Dynamic Programming (DP) is one of the most difficult topics in competitive programming. At first this topic scared me, but with time I realized that the main thing is the right approach. In this post, I will share my experience and the strategy that helped me master DP.

1. Understanding the basic idea

Dynamic Programming is based on two key principles:

Optimal structure of subtasks: A large problem is solved by solving its subtasks. Rewriting results: To avoid repeated computations, we save the results of subtasks. Simple explanation: instead of “going over” the same thing every time, we remember what we have already computed and use it.

2. Start with simple problems

The biggest mistake beginners make is trying to solve complex DP problems without understanding the basics. Start with the basics:

Fibonacci Numbers — learn how to read a value through an array. Knapsack Problem — understand optimization of subtasks. Solve problems with the “DP” category in the Codeforces filter, starting at the 800-1200 level.

3. Draw your solutions

I always use tables and graphs when solving problems. For example, if a task requires route optimization, I visualize it:

Draw a graph with nodes. Fill the array with values. This makes it easier to see repeating patterns.

4. Learning classic patterns

Most DP tasks can be categorized into several types. Here are some of them:

One-dimensional DP: Counting ways (e.g. staircase problem). Two-dimensional DP: Tableau problems (e.g., finding the maximum path). Subsets: Optimizing combinations (e.g., backpack problems). For each pattern, I recommend studying a few popular tasks and trying to modify them.

5. Practice, practice, and more practice.

Once I understood the basic concepts, I made it a rule to tackle 2-3 DP tasks per week. Important: don't be afraid to get stuck! Even if it takes a few hours, each task solved makes you stronger.

6. Don't forget about competitions

The best way to test your knowledge is to participate in competitions. If a DP task seems difficult, be sure to solve it after the contest.

Conclusion Dynamic programming is not magic, it's just an algorithmic approach that requires time and effort. Start simple, practice, and in an instant you will notice how your fear of DP turns into confidence.

What strategies have helped you master DP? Share your tips in the comments!