Problem 1: Fence Repair [Richard Ho, 2006]

Farmer John wants to repair a small length of the fence around the

pasture. He measures the fence and finds that he needs N (1 <= N

<= 20,000) planks of wood, each having some integer length Li (1

<= Li <= 50,000) units. He then purchases a single long board just

long enough to saw into the N planks (i.e., whose length is the sum

of the lengths Li). FJ is ignoring the "kerf", the extra length

lost to sawdust when a sawcut is made; you should ignore it, too.

FJ sadly realizes that he doesn't own a saw with which to cut the

wood, so he mosies over to Farmer Don's Farm with this long board

and politely asks if he may borrow a saw.

Farmer Don, a closet capitalist, doesn't lend FJ a saw but instead

offers to charge Farmer John for each of the N-1 cuts in the plank.

The charge to cut a piece of wood is exactly equal to its length.

Cutting a plank of length 21 costs 21 cents.

Farmer Don then lets Farmer John decide the order and locations to

cut the plank. Help Farmer John determine the minimum amount of

money he can spend to create the N planks. FJ knows that he can cut

the board in various different orders which will result in different

charges since the resulting intermediate planks are of different

lengths.

PROBLEM NAME: plank

INPUT FORMAT:

* Line 1: One integer N, the number of planks

* Lines 2..N+1: Each line contains a single integer describing the

        length of a needed plank

OUTPUT FORMAT:

* Line 1: One integer: the minimum amount of money he must spend to  make N-1 cuts

მაგალითები

შესატანი მონაცემები
3
8
5
8
                  დაკოპირება

გამოსატანი მონაცემები
34
                  დაკოპირება

შენიშვნა

He wants to cut a board of length 21 into pieces of lengths 8, 5, and 8.

The original board measures 8+5+8=21. The first cut will cost 21, and

should be used to cut the board into pieces measuring 13 and 8. The

second cut will cost 13, and should be used to cut the 13 into 8

and 5. This would cost 21+13=34. If the 21 was cut into 16 and 5

instead, the second cut would cost 16 for a total of 37 (which is

more than 34).