Russian Doll Envelopes

1. Clarify Constraints: Immediately ask about input size limits (e.g., N up to 10^5) to determine if an O(N^2) or O(N log N) solution is required. Microsoft values precision in complexity analysis. 2. Sort Strategically: Explain your sorting logic clearly. Sort primarily by width ascending, but crucially, sort secondary by height descending for equal widths. This prevents nesting envelopes with identical widths, which is impossible. 3. Reduce to LIS: State that after sorting, the problem strictly becomes finding the Longest Increasing Subsequence of the height array. Justify why the width constraint is now implicitly satisfied. 4. Optimize Implementation: Detail the binary search approach for LIS using a dynamic array to achieve O(N log N) time complexity. Avoid the naive O(N^2) DP unless constraints are small. 5. Validate Edge Cases: Discuss handling empty inputs, single envelopes, and the specific behavior when widths are equal due to the reverse height sort.