Dynamic Programming Interview Prep: A Practical Approach That Actually Sticks

Dynamic programming (DP) has a reputation as the hardest topic in coding interviews. Many candidates memorize solutions to famous problems, then freeze the moment a question is phrased slightly differently. The fix is not more memorization; it is a repeatable process for recognizing DP problems and building solutions step by step. How to recognize a DP problem Look for three signals. The question asks for a count, a minimum, a maximum, or whether something is possible. The input has a natural order, such as a string, an array, or a grid. And a brute-force solution would try many overlapping combinations, recomputing the same smaller answers again and again. Classic examples include climbing stairs, coin change, longest common subsequence, house robber, edit distance, and unique paths in a grid. The five-step process 1. Define the state in plain English. For example, "dp[i] is the minimum number of coins needed to make amount i." If you cannot say it in one sentence, the state is not clear yet. 2. Write the recurrence. How does the answer for i depend on smaller answers? For coin change: dp[i] = 1 + min(dp[i - c]) over every coin c that fits. 3. Set base cases. dp[0] = 0, and anything unreachable is infinity. 4. Choose the order of evaluation. Bottom-up means filling the table from small to large; top-down means recursion with memoization. Both are fine in interviews. Top-down is often easier to derive, bottom-up is easier to optimize. 5. Optimize space if asked. Many one-dimensional problems only need the last one or two values, and many grid problems only need the previous row. Start with recursion, then add memory If the recurrence is not obvious, write the brute-force recursive solution first and say so: "This is exponential because we recompute the same subproblems, so let me cache results by index." Adding a dictionary or array cache turns exponential time into polynomial time. Interviewers like seeing this progression because it shows you understand why DP works rather than reciting a final table. Talk through a small example Before coding, fill in the first few table entries by hand for a tiny input. This catches off-by-one errors and wrong base cases early, and it gives the interviewer confidence that your recurrence is right. Common patterns worth knowing Linear sequences (house robber, maximum subarray). Knapsack-style choices (coin change, partition equal subset sum). Two-string comparisons (longest common subsequence, edit distance). Grid paths (unique paths, minimum path sum). Interval problems (burst balloons, palindrome partitioning). Once you have solved two or three from each family, new problems start to look like variations. A study plan that works Spend two weeks on DP with about one hour a day. In week one, solve two problems per pattern, writing the state definition and recurrence in a comment before any code. In week two, revisit the same problems without notes, then try new ones under a 30-minute timer while explaining aloud. Keep a short notebook of state definitions; reviewing them is more useful than rereading full solutions. In the interview itself State the brute force, name the overlapping subproblems, define the state, give the recurrence, then code. Mention time and space complexity at the end. If nerves make it hard to keep the steps in order, some candidates use Linkjob AI (https://linkjob.ai), which gives real-time help during job interviews and technical interviews, as a safety net, but the five-step process is what turns DP from guesswork into a routine.