Classic DP problem but the O(n log n) patience sorting approach is where people trip up.
Start by clarifying the problem: define increasing (strict vs non-strict) and what to return (length or actual subsequence). Then present both the O(n^2) dynamic programming solution and the O(n log n) patience sorting approach, explaining the trade-offs and when each is appropriate.
Pro tip: Meta interviewers value clean, bug-free code and the ability to explain your thought process. Practice implementing the O(n log n) solution with binary search until you can write it without errors, and be ready to discuss how to reconstruct the actual subsequence if asked.
Ask whether the subsequence must be strictly increasing, whether to return the length or the subsequence itself, and confirm input constraints (e.g., array size, possible values).
Explain the O(n^2) dynamic programming solution where dp[i] stores the length of the LIS ending at index i, and how to compute it by checking all previous smaller elements.
Describe the patience sorting method using a tails array and binary search to maintain the smallest tail of increasing subsequences of various lengths, achieving O(n log n) time.
Write clean, well-commented code for the O(n log n) approach, handling edge cases like empty arrays and ensuring correct binary search implementation.
State time and space complexity, and walk through test cases including duplicates, negative numbers, and already sorted arrays to verify correctness.
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