Dynamic Programming Interview Questions & Solutions

Dynamic programming is the pattern candidates fear most, and the one FAANG interviewers lean on hardest to separate strong problem-solvers from the rest. At its core it's simple: when a problem breaks into overlapping subproblems, you solve each subproblem once and reuse the answer instead of recomputing it. The hard part is seeing that structure in the first place — recognizing that "minimum coins," "longest subsequence," and "number of ways" are all asking you to define a state and a recurrence.

The solutions below walk through that recognition step by step: how to define the DP state, write the transition, choose between top-down memoization and bottom-up tabulation, and reason about time and space. You'll see the classic 1-D problems (climbing stairs, house robber), the 2-D grid and string problems (edit distance, longest common subsequence), and the knapsack family that so many interview questions are secretly variations of. Work through them in order and the recurrences stop feeling like magic and start feeling like a checklist.