From d1f307e54765fd7d74c50ee4b4a95cbcfd623bde Mon Sep 17 00:00:00 2001
From: krahets <krahets@163.com>
Date: Sat, 4 May 2024 19:56:43 +0800
Subject: [PATCH] Bug fixes

---
 codes/ruby/chapter_sorting/quick_sort.rb                     | 3 +--
 en/docs/chapter_computational_complexity/space_complexity.md | 4 ++--
 en/docs/chapter_computational_complexity/time_complexity.md  | 4 ++--
 zh-hant/codes/ruby/chapter_sorting/quick_sort.rb             | 3 +--
 4 files changed, 6 insertions(+), 8 deletions(-)

diff --git a/codes/ruby/chapter_sorting/quick_sort.rb b/codes/ruby/chapter_sorting/quick_sort.rb
index 2dff14c6b..0ef9c48ff 100644
--- a/codes/ruby/chapter_sorting/quick_sort.rb
+++ b/codes/ruby/chapter_sorting/quick_sort.rb
@@ -9,7 +9,6 @@ class QuickSort
   class << self
     ### 哨兵划分 ###
     def partition(nums, left, right)
-
       # 以 nums[left] 为基准数
       i, j = left, right
       while i < j
@@ -116,7 +115,7 @@ class QuickSortTailCall
       i # 返回基准数的索引
     end
 
-    ### 快速排序（尾递归优化）
+    ### 快速排序（尾递归优化）###
     def quick_sort(nums, left, right)
       # 子数组长度不为 1 时递归
       while left < right
diff --git a/en/docs/chapter_computational_complexity/space_complexity.md b/en/docs/chapter_computational_complexity/space_complexity.md
index 96a60f835..a3ed5be69 100644
--- a/en/docs/chapter_computational_complexity/space_complexity.md
+++ b/en/docs/chapter_computational_complexity/space_complexity.md
@@ -729,8 +729,8 @@ Let the size of the input data be $n$, the following chart displays common types
 
 $$
 \begin{aligned}
-O(1) < O(\log n) < O(n) < O(n^2) < O(2^n) \newline
-\text{Constant Order} < \text{Logarithmic Order} < \text{Linear Order} < \text{Quadratic Order} < \text{Exponential Order}
+& O(1) < O(\log n) < O(n) < O(n^2) < O(2^n) \newline
+& \text{Constant} < \text{Logarithmic} < \text{Linear} < \text{Quadratic} < \text{Exponential}
 \end{aligned}
 $$
 
diff --git a/en/docs/chapter_computational_complexity/time_complexity.md b/en/docs/chapter_computational_complexity/time_complexity.md
index 585ca057d..b2f5e64d6 100644
--- a/en/docs/chapter_computational_complexity/time_complexity.md
+++ b/en/docs/chapter_computational_complexity/time_complexity.md
@@ -955,8 +955,8 @@ Let's consider the input data size as $n$. The common types of time complexities
 
 $$
 \begin{aligned}
-O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!) \newline
-\text{Constant Order} < \text{Logarithmic Order} < \text{Linear Order} < \text{Linear-Logarithmic Order} < \text{Quadratic Order} < \text{Exponential Order} < \text{Factorial Order}
+& O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!) \newline
+& \text{Constant} < \text{Log} < \text{Linear} < \text{Linear-Log} < \text{Quadratic} < \text{Exp} < \text{Factorial}
 \end{aligned}
 $$
 
diff --git a/zh-hant/codes/ruby/chapter_sorting/quick_sort.rb b/zh-hant/codes/ruby/chapter_sorting/quick_sort.rb
index aeb031dbe..221a17715 100644
--- a/zh-hant/codes/ruby/chapter_sorting/quick_sort.rb
+++ b/zh-hant/codes/ruby/chapter_sorting/quick_sort.rb
@@ -9,7 +9,6 @@ class QuickSort
   class << self
     ### 哨兵劃分 ###
     def partition(nums, left, right)
-
       # 以 nums[left] 為基準數
       i, j = left, right
       while i < j
@@ -116,7 +115,7 @@ class QuickSortTailCall
       i # 返回基準數的索引
     end
 
-    ### 快速排序（尾遞迴最佳化）
+    ### 快速排序（尾遞迴最佳化）###
     def quick_sort(nums, left, right)
       # 子陣列長度不為 1 時遞迴
       while left < right