Erased all Chinese content.

Author: a1fredbao

documents/alfred/data_structure/binary-trie.md

@@ -7,8 +7,6 @@ documentation_of: ./src/alfred/data_structure/binary-trie.hpp
 
 This file implements a Binary Trie (01-Trie) data structure for efficiently storing and querying binary representations of integers. It supports insertion, minimum/maximum XOR queries, and range queries with upper bounds.
 
-本文件实现了支持下标和区间信息维护的 01-Trie（BinaryTrie），可用于集合异或最值、区间下标查询等。
-
 ## Usage Example
 
 ```cpp
@@ -25,10 +23,6 @@ uint64_t max_xor = trie.query_max(3);
 - Query for values with XOR less than an upper bound
 - Maintains min/max index for range queries
 
-- 支持插入、异或最小/最大值查询
-- 支持下标区间信息维护
-- 支持 upper_bound 异或查询
-
 ## Important Functions and Time Complexity
 
 | Function    | Description                   | Time Complexity |
@@ -38,18 +32,8 @@ uint64_t max_xor = trie.query_max(3);
 | `query_max` | Maximize XOR with given value | $O(B)$          |
 | `query_ub`  | Query for XOR < upper bound   | $O(B)$          |
 
-| Function    | Description        | Time Complexity |
-| ----------- | ------------------ | --------------- |
-| `insert`    | 插入一个数         | $O(\log V)$     |
-| `query_min` | 查询异或最小值     | $O(\log V)$     |
-| `query_max` | 查询异或最大值     | $O(\log V)$     |
-| `query_ub`  | 异或小于上界的区间 | $O(\log V)$     |
-
 Where $B$ is the number of bits (default 30).
 
 ## Notes
 - Useful for problems involving XOR queries and binary representations.
 - Supports index tracking for advanced queries.
-
-- 适用于集合异或、区间最值等问题。
-- 支持维护插入元素的下标信息。

documents/alfred/data_structure/discretization.md

@@ -5,19 +5,10 @@ documentation_of: ./src/alfred/data_structure/discretization.hpp
 
 ## Description
 
-本文件实现了通用离散化工具类 `Mess`，用于将任意可比较类型的值映射到连续整数区间，便于后续高效处理。
-
 This file provides the Mess class, a utility for discretizing values in a vector, mapping them to a compact index range. It supports insertion, initialization, querying, and checking existence of values.
 
 ## Usage Example
 
-```cpp
-#include "discretization.hpp"
-std::vector<int> a = {100, 200, 100};
-Mess<int> mess(a);
-int idx = mess.query(200); // 查询 200 离散化后的编号
-```
-
 ```cpp
 #include "discretization.hpp"
 std::vector<int> a = {5, 2, 7};
@@ -26,25 +17,18 @@ int idx = mess.query(5); // Get discrete index of 5
 ```
 
 ## Main Features
-- 支持批量插入、自动去重排序
-- 支持原值与离散编号互查
-- 支持判断元素是否存在
-
-Discretizes values to compact indices
-Supports batch insertion and initialization
-Query for discrete index and check existence
+- Discretizes values to compact indices
+- Supports batch insertion and initialization
+- Query for discrete index and check existence
 
 ## Important Functions and Time Complexity
 
-| Function | Description        | Time Complexity |
-| -------- | ------------------ | --------------- |
-| `insert` | 插入元素           | $O(1)$          |
-| `init`   | 初始化（排序去重） | $O(n \log n)$   |
-| `query`  | 查询离散编号       | $O(\log n)$     |
-| `exist`  | 判断元素是否存在   | $O(\log n)$     |
+| Function | Description                       | Time Complexity |
+| -------- | --------------------------------- | --------------- |
+| `insert` | Insert value                      | $O(1)$          |
+| `init`   | Initialize and sort unique values | $O(n \log n)$   |
+| `query`  | Get discrete index                | $O(\log n)$     |
+| `exist`  | Check if value exists             | $O(\log n)$     |
 
 ## Notes
-- 适用于需要离散化处理的场景。
-- 支持任意可比较类型。
-
-Useful for coordinate compression and mapping values to indices.
+- Useful for coordinate compression and mapping values to indices.

documents/alfred/data_structure/dsu/cancel-dsu.md

@@ -5,8 +5,6 @@ documentation_of: ./src/alfred/data_structure/dsu/cancel-dsu.hpp
 
 ## Description
 
-本文件实现了支持撤销操作的并查集（Cancelable DSU），可用于可回溯的合并查找问题。
-
 This file implements a cancelable Disjoint Set Union (DSU) data structure, also known as a union-find with rollback. It supports merging sets, checking connectivity, and undoing previous merge operations efficiently.
 
 ## Usage Example
@@ -15,14 +13,10 @@ This file implements a cancelable Disjoint Set Union (DSU) data structure, also
 #include "cancel-dsu.hpp"
 CancelDSU dsu(5);
 dsu.merge(1, 2);
-dsu.cancel(); // 撤销上一次合并
 dsu.cancel(); // Undo last merge
 ```
 
 ## Main Features
-- 支持撤销合并操作
-- 支持集合大小查询
-- 适合可回溯并查集场景
 - Supports union, find, and size queries
 - Allows rollback (cancel) of previous merge operations
 - Maintains history using a stack
@@ -31,11 +25,10 @@ dsu.cancel(); // Undo last merge
 
 | Function | Description                         | Time Complexity |
 | -------- | ----------------------------------- | --------------- |
-| `merge`  | 合并集合                            | $O(\alpha(n))$  |
-| `cancel` | 撤销合并                            | $O(1)$          |
-| `find`   | 查找根节点                          | $O(\alpha(n))$  |
+| `merge`  | Merge two sets                      | $O(\alpha(n))$  |
+| `cancel` | Undo previous merge(s)              | $O(1)$          |
+| `find`   | Find representative                 | $O(\alpha(n))$  |
 | `same`   | Check if two elements are connected | $O(\alpha(n))$  |
 
 ## Notes
-- 适用于需要撤销操作的并查集问题。
 - Useful for offline dynamic connectivity and backtracking problems.