3073. Maximum Increasing Triplet Value

For each element, define right[i] as the value of the greatest element with an index greater than i.

Start iterating from the beginning, define a set containing the elements seen so far.

When you are at index i, use binary search on the set to find the greatest element on the left of index i that is smaller than nums[i] and name it greatest_left.

Also check that nums[i] < right[i].

If the above conditions hold, then ans = max(ans, greatest_left - nums[i] + right[i]).