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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
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Yudong Jin
2025-12-31 07:44:52 +08:00
committed by GitHub
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commit 2778a6f9c7
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en/docs/chapter_greedy/greedy_algorithm.md
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# Greedy algorithm
# Greedy Algorithm
<u>Greedy algorithm</u> is a common algorithm for solving optimization problems. Its basic idea is to make the seemingly best choice at each decision stage of the problem, that is, to greedily make locally optimal decisions in hopes of obtaining a globally optimal solution. Greedy algorithms are simple and efficient, and are widely applied in many practical problems.
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You might exclaim: So clean! The greedy algorithm solves the coin change problem in about ten lines of code.
## Advantages and limitations of greedy algorithms
## Advantages and Limitations of Greedy Algorithms
**Greedy algorithms are not only straightforward and simple to implement, but are also usually very efficient**. In the code above, if the smallest coin denomination is $\min(coins)$, the greedy choice loops at most $amt / \min(coins)$ times, giving a time complexity of $O(amt / \min(coins))$. This is an order of magnitude smaller than the time complexity of the dynamic programming solution $O(n \times amt)$.
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1. **Can guarantee finding the optimal solution**: In this situation, greedy algorithms are often the best choice, because they tend to be more efficient than backtracking and dynamic programming.
2. **Can find an approximate optimal solution**: Greedy algorithms are also applicable in this situation. For many complex problems, finding the global optimal solution is very difficult, and being able to find a suboptimal solution with high efficiency is also very good.
## Characteristics of greedy algorithms
## Characteristics of Greedy Algorithms
So the question arises: what kind of problems are suitable for solving with greedy algorithms? Or in other words, under what conditions can greedy algorithms guarantee finding the optimal solution?
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Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.
## Steps for solving problems with greedy algorithms
## Steps for Solving Problems with Greedy Algorithms
The problem-solving process for greedy problems can generally be divided into the following three steps.
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However, correctness proofs may also not be easy. If we have no clue, we usually choose to debug the code based on test cases, step by step modifying and verifying the greedy strategy.
## Typical problems solved by greedy algorithms
## Typical Problems Solved by Greedy Algorithms
Greedy algorithms are often applied to optimization problems that satisfy greedy choice property and optimal substructure. Below are some typical greedy algorithm problems.