docs: Update dsa-anal: time

Author: virtualguard101

.gitignore

@@ -2,8 +2,8 @@
 /site/
 /env/
 __pycache__/
-uv.lock
 .roo/
 docs/projects/log/
 docs/projects/assets/log/
 docs/draft/
+/en/

docs/credits.md

@@ -32,6 +32,7 @@ hide:
 [![bash](https://www.vectorlogo.zone/logos/gnu_bash/gnu_bash-ar21.svg)](https://www.gnu.org/software/bash/?utm_source=vectorlogozone&utm_medium=referrer){target="_blank"}
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+[![GeeksforGeeks](https://media.geeksforgeeks.org/gfg-gg-logo.svg)](https://www.geeksforgeeks.org/?utm_source=vectorlogozone&utm_medium=referrer){target="_blank"}
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docs/notes/dsa/anal/time.md

@@ -98,4 +98,53 @@ $$
 \end{aligned}
 $$
 
-### 常数阶
+### 常数阶 $O(1)$
+
+常数阶的操作数与输入数据量无关，即不随输入数据大小的变化而增大，始终为一个常数。
+
+如普通的赋值语句：
+```py
+def assign(n: int) -> int:
+    res = n # 常数阶
+    return res
+```
+
+!!! warning
+    需要注意的是，常数阶的定义是**操作数量与输入数据大小无关**，因此即便一个程序的输入数据大小很大（必须是一个常量），如下面的例子：
+    ```py
+    def sum_to_const(n: int) -> int:
+        """Sum from 0 with step n, size times."""
+        count = 0
+        size = 10000
+        for _ in range(size):
+            count += n
+        return count
+    ```
+    这是一个求和函数，用于将输入数据`n`相加`size`次。
+    
+    虽然我们在编写程序时可以将`size`设置得很大，但在程序运行时，无论输入数据的大小如何，求和的操作次数永远只执行`size`次，即**不随输入数据大小的变化而增大**，因此上面示例的时间复杂度只是一个**常数阶**。
+
+### 线性阶 $O(n)$
+
+线性阶的操作数与输入数据大小 $n$ 呈**线性相关**，常以单层循环的形式出现：
+
+```py
+def for_linear(n: int) -> int:
+    sum = 0 
+    for _ in range(n):
+        count += 1
+    return sum
+```
+
+线性阶算法常出现在[**线性表**](https://www.geeksforgeeks.org/dsa/introduction-to-linear-data-structures/)的遍历中；在这中情景下，输入数据一般为待遍历线性表的长度（或大小）:
+```py
+def throughout_arr(nums: list[int]) -> int:
+    count = 0
+    for num in nums:
+        count += num
+    return count
+```
+
+### 平方阶 $O(n^2)$
+
+平方阶的操作数可以看作是输入数据大小 $n$ 的一个二次函数，通常出现在**嵌套循环**中。

docs/notes/index.md

@@ -75,7 +75,7 @@ comments: true
 
 <!-- recent_notes_start -->
 <ul>
-<li><div style="display:flex; justify-content:space-between; align-items:center;"><a href="dsa/anal/time/">算法时间复杂度</a><span style="font-size:0.8em;">2025-08-16</span></div></li>
+<li><div style="display:flex; justify-content:space-between; align-items:center;"><a href="dsa/anal/time/">算法时间复杂度</a><span style="font-size:0.8em;">2025-08-20</span></div></li>
 <li><div style="display:flex; justify-content:space-between; align-items:center;"><a href="dsa/anal/iter_and_recu/">迭代与递归</a><span style="font-size:0.8em;">2025-08-15</span></div></li>
 <li><div style="display:flex; justify-content:space-between; align-items:center;"><a href="tools/git/">Git</a><span style="font-size:0.8em;">2025-08-13</span></div></li>
 <li><div style="display:flex; justify-content:space-between; align-items:center;"><a href="tools/linux/tmux/">tmux</a><span style="font-size:0.8em;">2025-08-13</span></div></li>

mkdocs.yml

@@ -203,6 +203,13 @@ validation:
 
 ## Additional configuration
 extra:
+  alternate:
+    # - name: 简体中文
+    #   link: /
+    #   lang: zh
+    # - name: English
+    #   link: /en/
+    #   lang: en
   status:
     new: Recently added
     deprecated: Deprecated
@@ -212,6 +219,8 @@ extra:
   social:
     - icon: fontawesome/brands/github
       link: https://github.com/virtualguard101
+    - icon: fontawesome/brands/x-twitter
+      link: https://x.com/virtualguardi01
 
 ## Page tree
 nav:

scripts/hooks/links.py

@@ -36,7 +36,7 @@ class LinkData:
     #     link_icon='material/notebook',
     # ),
     LinkData(
-        name='Blog with Hexo',
+        name='Blog with Anime',
         url='https://blog.virtualguard101.com',
         description='',  # 添加描述
         button_icon='fontawesome/solid/blog',