refine formula, use aligned

diff --git a/docs/dp/optimization.md b/docs/dp/optimization.md
index 444f4fc..00ae358 100644 (file)
--- a/docs/dp/optimization.md
+++ b/docs/dp/optimization.md
@@ -48,13 +48,16 @@ By [hsfzLZH1](https://github.com/hsfzLZH1)
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 我们假设 $x=idx_{i+1,j},y=idx_{i,j+1}$。不妨设 $x<=y$。\r
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-将 $x,y$ 带入得， $f_{i,j}+f_{i+1,j+1}=f_{i,x}+f_{x+1,j}+cost_{i,j}+f_{i+1,y}+f_{y+1,j+1}+cost_{i+1,j+1}$\r
+将 $x,y$ 带入得，$f_{i,j}+f_{i+1,j+1}=f_{i,x}+f_{x+1,j}+cost_{i,j}+f_{i+1,y}+f_{y+1,j+1}+cost_{i+1,j+1}$\r
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 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\r
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-$f_{i,x}+f_{x+1,j}+cost_{i,j}+f_{i+1,y}+f_{y+1,j+1}+cost_{i+1,j+1}$\r
-\r
-$\le f_{i,x}+f_{x+1,j+1}+cost_{i,j+1}+f_{i+1,y}+f_{y+1,j}+cost_{i+1,j}$\r
+$$\r
+\begin{aligned}\r
+&&f_{i,\,x}+f_{x+1,\,j}+cost_{i,\,j}+f_{i+1,\,y}+f_{y+1,\,j+1}+cost_{i+1,\,j+1}\\\r
+&\le&f_{i,\,x}+f_{x+1,\,j+1}+cost_{i,\,j+1}+f_{i+1,\,y}+f_{y+1,\,j}+cost_{i+1,\,j}\\\r
+\end{aligned}\r
+$$\r
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 消去公共项可得 $f_{i,j}+f_{i+1,j+1}\le f_{i+1,j}+f_{i,j+1}$\r
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