Help: Minimize merge operations

Revision en1, by Noam527, 2017-10-10 18:22:47

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.

Examples:

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.


#### History

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en1 Noam527 2017-10-10 18:22:47 994 Initial revision (published)