From: MingqiHuang <hmq011212@163.com>
Date: Wed, 29 Aug 2018 12:14:44 +0000 (+0800)
Subject: refine formula, use aligned
X-Git-Url: http://git.osdn.net/view?a=commitdiff_plain;h=3d1bdb9194434ae1614fd53273dade23ff082e2d;p=oi-wiki%2Fmain.git

refine formula, use aligned
---

diff --git a/docs/dp/optimization.md b/docs/dp/optimization.md
index 444f4fc5..00ae358b 100644
--- a/docs/dp/optimization.md
+++ b/docs/dp/optimization.md
@@ -48,13 +48,16 @@ By [hsfzLZH1](https://github.com/hsfzLZH1)
 
 我们假设 $x=idx_{i+1,j},y=idx_{i,j+1}$。不妨设 $x<=y$。
 
-将 $x,y$ 带入得， $f_{i,j}+f_{i+1,j+1}=f_{i,x}+f_{x+1,j}+cost_{i,j}+f_{i+1,y}+f_{y+1,j+1}+cost_{i+1,j+1}$
+将 $x,y$ 带入得，$f_{i,j}+f_{i+1,j+1}=f_{i,x}+f_{x+1,j}+cost_{i,j}+f_{i+1,y}+f_{y+1,j+1}+cost_{i+1,j+1}$
 
 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 $f_{i,j}+f_{i+1,j+1}\le f_{i+1,j}+f_{i,j+1}$