diff --git a/docs/chapter_appendix/index.md b/docs/chapter_appendix/index.md
index f9dc31458..d7f35ec58 100644
--- a/docs/chapter_appendix/index.md
+++ b/docs/chapter_appendix/index.md
@@ -5,12 +5,8 @@ icon: material/help-circle-outline
# 第 16 章 附录
-
-
![附录](../assets/covers/chapter_appendix.jpg){ class="cover-image" }
-
-
## 本章内容
- [16.1 编程环境安装](https://www.hello-algo.com/chapter_appendix/installation/)
diff --git a/docs/chapter_array_and_linkedlist/linked_list.md b/docs/chapter_array_and_linkedlist/linked_list.md
index 6145922d5..75079a6e3 100755
--- a/docs/chapter_array_and_linkedlist/linked_list.md
+++ b/docs/chapter_array_and_linkedlist/linked_list.md
@@ -184,8 +184,8 @@ comments: true
attr_accessor :val # 节点值
attr_accessor :next # 指向下一节点的引用
- def initialize(val=nil, next_node=nil)
- @val = val || 0
+ def initialize(val=0, next_node=nil)
+ @val = val
@next = next_node
end
end
@@ -1511,8 +1511,8 @@ comments: true
attr_accessor :next # 指向后继节点的引用
attr_accessor :prev # 指向前驱节点的引用
- def initialize(val=nil, next_node=nil, prev_node=nil)
- @val = val || 0
+ def initialize(val=0, next_node=nil, prev_node=nil)
+ @val = val
@next = next_node
@prev = prev_node
end
diff --git a/docs/chapter_array_and_linkedlist/list.md b/docs/chapter_array_and_linkedlist/list.md
index 7232800f4..1ec2ddb22 100755
--- a/docs/chapter_array_and_linkedlist/list.md
+++ b/docs/chapter_array_and_linkedlist/list.md
@@ -287,9 +287,9 @@ comments: true
```ruby title="list.rb"
# 访问元素
- num = nums[1]
+ num = nums[1] # 访问索引 1 处的元素
# 更新元素
- nums[1] = 0
+ nums[1] = 0 # 将索引 1 处的元素更新为 0
```
=== "Zig"
@@ -299,7 +299,7 @@ comments: true
var num = nums.items[1]; // 访问索引 1 处的元素
// 更新元素
- nums.items[1] = 0; // 将索引 1 处的元素更新为 0
+ nums.items[1] = 0; // 将索引 1 处的元素更新为 0
```
??? pythontutor "可视化运行"
@@ -551,10 +551,10 @@ comments: true
nums << 4
# 在中间插入元素
- nums.insert 3, 6
+ nums.insert 3, 6 # 在索引 3 处插入数字 6
# 删除元素
- nums.delete_at 3
+ nums.delete_at 3 # 删除索引 3 处的元素
```
=== "Zig"
@@ -718,7 +718,7 @@ comments: true
for (var i = 0; i < nums.length; i++) {
count += nums[i];
}
-
+
/* 直接遍历列表元素 */
count = 0;
for (var num in nums) {
@@ -972,7 +972,7 @@ comments: true
=== "JS"
```javascript title="list.js"
- /* 排序列表 */
+ /* 排序列表 */
nums.sort((a, b) => a - b); // 排序后,列表元素从小到大排列
```
@@ -1014,7 +1014,7 @@ comments: true
```ruby title="list.rb"
# 排序列表
- nums = nums.sort { |a, b| a <=> b }
+ nums = nums.sort { |a, b| a <=> b } # 排序后,列表元素从小到大排列
```
=== "Zig"
diff --git a/docs/chapter_backtracking/index.md b/docs/chapter_backtracking/index.md
index adc6878e9..43342b5d6 100644
--- a/docs/chapter_backtracking/index.md
+++ b/docs/chapter_backtracking/index.md
@@ -5,12 +5,8 @@ icon: material/map-marker-path
# 第 13 章 回溯
-
-
![回溯](../assets/covers/chapter_backtracking.jpg){ class="cover-image" }
-
-
!!! abstract
我们如同迷宫中的探索者,在前进的道路上可能会遇到困难。
diff --git a/docs/chapter_computational_complexity/index.md b/docs/chapter_computational_complexity/index.md
index 57f564211..4a0d7a5cd 100644
--- a/docs/chapter_computational_complexity/index.md
+++ b/docs/chapter_computational_complexity/index.md
@@ -5,12 +5,8 @@ icon: material/timer-sand
# 第 2 章 复杂度分析
-
-
![复杂度分析](../assets/covers/chapter_complexity_analysis.jpg){ class="cover-image" }
-
-
!!! abstract
复杂度分析犹如浩瀚的算法宇宙中的时空向导。
diff --git a/docs/chapter_computational_complexity/space_complexity.md b/docs/chapter_computational_complexity/space_complexity.md
index c91274919..a01ad4247 100755
--- a/docs/chapter_computational_complexity/space_complexity.md
+++ b/docs/chapter_computational_complexity/space_complexity.md
@@ -798,7 +798,7 @@ $$
图 2-16 常见的空间复杂度类型
-### 1. 常数阶 $O(1)$ {data-toc-label="常数阶"}
+### 1. 常数阶 $O(1)$ {data-toc-label="1. 常数阶"}
常数阶常见于数量与输入数据大小 $n$ 无关的常量、变量、对象。
@@ -1178,7 +1178,7 @@ $$
-### 2. 线性阶 $O(n)$ {data-toc-label="线性阶"}
+### 2. 线性阶 $O(n)$ {data-toc-label="2. 线性阶"}
线性阶常见于元素数量与 $n$ 成正比的数组、链表、栈、队列等:
@@ -1643,7 +1643,7 @@ $$
图 2-17 递归函数产生的线性阶空间复杂度
-### 3. 平方阶 $O(n^2)$ {data-toc-label="平方阶"}
+### 3. 平方阶 $O(n^2)$ {data-toc-label="3. 平方阶"}
平方阶常见于矩阵和图,元素数量与 $n$ 成平方关系:
@@ -2079,7 +2079,7 @@ $$
图 2-18 递归函数产生的平方阶空间复杂度
-### 4. 指数阶 $O(2^n)$ {data-toc-label="指数阶"}
+### 4. 指数阶 $O(2^n)$ {data-toc-label="4. 指数阶"}
指数阶常见于二叉树。观察图 2-19 ,层数为 $n$ 的“满二叉树”的节点数量为 $2^n - 1$ ,占用 $O(2^n)$ 空间:
@@ -2279,7 +2279,7 @@ $$
图 2-19 满二叉树产生的指数阶空间复杂度
-### 5. 对数阶 $O(\log n)$ {data-toc-label="对数阶"}
+### 5. 对数阶 $O(\log n)$ {data-toc-label="5. 对数阶"}
对数阶常见于分治算法。例如归并排序,输入长度为 $n$ 的数组,每轮递归将数组从中点处划分为两半,形成高度为 $\log n$ 的递归树,使用 $O(\log n)$ 栈帧空间。
diff --git a/docs/chapter_computational_complexity/time_complexity.md b/docs/chapter_computational_complexity/time_complexity.md
index c70aaec08..8053318bc 100755
--- a/docs/chapter_computational_complexity/time_complexity.md
+++ b/docs/chapter_computational_complexity/time_complexity.md
@@ -1047,7 +1047,7 @@ $$
图 2-9 常见的时间复杂度类型
-### 1. 常数阶 $O(1)$ {data-toc-label="常数阶"}
+### 1. 常数阶 $O(1)$ {data-toc-label="1. 常数阶"}
常数阶的操作数量与输入数据大小 $n$ 无关,即不随着 $n$ 的变化而变化。
@@ -1240,7 +1240,7 @@ $$
-### 2. 线性阶 $O(n)$ {data-toc-label="线性阶"}
+### 2. 线性阶 $O(n)$ {data-toc-label="2. 线性阶"}
线性阶的操作数量相对于输入数据大小 $n$ 以线性级别增长。线性阶通常出现在单层循环中:
@@ -1611,7 +1611,7 @@ $$
值得注意的是,**输入数据大小 $n$ 需根据输入数据的类型来具体确定**。比如在第一个示例中,变量 $n$ 为输入数据大小;在第二个示例中,数组长度 $n$ 为数据大小。
-### 3. 平方阶 $O(n^2)$ {data-toc-label="平方阶"}
+### 3. 平方阶 $O(n^2)$ {data-toc-label="3. 平方阶"}
平方阶的操作数量相对于输入数据大小 $n$ 以平方级别增长。平方阶通常出现在嵌套循环中,外层循环和内层循环的时间复杂度都为 $O(n)$ ,因此总体的时间复杂度为 $O(n^2)$ :
@@ -2146,7 +2146,7 @@ $$
-### 4. 指数阶 $O(2^n)$ {data-toc-label="指数阶"}
+### 4. 指数阶 $O(2^n)$ {data-toc-label="4. 指数阶"}
生物学的“细胞分裂”是指数阶增长的典型例子:初始状态为 $1$ 个细胞,分裂一轮后变为 $2$ 个,分裂两轮后变为 $4$ 个,以此类推,分裂 $n$ 轮后有 $2^n$ 个细胞。
@@ -2564,7 +2564,7 @@ $$
指数阶增长非常迅速,在穷举法(暴力搜索、回溯等)中比较常见。对于数据规模较大的问题,指数阶是不可接受的,通常需要使用动态规划或贪心算法等来解决。
-### 5. 对数阶 $O(\log n)$ {data-toc-label="对数阶"}
+### 5. 对数阶 $O(\log n)$ {data-toc-label="5. 对数阶"}
与指数阶相反,对数阶反映了“每轮缩减到一半”的情况。设输入数据大小为 $n$ ,由于每轮缩减到一半,因此循环次数是 $\log_2 n$ ,即 $2^n$ 的反函数。
@@ -2934,7 +2934,7 @@ $$
也就是说,底数 $m$ 可以在不影响复杂度的前提下转换。因此我们通常会省略底数 $m$ ,将对数阶直接记为 $O(\log n)$ 。
-### 6. 线性对数阶 $O(n \log n)$ {data-toc-label="线性对数阶"}
+### 6. 线性对数阶 $O(n \log n)$ {data-toc-label="6. 线性对数阶"}
线性对数阶常出现于嵌套循环中,两层循环的时间复杂度分别为 $O(\log n)$ 和 $O(n)$ 。相关代码如下:
@@ -3149,7 +3149,7 @@ $$
主流排序算法的时间复杂度通常为 $O(n \log n)$ ,例如快速排序、归并排序、堆排序等。
-### 7. 阶乘阶 $O(n!)$ {data-toc-label="阶乘阶"}
+### 7. 阶乘阶 $O(n!)$ {data-toc-label="7. 阶乘阶"}
阶乘阶对应数学上的“全排列”问题。给定 $n$ 个互不重复的元素,求其所有可能的排列方案,方案数量为:
diff --git a/docs/chapter_data_structure/index.md b/docs/chapter_data_structure/index.md
index 79382f37c..440dac468 100644
--- a/docs/chapter_data_structure/index.md
+++ b/docs/chapter_data_structure/index.md
@@ -5,12 +5,8 @@ icon: material/shape-outline
# 第 3 章 数据结构
-
-
![数据结构](../assets/covers/chapter_data_structure.jpg){ class="cover-image" }
-
-
!!! abstract
数据结构如同一副稳固而多样的框架。
diff --git a/docs/chapter_divide_and_conquer/index.md b/docs/chapter_divide_and_conquer/index.md
index 4afa1758e..6ee3a06c3 100644
--- a/docs/chapter_divide_and_conquer/index.md
+++ b/docs/chapter_divide_and_conquer/index.md
@@ -5,12 +5,8 @@ icon: material/set-split
# 第 12 章 分治
-
-
![分治](../assets/covers/chapter_divide_and_conquer.jpg){ class="cover-image" }
-
-
!!! abstract
难题被逐层拆解,每一次的拆解都使它变得更为简单。
diff --git a/docs/chapter_dynamic_programming/index.md b/docs/chapter_dynamic_programming/index.md
index 6bf09ad3c..5bed2aaba 100644
--- a/docs/chapter_dynamic_programming/index.md
+++ b/docs/chapter_dynamic_programming/index.md
@@ -5,12 +5,8 @@ icon: material/table-pivot
# 第 14 章 动态规划
-
-
![动态规划](../assets/covers/chapter_dynamic_programming.jpg){ class="cover-image" }
-
-
!!! abstract
小溪汇入河流,江河汇入大海。
diff --git a/docs/chapter_graph/index.md b/docs/chapter_graph/index.md
index 318d3b00c..f7343b740 100644
--- a/docs/chapter_graph/index.md
+++ b/docs/chapter_graph/index.md
@@ -5,12 +5,8 @@ icon: material/graphql
# 第 9 章 图
-
-
![图](../assets/covers/chapter_graph.jpg){ class="cover-image" }
-
-
!!! abstract
在生命旅途中,我们就像是一个个节点,被无数看不见的边相连。
diff --git a/docs/chapter_greedy/index.md b/docs/chapter_greedy/index.md
index aa81269c7..dd7148f3b 100644
--- a/docs/chapter_greedy/index.md
+++ b/docs/chapter_greedy/index.md
@@ -5,12 +5,8 @@ icon: material/head-heart-outline
# 第 15 章 贪心
-
-
![贪心](../assets/covers/chapter_greedy.jpg){ class="cover-image" }
-
-
!!! abstract
向日葵朝着太阳转动,时刻追求自身成长的最大可能。
diff --git a/docs/chapter_hashing/index.md b/docs/chapter_hashing/index.md
index c4c23b52a..43fc5a603 100644
--- a/docs/chapter_hashing/index.md
+++ b/docs/chapter_hashing/index.md
@@ -5,12 +5,8 @@ icon: material/table-search
# 第 6 章 哈希表
-
-
![哈希表](../assets/covers/chapter_hashing.jpg){ class="cover-image" }
-
-
!!! abstract
在计算机世界中,哈希表如同一位聪慧的图书管理员。
diff --git a/docs/chapter_heap/index.md b/docs/chapter_heap/index.md
index ff6625721..b88d3d8ea 100644
--- a/docs/chapter_heap/index.md
+++ b/docs/chapter_heap/index.md
@@ -5,12 +5,8 @@ icon: material/family-tree
# 第 8 章 堆
-
-
![堆](../assets/covers/chapter_heap.jpg){ class="cover-image" }
-
-
!!! abstract
堆就像是山岳峰峦,层叠起伏、形态各异。
diff --git a/docs/chapter_introduction/index.md b/docs/chapter_introduction/index.md
index 1aa715584..7574b3a6f 100644
--- a/docs/chapter_introduction/index.md
+++ b/docs/chapter_introduction/index.md
@@ -5,12 +5,8 @@ icon: material/calculator-variant-outline
# 第 1 章 初识算法
-
-
![初识算法](../assets/covers/chapter_introduction.jpg){ class="cover-image" }
-
-
!!! abstract
一位少女翩翩起舞,与数据交织在一起,裙摆上飘扬着算法的旋律。
diff --git a/docs/chapter_preface/index.md b/docs/chapter_preface/index.md
index cf1e30380..1edcd958c 100644
--- a/docs/chapter_preface/index.md
+++ b/docs/chapter_preface/index.md
@@ -5,12 +5,8 @@ icon: material/book-open-outline
# 第 0 章 前言
-
-
![前言](../assets/covers/chapter_preface.jpg){ class="cover-image" }
-
-
!!! abstract
算法犹如美妙的交响乐,每一行代码都像韵律般流淌。
diff --git a/docs/chapter_searching/index.md b/docs/chapter_searching/index.md
index b709e4dca..8d2fcb0f8 100644
--- a/docs/chapter_searching/index.md
+++ b/docs/chapter_searching/index.md
@@ -5,12 +5,8 @@ icon: material/text-search
# 第 10 章 搜索
-
-
![搜索](../assets/covers/chapter_searching.jpg){ class="cover-image" }
-
-
!!! abstract
搜索是一场未知的冒险,我们或许需要走遍神秘空间的每个角落,又或许可以快速锁定目标。
diff --git a/docs/chapter_sorting/index.md b/docs/chapter_sorting/index.md
index 97265cf2f..69a542a7c 100644
--- a/docs/chapter_sorting/index.md
+++ b/docs/chapter_sorting/index.md
@@ -5,12 +5,8 @@ icon: material/sort-ascending
# 第 11 章 排序
-
-
![排序](../assets/covers/chapter_sorting.jpg){ class="cover-image" }
-
-
!!! abstract
排序犹如一把将混乱变为秩序的魔法钥匙,使我们能以更高效的方式理解与处理数据。
diff --git a/docs/chapter_stack_and_queue/index.md b/docs/chapter_stack_and_queue/index.md
index 11ca906d2..05db5e5c4 100644
--- a/docs/chapter_stack_and_queue/index.md
+++ b/docs/chapter_stack_and_queue/index.md
@@ -5,12 +5,8 @@ icon: material/stack-overflow
# 第 5 章 栈与队列
-
-
![栈与队列](../assets/covers/chapter_stack_and_queue.jpg){ class="cover-image" }
-
-
!!! abstract
栈如同叠猫猫,而队列就像猫猫排队。
diff --git a/docs/chapter_tree/index.md b/docs/chapter_tree/index.md
index 0ef1ac0b6..3a6012819 100644
--- a/docs/chapter_tree/index.md
+++ b/docs/chapter_tree/index.md
@@ -5,12 +5,8 @@ icon: material/graph-outline
# 第 7 章 树
-
-
![树](../assets/covers/chapter_tree.jpg){ class="cover-image" }
-
-
!!! abstract
参天大树充满生命力,根深叶茂,分枝扶疏。
diff --git a/en/docs/chapter_computational_complexity/index.md b/en/docs/chapter_computational_complexity/index.md
index 2e4a3eb51..4889d18d9 100644
--- a/en/docs/chapter_computational_complexity/index.md
+++ b/en/docs/chapter_computational_complexity/index.md
@@ -5,12 +5,8 @@ icon: material/timer-sand
# Chapter 2. Complexity Analysis
-
-
![complexity_analysis](../assets/covers/chapter_complexity_analysis.jpg){ class="cover-image" }
-
-
!!! abstract
Complexity analysis is like a space-time navigator in the vast universe of algorithms.
diff --git a/en/docs/chapter_computational_complexity/space_complexity.md b/en/docs/chapter_computational_complexity/space_complexity.md
index cbfc66583..31349d845 100644
--- a/en/docs/chapter_computational_complexity/space_complexity.md
+++ b/en/docs/chapter_computational_complexity/space_complexity.md
@@ -744,7 +744,7 @@ $$
Figure 2-16 Common Types of Space Complexity
-### 1. Constant Order $O(1)$ {data-toc-label="Constant Order"}
+### 1. Constant Order $O(1)$ {data-toc-label="1. Constant Order"}
Constant order is common in constants, variables, objects that are independent of the size of input data $n$.
@@ -1124,7 +1124,7 @@ Note that memory occupied by initializing variables or calling functions in a lo
-### 2. Linear Order $O(n)$ {data-toc-label="Linear Order"}
+### 2. Linear Order $O(n)$ {data-toc-label="2. Linear Order"}
Linear order is common in arrays, linked lists, stacks, queues, etc., where the number of elements is proportional to $n$:
@@ -1589,7 +1589,7 @@ As shown below, this function's recursive depth is $n$, meaning there are $n$ in
Figure 2-17 Recursive Function Generating Linear Order Space Complexity
-### 3. Quadratic Order $O(n^2)$ {data-toc-label="Quadratic Order"}
+### 3. Quadratic Order $O(n^2)$ {data-toc-label="3. Quadratic Order"}
Quadratic order is common in matrices and graphs, where the number of elements is quadratic to $n$:
@@ -2025,7 +2025,7 @@ As shown below, the recursive depth of this function is $n$, and in each recursi
Figure 2-18 Recursive Function Generating Quadratic Order Space Complexity
-### 4. Exponential Order $O(2^n)$ {data-toc-label="Exponential Order"}
+### 4. Exponential Order $O(2^n)$ {data-toc-label="4. Exponential Order"}
Exponential order is common in binary trees. Observe the below image, a "full binary tree" with $n$ levels has $2^n - 1$ nodes, occupying $O(2^n)$ space:
@@ -2225,7 +2225,7 @@ Exponential order is common in binary trees. Observe the below image, a "full bi
Figure 2-19 Full Binary Tree Generating Exponential Order Space Complexity
-### 5. Logarithmic Order $O(\log n)$ {data-toc-label="Logarithmic Order"}
+### 5. Logarithmic Order $O(\log n)$ {data-toc-label="5. Logarithmic Order"}
Logarithmic order is common in divide-and-conquer algorithms. For example, in merge sort, an array of length $n$ is recursively divided in half each round, forming a recursion tree of height $\log n$, using $O(\log n)$ stack frame space.
diff --git a/en/docs/chapter_computational_complexity/time_complexity.md b/en/docs/chapter_computational_complexity/time_complexity.md
index c1163f5a1..934dff132 100644
--- a/en/docs/chapter_computational_complexity/time_complexity.md
+++ b/en/docs/chapter_computational_complexity/time_complexity.md
@@ -976,7 +976,7 @@ $$
Figure 2-9 Common Types of Time Complexity
-### 1. Constant Order $O(1)$ {data-toc-label="Constant Order"}
+### 1. Constant Order $O(1)$ {data-toc-label="1. Constant Order"}
Constant order means the number of operations is independent of the input data size $n$. In the following function, although the number of operations `size` might be large, the time complexity remains $O(1)$ as it's unrelated to $n$:
@@ -1167,7 +1167,7 @@ Constant order means the number of operations is independent of the input data s
-### 2. Linear Order $O(n)$ {data-toc-label="Linear Order"}
+### 2. Linear Order $O(n)$ {data-toc-label="2. Linear Order"}
Linear order indicates the number of operations grows linearly with the input data size $n$. Linear order commonly appears in single-loop structures:
@@ -1538,7 +1538,7 @@ Operations like array traversal and linked list traversal have a time complexity
It's important to note that **the input data size $n$ should be determined based on the type of input data**. For example, in the first example, $n$ represents the input data size, while in the second example, the length of the array $n$ is the data size.
-### 3. Quadratic Order $O(n^2)$ {data-toc-label="Quadratic Order"}
+### 3. Quadratic Order $O(n^2)$ {data-toc-label="3. Quadratic Order"}
Quadratic order means the number of operations grows quadratically with the input data size $n$. Quadratic order typically appears in nested loops, where both the outer and inner loops have a time complexity of $O(n)$, resulting in an overall complexity of $O(n^2)$:
@@ -2073,7 +2073,7 @@ For instance, in bubble sort, the outer loop runs $n - 1$ times, and the inner l
-### 4. Exponential Order $O(2^n)$ {data-toc-label="Exponential Order"}
+### 4. Exponential Order $O(2^n)$ {data-toc-label="4. Exponential Order"}
Biological "cell division" is a classic example of exponential order growth: starting with one cell, it becomes two after one division, four after two divisions, and so on, resulting in $2^n$ cells after $n$ divisions.
@@ -2491,7 +2491,7 @@ In practice, exponential order often appears in recursive functions. For example
Exponential order growth is extremely rapid and is commonly seen in exhaustive search methods (brute force, backtracking, etc.). For large-scale problems, exponential order is unacceptable, often requiring dynamic programming or greedy algorithms as solutions.
-### 5. Logarithmic Order $O(\log n)$ {data-toc-label="Logarithmic Order"}
+### 5. Logarithmic Order $O(\log n)$ {data-toc-label="5. Logarithmic Order"}
In contrast to exponential order, logarithmic order reflects situations where "the size is halved each round." Given an input data size $n$, since the size is halved each round, the number of iterations is $\log_2 n$, the inverse function of $2^n$.
@@ -2861,7 +2861,7 @@ Logarithmic order is typical in algorithms based on the divide-and-conquer strat
This means the base $m$ can be changed without affecting the complexity. Therefore, we often omit the base $m$ and simply denote logarithmic order as $O(\log n)$.
-### 6. Linear-Logarithmic Order $O(n \log n)$ {data-toc-label="Linear-Logarithmic Order"}
+### 6. Linear-Logarithmic Order $O(n \log n)$ {data-toc-label="6. Linear-Logarithmic Order"}
Linear-logarithmic order often appears in nested loops, with the complexities of the two loops being $O(\log n)$ and $O(n)$ respectively. The related code is as follows:
@@ -3076,7 +3076,7 @@ The image below demonstrates how linear-logarithmic order is generated. Each lev
Mainstream sorting algorithms typically have a time complexity of $O(n \log n)$, such as quicksort, mergesort, and heapsort.
-### 7. Factorial Order $O(n!)$ {data-toc-label="Factorial Order"}
+### 7. Factorial Order $O(n!)$ {data-toc-label="7. Factorial Order"}
Factorial order corresponds to the mathematical problem of "full permutation." Given $n$ distinct elements, the total number of possible permutations is:
diff --git a/en/docs/chapter_data_structure/index.md b/en/docs/chapter_data_structure/index.md
index 4507bc447..94c454dd6 100644
--- a/en/docs/chapter_data_structure/index.md
+++ b/en/docs/chapter_data_structure/index.md
@@ -5,12 +5,8 @@ icon: material/shape-outline
# Chapter 3. Data Structures
-
-
![Data Structures](../assets/covers/chapter_data_structure.jpg){ class="cover-image" }
-
-
!!! abstract
Data structures serve as a robust and diverse framework.
diff --git a/en/docs/chapter_hashing/index.md b/en/docs/chapter_hashing/index.md
index 324a36a3a..78c1284c5 100644
--- a/en/docs/chapter_hashing/index.md
+++ b/en/docs/chapter_hashing/index.md
@@ -5,12 +5,8 @@ icon: material/table-search
# Chapter 6. Hash Table
-
-
![Hash Table](../assets/covers/chapter_hashing.jpg){ class="cover-image" }
-
-
!!! abstract
In the world of computing, a hash table is akin to an intelligent librarian.
diff --git a/en/docs/chapter_introduction/index.md b/en/docs/chapter_introduction/index.md
index 77c7e10d3..553205b82 100644
--- a/en/docs/chapter_introduction/index.md
+++ b/en/docs/chapter_introduction/index.md
@@ -5,12 +5,8 @@ icon: material/calculator-variant-outline
# Chapter 1. Introduction to Algorithms
-
-
![A first look at the algorithm](../assets/covers/chapter_introduction.jpg){ class="cover-image" }
-
-
!!! abstract
A graceful maiden dances, intertwined with the data, her skirt swaying to the melody of algorithms.
diff --git a/en/docs/chapter_preface/index.md b/en/docs/chapter_preface/index.md
index e727ac714..34a61d829 100644
--- a/en/docs/chapter_preface/index.md
+++ b/en/docs/chapter_preface/index.md
@@ -5,12 +5,8 @@ icon: material/book-open-outline
# Chapter 0. Preface
-
-
![Preface](../assets/covers/chapter_preface.jpg){ class="cover-image" }
-
-
!!! abstract
Algorithms are like a beautiful symphony, with each line of code flowing like a rhythm.
diff --git a/en/docs/chapter_stack_and_queue/index.md b/en/docs/chapter_stack_and_queue/index.md
index 9668fdaa2..34cb5130f 100644
--- a/en/docs/chapter_stack_and_queue/index.md
+++ b/en/docs/chapter_stack_and_queue/index.md
@@ -5,12 +5,8 @@ icon: material/stack-overflow
# Chapter 5. Stack and Queue
-
-
![Stack and Queue](../assets/covers/chapter_stack_and_queue.jpg){ class="cover-image" }
-
-
!!! abstract
A stack is like cats placed on top of each other, while a queue is like cats lined up one by one.