I knew this problem but still fumbled the opening.
Start by clarifying the problem and constraints, then present both the O(n^2) dynamic programming solution and the O(n log n) patience sorting approach. Emphasize the trade-offs and choose the optimal solution for large-scale data, which is common in ML engineering roles.
Pro tip: Mention that the O(n log n) approach uses binary search on a tails array and is essentially the same as the patience sorting algorithm. Also, relate it to real-world ML scenarios like feature engineering or sequence modeling to show practical insight.
Confirm that the subsequence must be strictly increasing and that elements need not be contiguous. Ask about input size and constraints to determine the expected time complexity.
Explain the O(n^2) dynamic programming solution where dp[i] stores the length of the longest increasing subsequence ending at index i. This shows foundational understanding.
Describe the O(n log n) patience sorting method: maintain a tails array where tails[i] is the smallest tail of all increasing subsequences of length i+1. For each number, use binary search to find its position and update tails.
State time and space complexity for both approaches. Discuss edge cases like empty array, all decreasing, or all equal elements.
Connect the problem to ML applications, such as finding monotonic trends in time-series data or optimizing sequence alignment in NLP tasks.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.