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Translate all code to English (#1836)

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* Review the EN heading format.

* Fix pythontutor headings.

* Fix pythontutor headings.

* bug fixes

* Fix headings in **/summary.md

* Revisit the CN-to-EN translation for Python code using Claude-4.5

* Revisit the CN-to-EN translation for Java code using Claude-4.5

* Revisit the CN-to-EN translation for Cpp code using Claude-4.5.

* Fix the dictionary.

* Fix cpp code translation for the multipart strings.

* Translate Go code to English.

* Update workflows to test EN code.

* Add EN translation for C.

* Add EN translation for CSharp.

* Add EN translation for Swift.

* Trigger the CI check.

* Revert.

* Update en/hash_map.md

* Add the EN version of Dart code.

* Add the EN version of Kotlin code.

* Add missing code files.

* Add the EN version of JavaScript code.

* Add the EN version of TypeScript code.

* Fix the workflows.

* Add the EN version of Ruby code.

* Add the EN version of Rust code.

* Update the CI check for the English version  code.

* Update Python CI check.

* Fix cmakelists for en/C code.

* Fix Ruby comments
This commit is contained in:
Yudong Jin
2025-12-31 07:44:52 +08:00
committed by GitHub
parent 45e1295241
commit 2778a6f9c7
1284 changed files with 71557 additions and 3275 deletions
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en/docs/chapter_tree/binary_tree_traversal.md
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# Binary tree traversal
# Binary Tree Traversal
From a physical structure perspective, 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.
The common traversal methods for binary trees include level-order traversal, pre-order traversal, in-order traversal, and post-order traversal.
## Level-order traversal
## Level-Order Traversal
As shown in the figure below, <u>level-order traversal</u> traverses the binary tree from top to bottom, layer by layer. Within each level, it visits nodes from left to right.
@@ -12,7 +12,7 @@ Level-order traversal is essentially <u>breadth-first traversal</u>, also known
![Level-order traversal of a binary tree](binary_tree_traversal.assets/binary_tree_bfs.png)
### Code implementation
### Code Implementation
Breadth-first traversal is typically 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:
@@ -20,12 +20,12 @@ Breadth-first traversal is typically implemented with the help of a "queue". The
[file]{binary_tree_bfs}-[class]{}-[func]{level_order}
```
### Complexity analysis
### 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 bottom level, the queue contains at most $(n + 1) / 2$ nodes simultaneously, occupying $O(n)$ space.
## Preorder, inorder, and postorder traversal
## Preorder, Inorder, and Postorder Traversal
Correspondingly, preorder, inorder, and postorder traversals all belong to <u>depth-first traversal</u>, also known as <u>depth-first search (DFS)</u>, which embodies a "first go to the end, then backtrack and continue" traversal method.
@@ -33,7 +33,7 @@ The figure below shows how depth-first traversal works on a binary tree. **Depth
![Preorder, inorder, and postorder traversal of a binary tree](binary_tree_traversal.assets/binary_tree_dfs.png)
### Code implementation
### Code Implementation
Depth-first search is usually implemented based on recursion:
@@ -83,7 +83,7 @@ The figure below shows the recursive process of preorder traversal of a binary t
=== "<11>"
![preorder_step11](binary_tree_traversal.assets/preorder_step11.png)
### Complexity analysis
### 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 degenerates into a linked list, the recursion depth reaches $n$, and the system occupies $O(n)$ stack frame space.