![162233151122600.png][]

思路：

![162234196285022.png][]

![162236274565971.png][]这里有错，是Hi(x)=sigama(Hji)(j属于x)

const int N=18;
    
    int m,n;
    double p[N],H[N][N];
    
    double f[N][1<<N];
    double dp[N][1<<N];
    
    
    double a[1<<N],aa[1<<N];
    
    double pp[1<<N],qq[1<<N];
    
    int cnt[1<<N];
    
    void init()
    {
        int i;
        for(i=1;i<(1<<N);i++) cnt[i]=cnt[i>>1]+(i&1);
    }
    
    int sgn(double x)
    {
        if(x>1e-20) return 1;
        if(x<-1e-20) return -1;
        return 0;
    }
    
    int main()
    {
    
        init();
        while(scanf("%d%d",&m,&n)!=-1)
        {
            int i,j,k;
            for(i=0;i<m;i++) 
            {
                scanf("%lf",&p[i]);
                if(sgn(p[i]-1)==0) p[i]-=1e-10;
            }
            for(i=0;i<(1<<m);i++)
            {
                pp[i]=qq[i]=1;
                for(j=0;j<m;j++) if(i&(1<<j)) pp[i]*=p[j],qq[i]*=1-p[j];
            }
            for(i=0;i<m;i++) for(j=1;j<=n;j++) scanf("%lf",&H[i][j]);
            for(i=0;i<(1<<m);i++)
            {
                dp[n][i]=0;
                f[n][i]=0;
                for(j=0;j<m;j++) if(i&(1<<j)) 
                {
                    f[n][i]+=H[j][n];
                    dp[n][i]+=H[j][n];
                }
            }
            for(i=n-1;i>=1;i--)
            {
                for(j=0;j<(1<<m);j++) 
                {
                    a[j]=f[i+1][j]*pp[j]/qq[j];
                    aa[j]=dp[i+1][j]*cnt[j]*pp[j]/qq[j];
                }
                for(k=1;k<=m;k++) for(j=(1<<m)-1;j>=0;j--)
                {
                    if(j&(1<<(k-1))) 
                    {
                        a[j]=a[j]+a[j^(1<<(k-1))];
                        aa[j]=aa[j]+aa[j^(1<<(k-1))];
                    }
                }
    
                f[i][0]=dp[i][0]=0;
    
                for(j=1;j<(1<<m);j++)
                {
                    dp[i][j]=0;
                    for(k=0;k<m;k++) if(j&(1<<k)) dp[i][j]+=H[k][i];
                    f[i][j]=dp[i][j]+qq[j]*a[j]+qq[j]/cnt[j]*aa[j];
                }
            }
            printf("%.10lf\n",f[1][(1<<m)-1]);
        }
    }

[162233151122600.png]: /images/20220328/6aff817d792f40118b28a261dc58b037.png
[162234196285022.png]: /images/20220328/02f2f1ebda1c4ba1a987d63dac57382c.png
[162236274565971.png]: /images/20220328/ed93327c2a48486997ef14bc13a6f183.png