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diff --git a/排序问题/report.md b/排序问题/report.md
index fead24c..b827ae8 100644
--- a/排序问题/report.md
+++ b/排序问题/report.md
@@ -2,15 +2,17 @@
 
 ## T1
 
-### T1.1 
+### T1.1
 
 对于 $\boldsymbol{\mu}$ 的任一分量 $\mu_{i}$, 我们可以知道 $\forall\mu\in\mathbb{R}$, $|\mu-\sigma_{i}^{1}|+|\mu-\sigma_{i}^{2}|+\cdots+|\mu-\sigma_{i}^{k}|>|\mu_{i}-\sigma_{i}^{1}|+|\mu_{i}-\sigma_{i}^{2}|+\cdots+|\mu_{i}-\sigma_{i}^{k}|$, 我们可以知道, $\mu_{i}$ 为 $\set{\sigma_{i}^{1},\sigma_{i}^{2},\cdots,\sigma_{i}^{k}}$ 的中位数
+
 $$
 \therefore \mu_{i} = \begin{align}\left\{\begin{aligned}
     \sigma_{i}^{k/2}, k为偶数\\
     \sigma_{i}^{(k+1)/2}, k为奇数
 \end{aligned}\right.\end{align}
 $$
+
 我们取 $\boldsymbol{\sigma}_{i}^{\prime}$ 为 $\mu_{i}$ 在 $\set{\mu_{0},\mu_{1},\cdots,\mu_{k}}$ 中的排序，对于相同的值则随机排序，即为一种综合排序。然而，$\boldsymbol{\sigma^{\star}}$ 不能从中得出，因为可能有相同的值。
 
 ### T1.2
@@ -22,6 +24,7 @@ $$
 $$
 \sum\limits_{i=0}^{n}|\boldsymbol{\beta}_j-\sigma_j^i|=C+x_1
 $$
+
 $$
 \sum\limits_{i=0}^{n}|\boldsymbol{\mu}_j-\sigma_j^i|=C+x_2
 $$
@@ -41,7 +44,7 @@ $$
 $\mu_j$ 为中位数，所以 $\mu_j$ 与 N 点重合
 
 $$
-\sum\limits_{i=0}^{n}|\boldsymbol{\mu}_j-\sigma_j^i|= x
+\sum\limits_{i=0}^{n}|\mu_j-\sigma_j^i|= x
 $$
 
 $\mu_j$ 为平均数， $|\mu_j - N|=\frac{x}{n}$
@@ -61,19 +64,19 @@ $$
 ### T1.3
 
 $$
-d(\boldsymbol{\sigma^{\prime}},\boldsymbol{\Sigma}) = \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma^{\prime}},\boldsymbol{\sigma})\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma^{\prime}},\boldsymbol{\mu}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma}) 
+d(\boldsymbol{\sigma^{\prime}},\boldsymbol{\Sigma}) = \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma^{\prime}},\boldsymbol{\sigma})\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma^{\prime}},\boldsymbol{\mu}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma})
 $$
 
 $$
-\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\mu}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma}) 
+\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\mu}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma})
 $$
 
 $$
-\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\sigma}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma},\boldsymbol{\mu}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma}) 
+\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\sigma}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma},\boldsymbol{\mu}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma})
 $$
 
 $$
-= \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\sigma}) + 2\sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma}) 
+= \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\sigma}) + 2\sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma})
 $$
 
 $$
@@ -91,15 +94,15 @@ $$
 $$
 
 $$
-d(\boldsymbol{\sigma^{\prime}},\boldsymbol{\Sigma}) = \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma^{\prime}},\boldsymbol{\sigma})\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma^{\prime}},\boldsymbol{\beta}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\beta},\boldsymbol{\sigma}) 
+d(\boldsymbol{\sigma^{\prime}},\boldsymbol{\Sigma}) = \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma^{\prime}},\boldsymbol{\sigma})\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma^{\prime}},\boldsymbol{\beta}) + \sum\limits_{i=1}^{k}L_1(\boldsymbol{\beta},\boldsymbol{\sigma})
 $$
 
 $$
-\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\sigma}) + 2\sum\limits_{i=1}^{k}L_1(\boldsymbol{\beta},\boldsymbol{\sigma}) 
+\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\sigma}) + 2\sum\limits_{i=1}^{k}L_1(\boldsymbol{\beta},\boldsymbol{\sigma})
 $$
 
 $$
-\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\sigma}) + 4\sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma}) 
+\leq \sum\limits_{i=1}^{k}L_1(\boldsymbol{\sigma}^*,\boldsymbol{\sigma}) + 4\sum\limits_{i=1}^{k}L_1(\boldsymbol{\mu},\boldsymbol{\sigma})
 $$
 
 $$
@@ -150,7 +153,7 @@ $$
 
 ### T2.4
 
-我们易知 
+我们易知
 
 $$
 \boldsymbol{S}^{(3)}=\boldsymbol{M}\boldsymbol{S}^{(2)}+l^2\boldsymbol{S}
@@ -160,8 +163,8 @@ $$
 \boldsymbol{S}^{(n)}=\boldsymbol{M}\boldsymbol{S}^{(n-1)}+l^{n-1}\boldsymbol{S}
 $$
 
-所以递推得到 
+所以递推得到
 
 $$
 \boldsymbol{S}^{(n)}=\boldsymbol{M}^{n-1}\boldsymbol{S} + (\boldsymbol{M}^{n-1}-l^{n-1}\boldsymbol{E})(\boldsymbol{M}-l\boldsymbol{E})^{-1}l\boldsymbol{S}
-$$
\ No newline at end of file
+$$
diff --git a/排序问题/report.pdf b/排序问题/report.pdf
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