When the Problem setter doesn't want to type a lot...

when I read the question, I was like:

WHAT THE CUT!!

Understanding the assignment is often the hard part

So the task is about finding the ideal pivot element at each step?

Sounds fun. Calculate lengths of sticks once all cuts are made. Recursively merge adjacent segments that give the shortest segment length when merged. Reverse merge order for result.

@Fast-Nop still trying to identify what's the task...lol

if you have cuts at length 3, 7 and 8, stick length 10:

if cuts done 7,3,8, costs 10+7+3,
if cut done 3,7,8 cost is 10+7+3
Cuts done 3,8,7 cost is 10+7+5
Cuts done 8,7,3 cost is 10+8+7
Cuts done 8,3,7 cost is 10+8+4
Other permutations aren't interesting