xinyin025/hello-algo
1
0
Fork 0
mirror of https://github.com/krahets/hello-algo.git synced 2026-06-28 00:24:21 +00:00
Code Issues Packages Projects Releases Wiki Activity

Translate all code to English (#1836)

Browse Source 
* 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
Download Patch File Download Diff File Expand all files Collapse all files
en/docs/chapter_dynamic_programming/intro_to_dynamic_programming.md
+4 -4
View File
@@ -1,4 +1,4 @@
# Introduction to dynamic programming
# Introduction to Dynamic Programming
<u>Dynamic programming</u> is an important algorithmic paradigm that decomposes a problem into a series of smaller subproblems and avoids redundant computation by storing the solutions to subproblems, thereby significantly improving time efficiency.
@@ -18,7 +18,7 @@ The goal of this problem is to find the number of ways, **we can consider using
[file]{climbing_stairs_backtrack}-[class]{}-[func]{climbing_stairs_backtrack}
```
## Method 1: Brute force search
## Method 1: Brute Force Search
Backtracking algorithms typically do not explicitly decompose problems, but rather treat solving the problem as a series of decision steps, searching for all possible solutions through trial and pruning.
@@ -73,7 +73,7 @@ Observe the figure below, **after memoization, all overlapping subproblems only
![Recursion tree with memoization](intro_to_dynamic_programming.assets/climbing_stairs_dfs_memo_tree.png)
## Method 3: Dynamic programming
## Method 3: Dynamic Programming
**Memoization is a "top-down" method**: we start from the original problem (root node), recursively decompose larger subproblems into smaller ones, until reaching the smallest known subproblems (leaf nodes). Afterward, by backtracking, we collect the solutions to the subproblems layer by layer to construct the solution to the original problem.
@@ -97,7 +97,7 @@ Based on the above content, we can summarize the commonly used terminology in dy
- The states corresponding to the smallest subproblems (the $1$st and $2$nd steps) are called <u>initial states</u>.
- The recurrence formula $dp[i] = dp[i-1] + dp[i-2]$ is called the <u>state transition equation</u>.
## Space optimization
## Space Optimization
Observant readers may have noticed that **since $dp[i]$ is only related to $dp[i-1]$ and $dp[i-2]$, we do not need to use an array `dp` to store the solutions to all subproblems**, but can simply use two variables to roll forward. The code is as follows: