Given an array of integers, find the longest non-decreasing subsequences (the subsequence does not need to be consecutive). For example, A = [8,5,2,10,3,6,9,7] contains the longest subsequences [2,3,6,9] and [2,3,6,7]. (1) Formulate the recursive relation of the optimal solution (do not miss the base case); (2) Design a bottom-up (iterative) algorithm to calculate the length of the longest non-decreasing subsequences (pseudo code); (3) Analyze the complexity of your algorithm

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A: analysis for the above example is in step 2.

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