Mastering Dynamic Programming: Recognizing the Patterns

Dynamic Programming (DP) strikes fear into the hearts of many interview candidates. However, once you learn to recognize the underlying patterns, it becomes much more manageable.

How to Identify a DP Problem

• It asks for the maximum/minimum of something (optimization).
• It asks for the total number of ways to do something (combinatorics).
• Future decisions depend on earlier decisions (overlapping subproblems).

The 5-Step DP Framework

1. Define the objective function: What does f(i) represent?
2. Identify the base cases: What are the simplest inputs?
3. Write the recurrence relation: How does f(i) relate to f(i-1), f(i-2), etc.?
4. Determine the execution order: Bottom-up or top-down?
5. Analyze Time/Space Complexity: Can you optimize space? (e.g., keeping only the last two variables instead of a full array).