I came up (I think, I just didn't see it anywhere) with this problem earlier today and I think it's better if I ask for help here as I still don't know its solution:
You have an array of N integers and in each step you can merge any 2 of them into a single integer (and then this integer is added to the array while the previous 2 are erased from it). The cost of merging two elements X and Y is max(X, Y).
You need to find the minimal cost you can get after merging all the integers into 1 (essentially, doing N — 1 merges).
Currently there's no constraint (not on N, nor on the limit of the integers) so just try to come up with the best complexity you can.
input: 3 4 6 8 output: 16
(merging 4 and 6 to 10 with the cost of 6, and then merging 8 and 10 with the cost of 10, giving a total of 16).
input: 4 10 11 13 16 output: 55 (10->16) + (11->13) + (24->26) = 16 + 13 + 26 = 55.