Started with the DP approach where dp[i] is the LIS ending at index i, which is fine, but they immediately asked if I could do better.
Start by clarifying the problem and constraints, then present the O(n^2) dynamic programming solution as a baseline, followed by the optimal O(n log n) patience sorting approach. Explain the trade-offs between time and space complexity, and discuss edge cases and potential optimizations.
Pro tip: Demonstrate strong communication by walking through a small example step-by-step, and mention that the O(n log n) solution is based on patience sorting, which shows depth of knowledge beyond rote memorization.
Ask clarifying questions about input size, whether the subsequence needs to be contiguous, and if there are any constraints on time/space complexity.
Explain the O(n^2) dynamic programming solution where dp[i] stores the length of the longest increasing subsequence ending at index i, and how to compute it.
Describe the O(n log n) patience sorting algorithm using binary search on tails array, and why it works.
Compare the two approaches in terms of time and space complexity, and discuss when each might be preferable.
Mention edge cases like empty array, all decreasing, all equal, and walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.