Start by clarifying the problem and identifying the decision space, constraints, and base cases. Then outline a recursive backtracking solution with pruning, analyze its time/space complexity, and discuss potential optimizations or iterative alternatives.
Pro tip: Demonstrate maturity by discussing trade-offs: when backtracking is appropriate versus dynamic programming or greedy approaches, and how to handle large inputs with pruning and memoization.
Ask questions to understand input/output, constraints, and edge cases. Confirm whether the solution needs to find all solutions, one solution, or an optimal one.
Identify the state parameters, base cases, and the choices at each step. Explain how the recursion explores the decision tree.
Write pseudocode or actual code, ensuring to undo choices (backtrack) and incorporate pruning to cut off invalid or non-promising branches early.
Discuss time and space complexity, and suggest optimizations like memoization, sorting, or iterative deepening if applicable.
Walk through a small example to verify correctness, and consider edge cases like empty input or large constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.