本文章由 WyOJ Shojo 从洛谷专栏拉取，原发布时间为 2024-06-22 19:57:53

有一个东西：

$$ \begin{aligned} E(x) &= \sum\limits_{i=1}^V\sum\limits_{j=1}^V \dfrac {\lvert j - i + 1\rvert} {V^2}\ &= \sum\limits_{i=1}^V\bigg(\sum\limits_{j=i}^V \dfrac{j - i + 1}{V^2} + \sum\limits_{j=1}^{i-1}\dfrac{i-j+1}{V^2}\bigg)\ &=\sum\limits_{i=1}^V \dfrac 1{V^2}\bigg(\sum\limits_{j=1}^{V - i + 1} 1 + \sum\limits_{j=2}^i 1\bigg) \ &=\dfrac{1}{V^2} \sum\limits_{i=1}^V\bigg(\dfrac 1 2 (V-i+2)(V-i+1) + \dfrac{1}{2} (i+2)(i - 1)\bigg)\

\end{aligned} $$