Clarifying Some Questions About Dynamic Programming

This article is a revised version of the previous article Dynamic Programming Q&A. Based on my continued learning and feedback from readers, I have expanded it with more content. I aim to make this a comprehensive Q&A article following the Core Patterns of Dynamic Programming. The main content is below.

This article will answer 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, that is, how to identify overlapping subproblems.

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

4. Why are there so many ways to traverse the dp array in dynamic programming: sometimes forward, sometimes backward, and sometimes diagonally?

1. Understanding Optimal Substructure

2. How to Identify Overlapping Subproblems at a Glance

III. Setting the Size of the dp Array

4. Traversal Direction of the dp Array