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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_backtracking/n_queens_problem.md
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# n-queens problem
# N-Queens Problem
!!! question
@@ -12,7 +12,7 @@ The figure below illustrates the three constraints of this problem: **multiple q
![Constraints of the n-queens problem](n_queens_problem.assets/n_queens_constraints.png)
### Row-by-row placement strategy
### Row-By-Row Placement Strategy
Since both the number of queens and the number of rows on the chessboard are $n$, we can easily derive a conclusion: **each row of the chessboard allows and only allows exactly one queen to be placed**.
@@ -24,7 +24,7 @@ The figure below shows the row-by-row placement process for the 4-queens problem
Essentially, **the row-by-row placement strategy serves a pruning function**, as it avoids all search branches where multiple queens appear in the same row.
### Column and diagonal pruning
### Column and Diagonal Pruning
To satisfy the column constraint, we can use a boolean array `cols` of length $n$ to record whether each column has a queen. Before each placement decision, we use `cols` to prune columns that already have queens, and dynamically update the state of `cols` during backtracking.
@@ -40,7 +40,7 @@ Similarly, **for all squares on an anti-diagonal, the sum $row + col$ is a const
![Handling column and diagonal constraints](n_queens_problem.assets/n_queens_cols_diagonals.png)
### Code implementation
### Code Implementation
Please note that in an $n$-dimensional square matrix, the range of $row - col$ is $[-n + 1, n - 1]$, and the range of $row + col$ is $[0, 2n - 2]$. Therefore, the number of both main diagonals and anti-diagonals is $2n - 1$, meaning the length of both arrays `diags1` and `diags2` is $2n - 1$.