Here is a better approach Link

Define function F(id) — "longest non-decreasing subsequence that ends at position id".

Recurrence formula : $$$ F(id) = max(F(id) , F(k) + 1) , 0 <= k < id,value[id] >= value[k]$$$

$$$Answer = max(F(i)), 0 <= i < n$$$ — where n is the number of elements.

IDEA: Find the longest non-decreasing subsequence ending at each position. Now the longest subsequence ends at some position i, so all we need is to find the position such that length of non-decreasing subsequence ending at that position is maximum.

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