min-max容斥

<p>$$\max(S)=\sum_{T\subseteq S}\min(T)\cdot (-1)^{|T|-1}$$</p> <p>$$E(\max(S))=\sum_{T\subseteq S}E(\min(T))\cdot (-1)^{|T|-1} $$</p> <p>一般来说$$E(min(T))=\frac{1}{\sum_{i\in T}p_i}$$</p>