Problem S4: Combining Riceballs

Problem DescriptionCopy Anchor Link

Alphonse has $N$ rice balls of various sizes in a row. He wants to form the largest rice ball possible for his friend to eat. Alphonse can perform the following operations:

• If two adjacent rice balls have the same size, Alphonse can combine them to make a new rice ball. The new rice ball’s size is the sum of the two old rice balls’ sizes. It occupies the position in the row previously occupied by the two old rice balls.

• If two rice balls have the same size, and there is exactly one rice ball between them, Alphonse can combine all three rice balls to make a new rice ball. (The middle rice ball does not need to have the same size as the other two.) The new rice ball’s size is the sum of the three old rice balls’ sizes. It occupies the position in the row previously occupied by the three old rice balls.

Alphonse can perform each operation as many times as he wants.

Determine the size of the largest rice ball in the row after performing 0 or more operations.

Input SpecificationCopy Anchor Link

The first line will contain the integer, $N$ $(1 \leq N \leq 400)$.

The next line will contain $N$ space separated integers representing the sizes of the riceballs, in order from left to right. Each integer is at least $1$ and at most $1\ 000\ 000$.

• For 1 of the 15 available marks, $N = 4$.

• For an additional 2 of the 15 available marks, $N \leq 10$.

• For an additional 5 of the 15 available marks, $N \leq 50$.

Output SpecificationCopy Anchor Link

Output the size of the largest riceball Alphonse can form.

Sample Input 1Copy Anchor Link

7
47 12 12 3 9 9 3

Output for Sample InputCopy Anchor Link

48

Explanation for Output for Sample Input 1Copy Anchor Link

One possible set of moves to create a riceball of size 48 is to combine 12 and 12, forming a riceball of size 24. Then, combine 9 and 9 to form a riceball of size 18. Then, combine 3, 18 and 3 to form a riceball of size 24. Finally, combine the two riceballs of size 24 to form a riceball of size 48.

Sample Input 2Copy Anchor Link

4
1 2 3 1

Output for Sample Input 2Copy Anchor Link

3

Explanation for Output for Sample Input 2Copy Anchor Link

There are no moves to make, thus the largest riceball in the row is size 3.