Standard DP problem, the kind that shows up enough that you really should just know it.
Start by clarifying the problem statement and constraints, then define the subproblem and recurrence relation. Implement the DP solution with optimal time and space complexity, and test with edge cases.
Pro tip: At Amazon, always discuss trade-offs between different DP approaches (e.g., top-down vs bottom-up) and consider space optimization. Also, relate the problem to real-world scenarios if possible.
Ask clarifying questions to ensure you understand the problem, input/output, and constraints. Identify if it's a classic DP problem (e.g., knapsack, LCS, etc.).
Break the problem into smaller subproblems and define the state (e.g., dp[i] represents the optimal solution up to index i).
Derive the recurrence relation that relates the current state to previous states. Consider all possible choices at each step.
Write the code using either top-down (memoization) or bottom-up (tabulation) approach. Optimize space if possible (e.g., using rolling arrays).
Test with provided examples, edge cases (empty input, large input), and analyze time/space complexity.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.