【一天一DP计划】概率期望DP

##换教室

floyd三看：

• dis[u][v]=dis[v][u]=min(dis[u][v],w)
• mem了dis后，rep(i,1,点的个数)dis[i][i]=0

/*
debug:
    注意读题啊……是双向通行的
reference:
    ccf提高篇P279
Date:
    2019.10.07
sol:

*/
const int N=2e3+10;
int n,m,v,e;
int c[N],d[N];
double k[N],f[N][N][2];
int dis[310][310];

int main(){
    #ifdef WIN32
    freopen("huanjiaoshi.txt","r",stdin);
    #endif
    rd(n),rd(m),rd(v),rd(e);
    rep(i,1,n)rd(c[i]);rep(i,1,n)rd(d[i]);rep(i,1,n)scanf("%lf",&k[i]);
    mem(dis,0x3f);
    rep(i,1,v)dis[i][i]=0;
    rep(i,1,e){
        int u,v,w;rd(u),rd(v),rd(w);
        dis[u][v]=dis[v][u]=min(dis[u][v],w);///////////////////////无向边！！！
    }
    rep(kk,1,v)
        rep(i,1,v)
            rep(j,1,v)
                dis[i][j]=min(dis[i][j],dis[i][kk]+dis[kk][j]);
    rep(i,1,n)
        rep(j,0,m)
            f[i][j][0]=f[i][j][1]=1.0*1e9;
    f[1][0][0]=f[1][1][1]=0;
    rep(i,2,n){
        rep(j,0,min(i,m)){
            //第i节课不申请
            f[i][j][0]=min(f[i][j][0],
                f[i-1][j][1]+k[i-1]*dis[d[i-1]][c[i]]+(1.0-k[i-1])*dis[c[i-1]][c[i]]);
            f[i][j][0]=min(f[i][j][0],
                f[i-1][j][0]+dis[c[i-1]][c[i]]);
            //第i节课要申请
            if(j>0){//得保证有上一堂课
                f[i][j][1]=min(f[i][j][1],
                    f[i-1][j-1][0]+k[i]*dis[c[i-1]][d[i]]+(1.0-k[i])*dis[c[i-1]][c[i]]);
                f[i][j][1]=min(f[i][j][1],
                    f[i-1][j-1][1]+
                    k[i-1]*k[i]*dis[d[i-1]][d[i]]+
                    k[i-1]*(1.0-k[i])*dis[d[i-1]][c[i]]+
                    (1.0-k[i-1])*k[i]*dis[c[i-1]][d[i]]+
                    (1.0-k[i-1])*(1.0-k[i])*dis[c[i-1]][c[i]]);
            }
        }
    }
    double ans=1e9*1.0;
    rep(i,0,m)
        ans=min(ans,min(f[n][i][0],f[n][i][1]));
    printf("%.2lf",ans);
    return 0;
}

原文地址：https://www.cnblogs.com/sjsjsj-minus-Si/p/11634646.html