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## 切比雪夫转曼哈顿
把上面反过来:
$$
\begin{aligned}
&\ \ \ \ \max(|x_i - x_j|, |y_i - y_j|) \\
&= \max(x_i - x_j, -x_i + x_j, y_i - y_j, -y_i + y_j) \\
& 令\ u_i = \frac{x_i + y_i}{2}, v_i = \frac{x_i - y_i}{2} \\
&= \max(u_i + v_i - (u_j + v_j), -(u_i + v_i) + u_j + v_j, u_i - v_i - (u_j - v_j), -(u_i - v_i) + u_j - v_j) \\
&= \max(u_i - u_j + v_i - v_j, -u_i + u_j - v_i + v_j, u_i - u_j - v_i + v_j, -u_i + u_j + v_i - v_j) \\
&= |u_i - u_j| + |v_i - v_j|
\end{aligned}
$$
witnote results
expected: (from Typora)

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