translation: Add the initial translation for the tree chapter (#1208)

* Add the initial translation for the tree chapter

* Add intial translation of array_representation_of_tree.md

* Fix the code link of avl_tree

en/docs/chapter_tree/binary_tree_traversal.md

@@ -0,0 +1,89 @@
+# Binary tree traversal
+
+From the perspective of physical structure, a tree is a data structure based on linked lists, hence its traversal method involves accessing nodes one by one through pointers. However, a tree is a non-linear data structure, which makes traversing a tree more complex than traversing a linked list, requiring the assistance of search algorithms to achieve.
+
+Common traversal methods for binary trees include level-order traversal, preorder traversal, inorder traversal, and postorder traversal, among others.
+
+## Level-order traversal
+
+As shown in the figure below, "level-order traversal" traverses the binary tree from top to bottom, layer by layer, and accesses nodes in each layer in a left-to-right order.
+
+Level-order traversal essentially belongs to "breadth-first traversal", also known as "breadth-first search (BFS)", which embodies a "circumferentially outward expanding" layer-by-layer traversal method.
+
+![Level-order traversal of a binary tree](binary_tree_traversal.assets/binary_tree_bfs.png)
+
+### Code implementation
+
+Breadth-first traversal is usually implemented with the help of a "queue". The queue follows the "first in, first out" rule, while breadth-first traversal follows the "layer-by-layer progression" rule, the underlying ideas of the two are consistent. The implementation code is as follows:
+
+```src
+[file]{binary_tree_bfs}-[class]{}-[func]{level_order}
+```
+
+### Complexity analysis
+
+- **Time complexity is $O(n)$**: All nodes are visited once, using $O(n)$ time, where $n$ is the number of nodes.
+- **Space complexity is $O(n)$**: In the worst case, i.e., a full binary tree, before traversing to the lowest level, the queue can contain at most $(n + 1) / 2$ nodes at the same time, occupying $O(n)$ space.
+
+## Preorder, inorder, and postorder traversal
+
+Correspondingly, preorder, inorder, and postorder traversal all belong to "depth-first traversal", also known as "depth-first search (DFS)", which embodies a "proceed to the end first, then backtrack and continue" traversal method.
+
+The figure below shows the working principle of performing a depth-first traversal on a binary tree. **Depth-first traversal is like walking around the perimeter of the entire binary tree**, encountering three positions at each node, corresponding to preorder traversal, inorder traversal, and postorder traversal.
+
+![Preorder, inorder, and postorder traversal of a binary search tree](binary_tree_traversal.assets/binary_tree_dfs.png)
+
+### Code implementation
+
+Depth-first search is usually implemented based on recursion:
+
+```src
+[file]{binary_tree_dfs}-[class]{}-[func]{post_order}
+```
+
+!!! tip
+
+    Depth-first search can also be implemented based on iteration, interested readers can study this on their own.
+
+The figure below shows the recursive process of preorder traversal of a binary tree, which can be divided into two opposite parts: "recursion" and "return".
+
+1. "Recursion" means starting a new method, the program accesses the next node in this process.
+2. "Return" means the function returns, indicating the current node has been fully accessed.
+
+=== "<1>"
+    ![The recursive process of preorder traversal](binary_tree_traversal.assets/preorder_step1.png)
+
+=== "<2>"
+    ![preorder_step2](binary_tree_traversal.assets/preorder_step2.png)
+
+=== "<3>"
+    ![preorder_step3](binary_tree_traversal.assets/preorder_step3.png)
+
+=== "<4>"
+    ![preorder_step4](binary_tree_traversal.assets/preorder_step4.png)
+
+=== "<5>"
+    ![preorder_step5](binary_tree_traversal.assets/preorder_step5.png)
+
+=== "<6>"
+    ![preorder_step6](binary_tree_traversal.assets/preorder_step6.png)
+
+=== "<7>"
+    ![preorder_step7](binary_tree_traversal.assets/preorder_step7.png)
+
+=== "<8>"
+    ![preorder_step8](binary_tree_traversal.assets/preorder_step8.png)
+
+=== "<9>"
+    ![preorder_step9](binary_tree_traversal.assets/preorder_step9.png)
+
+=== "<10>"
+    ![preorder_step10](binary_tree_traversal.assets/preorder_step10.png)
+
+=== "<11>"
+    ![preorder_step11](binary_tree_traversal.assets/preorder_step11.png)
+
+### Complexity analysis
+
+- **Time complexity is $O(n)$**: All nodes are visited once, using $O(n)$ time.
+- **Space complexity is $O(n)$**: In the worst case, i.e., the tree degrades into a linked list, the recursion depth reaches $n$, the system occupies $O(n)$ stack frame space.