Dynamic Programming Patterns for Coding Interviews

Dynamic programming is widely considered the most challenging topic in coding interviews. Many candidates struggle with DP problems not because the concept is inherently difficult, but because they lack a systematic approach to recognizing and solving DP patterns. This guide breaks down the most common patterns and provides a framework for tackling any DP problem you encounter.

The fundamental idea behind dynamic programming is simple: if a problem can be broken down into overlapping subproblems with optimal substructure, we can solve each subproblem once, store the result, and reuse it. Overlapping subproblems means the same subproblem appears multiple times in the recursive solution. Optimal substructure means the optimal solution to the problem contains optimal solutions to its subproblems. When both conditions are met, DP can transform an exponential-time recursive solution into a polynomial-time solution.

The first step in solving any DP problem is defining the state. What information do you need to uniquely identify a subproblem? For the classic Fibonacci sequence, the state is simply the index n. For the knapsack problem, the state is (index, remaining_capacity). For the longest common subsequence, the state is (index_in_string_A, index_in_string_B). Getting the state definition right is crucial — too few dimensions and you cannot capture all necessary information; too many and the solution becomes unnecessarily complex.