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Revisit the English version (#1885)

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Yudong Jin
2026-04-10 23:03:03 +08:00
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en/docs/chapter_greedy/summary.md
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- In the coin change problem, for certain coin combinations, greedy algorithms can guarantee finding the optimal solution; for other coin combinations, however, greedy algorithms may find very poor solutions.
- Problems suitable for solving with greedy algorithms have two major properties: greedy choice property and optimal substructure. The greedy choice property represents the effectiveness of the greedy strategy.
- For some complex problems, proving the greedy choice property is not simple. Relatively speaking, disproving it is easier, such as in the coin change problem.
- Solving greedy problems mainly consists of three steps: problem analysis, determining the greedy strategy, and correctness proof. Among these, determining the greedy strategy is the core step, and correctness proof is often the difficult point.
- The fractional knapsack problem, based on the 0-1 knapsack problem, allows selecting a portion of items, and therefore can be solved using greedy algorithms. The correctness of the greedy strategy can be proven using proof by contradiction.
- The max capacity problem can be solved using exhaustive enumeration with time complexity $O(n^2)$. By designing a greedy strategy to move the short partition inward in each round, the time complexity can be optimized to $O(n)$.
- Solving greedy problems mainly consists of three steps: problem analysis, determining the greedy strategy, and correctness proof. Among these, determining the greedy strategy is the core step, and correctness proof is often the main difficulty.
- The fractional knapsack problem, based on the 0-1 knapsack problem, allows selecting fractions of items, and therefore can be solved using greedy algorithms. The correctness of the greedy strategy can be proven using proof by contradiction.
- The max capacity problem can be solved using exhaustive enumeration with time complexity $O(n^2)$. By designing a greedy strategy to move the shorter side inward in each round, the time complexity can be optimized to $O(n)$.
- In the max product cutting problem, we successively derive two greedy strategies: integers $\geq 4$ should all continue to be split, and the optimal splitting factor is $3$. The code includes exponentiation operations, and the time complexity depends on the implementation method of exponentiation, typically being $O(1)$ or $O(\log n)$.