Given an integer array nums, return the length of the longest strictly increasing subsequence.
A subsequence is a sequence that can be derived from the array by deleting some or no elements without changing the order of the remaining elements.
Input:
[10,9,2,5,3,7,101,18]
Output: 4
Input:
[0,1,0,3,2,3]
Output: 4
Output should be a single integer representing the length of the longest increasing subsequence.
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Discuss dynamic programming (O(n²)) vs binary search optimization (O(n log n)).