最优子结构原理和 dp 数组遍历方向

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Prerequisites

Before reading this article, you should learn:

• Dynamic Programming Core Framework

Tip

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This article is a revised version of the old article Dynamic Programming Q&A. Based on my continuous learning and summarization, as well as feedback from readers, I have expanded the content to make this article a comprehensive Q&A follow-up to Dynamic Programming Core Framework. Here is the main content.

This article will clarify the following questions for you:

1. What exactly is "optimal substructure" and how is it related to dynamic programming.

2. How to determine if a problem is a dynamic programming problem, i.e., how to identify if there are overlapping subproblems.

3. Why is the size of the dp array often set to n + 1 instead of n.

4. Why are there various ways to traverse the dp array in dynamic programming, such as forward, backward, and diagonal traversal.

1. Understanding Optimal Substructure

2. How to Quickly Identify Overlapping Subproblems

III. Setting the Size of the dp Array

IV. Traversal Direction of the `dp` Array

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