Unverified Commit 3d1bdb91 authored by MingqiHuang's avatar MingqiHuang Committed by GitHub
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refine formula, use aligned

parent 31f29ad3
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+7 −4
Original line number Diff line number Diff line
@@ -52,9 +52,12 @@ By [hsfzLZH1](https://github.com/hsfzLZH1)

由于上一步已经证明出了$cost$满足四边形不等式,而该不等式的左边在上式出现过,将其替换得

$f_{i,x}+f_{x+1,j}+cost_{i,j}+f_{i+1,y}+f_{y+1,j+1}+cost_{i+1,j+1}$

$\le f_{i,x}+f_{x+1,j+1}+cost_{i,j+1}+f_{i+1,y}+f_{y+1,j}+cost_{i+1,j}$
$$
\begin{aligned}
&&f_{i,\,x}+f_{x+1,\,j}+cost_{i,\,j}+f_{i+1,\,y}+f_{y+1,\,j+1}+cost_{i+1,\,j+1}\\
&\le&f_{i,\,x}+f_{x+1,\,j+1}+cost_{i,\,j+1}+f_{i+1,\,y}+f_{y+1,\,j}+cost_{i+1,\,j}\\
\end{aligned}
$$

消去公共项可得 $f_{i,j}+f_{i+1,j+1}\le f_{i+1,j}+f_{i,j+1}$