Compute longest increasing subsequence

Q: Compute longest increasing subsequence

This question evaluates understanding of sequence algorithms, dynamic programming concepts, and algorithmic optimization for the longest increasing subsequence problem, including subsequence reconstruction and complexity analysis.

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Question

Given an integer array nums, compute the length of a longest strictly increasing subsequence and also output one valid subsequence. Aim for an O(n log n) approach; explain the binary-search (patience sorting) technique, how to reconstruct the subsequence, and analyze time/space complexity. Follow-ups: adapt to non-decreasing subsequences, handle duplicates carefully, and discuss how to count how many LIS exist.

Compute longest increasing subsequence

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