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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
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en/docs/chapter_graph/graph_traversal.md
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# Graph traversal
# Graph Traversal
Trees represent "one-to-many" relationships, while graphs have a higher degree of freedom and can represent any "many-to-many" relationships. Therefore, we can view trees as a special case of graphs. Clearly, **tree traversal operations are also a special case of graph traversal operations**.
Both graphs and trees require the application of search algorithms to implement traversal operations. Graph traversal methods can also be divided into two types: <u>breadth-first traversal</u> and <u>depth-first traversal</u>.
## Breadth-first search
## Breadth-First Search
**Breadth-first search is a near-to-far traversal method that, starting from a certain node, always prioritizes visiting the nearest vertices and expands outward layer by layer**. As shown in the figure below, starting from the top-left vertex, first traverse all adjacent vertices of that vertex, then traverse all adjacent vertices of the next vertex, and so on, until all vertices have been visited.
![Breadth-first search of a graph](graph_traversal.assets/graph_bfs.png)
### Algorithm implementation
### Algorithm Implementation
BFS is typically implemented with the help of a queue, as shown in the code below. The queue has a "first in, first out" property, which aligns with the BFS idea of "near to far".
@@ -67,19 +67,19 @@ The code is relatively abstract; it is recommended to refer to the figure below
Not unique. Breadth-first search only requires traversing in a "near to far" order, **and the traversal order of vertices at the same distance can be arbitrarily shuffled**. Taking the figure above as an example, the visit order of vertices $1$ and $3$ can be swapped, as can the visit order of vertices $2$, $4$, and $6$.
### Complexity analysis
### Complexity Analysis
**Time complexity**: All vertices will be enqueued and dequeued once, using $O(|V|)$ time; in the process of traversing adjacent vertices, since it is an undirected graph, all edges will be visited $2$ times, using $O(2|E|)$ time; overall using $O(|V| + |E|)$ time.
**Space complexity**: The list `res`, hash set `visited`, and queue `que` can contain at most $|V|$ vertices, using $O(|V|)$ space.
## Depth-first search
## Depth-First Search
**Depth-first search is a traversal method that prioritizes going as far as possible, then backtracks when no path remains**. As shown in the figure below, starting from the top-left vertex, visit an adjacent vertex of the current vertex, continuing until reaching a dead end, then return and continue going as far as possible before returning again, and so on, until all vertices have been traversed.
![Depth-first search of a graph](graph_traversal.assets/graph_dfs.png)
### Algorithm implementation
### Algorithm Implementation
This "go as far as possible then return" algorithm paradigm is typically implemented using recursion. Similar to breadth-first search, in depth-first search we also need a hash set `visited` to record visited vertices and avoid revisiting.
@@ -133,7 +133,7 @@ To deepen understanding, it is recommended to combine the figure below with the
Taking tree traversal as an example, "root $\rightarrow$ left $\rightarrow$ right", "left $\rightarrow$ root $\rightarrow$ right", and "left $\rightarrow$ right $\rightarrow$ root" correspond to pre-order, in-order, and post-order traversals, respectively. They represent three different traversal priorities, yet all three belong to depth-first search.
### Complexity analysis
### Complexity Analysis
**Time complexity**: All vertices will be visited $1$ time, using $O(|V|)$ time; all edges will be visited $2$ times, using $O(2|E|)$ time; overall using $O(|V| + |E|)$ time.