## luoOJ1898 运动会（Race）题解

[题目传送门][1]

$\displaystyle\sum_{sta\subseteq \lbrace 1,2,3,…,m \rbrace }{(\displaystyle\sum_{i=1}^{m}{[i\in sta]p[i]})^2}$

$\displaystyle\sum_{sta\subseteq \lbrace 1,2,3,…,m-1 \rbrace }{(p[m]+\displaystyle\sum_{i=1}^{m-1}{[i\in sta]p[i]})^2}+\displaystyle\sum_{sta\subseteq \lbrace 1,2,3,…,m-1 \rbrace }{(\displaystyle\sum_{i=1}^{m-1}{[i\in sta]p[i]})^2}$

$2^{m-1}p[m]^2+2p[m]\displaystyle\sum_{sta\subseteq \lbrace 1,2,3,…,m-1 \rbrace }{\displaystyle\sum_{i=1}^{m-1}{[i\in sta]p[i]}}+2\displaystyle\sum_{sta\subseteq \lbrace 1,2,3,…,m-1 \rbrace }{(\displaystyle\sum_{i=1}^{m-1}{[i\in sta]p[i]})^2}$

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