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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_dynamic_programming/knapsack_problem.md
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# 0-1 knapsack problem
# 0-1 Knapsack Problem
The knapsack problem is an excellent introductory problem for dynamic programming and is one of the most common problem forms in dynamic programming. It has many variants, such as the 0-1 knapsack problem, the unbounded knapsack problem, and the multiple knapsack problem.
@@ -47,7 +47,7 @@ The current state $[i, c]$ is transferred from the state above $[i-1, c]$ and th
Based on the above analysis, we will next implement the brute force search, memoization, and dynamic programming solutions in order.
### Method 1: Brute force search
### Method 1: Brute Force Search
The search code includes the following elements.
@@ -80,7 +80,7 @@ The figure below shows the search branches pruned in memoization.
![Memoization recursion tree for 0-1 knapsack problem](knapsack_problem.assets/knapsack_dfs_mem.png)
### Method 3: Dynamic programming
### Method 3: Dynamic Programming
Dynamic programming is essentially the process of filling the $dp$ table during state transitions. The code is as follows:
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=== "<14>"
![knapsack_dp_step14](knapsack_problem.assets/knapsack_dp_step14.png)
### Space optimization
### Space Optimization
Since each state is only related to the state in the row above it, we can use two arrays rolling forward to reduce the space complexity from $O(n^2)$ to $O(n)$.