Clarifying Some Questions About Dynamic Programming

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.