Adjacent Merge Cost (APCS 2024-01 Expert)

2.0s 256M

There are \(n\) integers in a row. Merge two adjacent values \(u,v\) into \(u+v\) at cost \(|u-v|\), preserving the remaining order. Find the minimum cost to leave a single value.

Input Format

Read \(n\), then the \(n\) integers.

Output Format

Print the minimum total cost.

Constraints

\(1\le n\le100\); each value lies in \([-1000,1000]\).

Scoring

  • 30 points: \(n\le13\).
  • 70 points: No additional restrictions.

Each scored test is worth 5 points.

Sample Input 1

4
3 -1 2 5

Sample Output 1

5

Sample Input 2

6
-5 3 0 -4 3 -2

Sample Output 2

18

Sample Input 3

7
-1 -6 6 -8 7 0 -9

Sample Output 3

36

Source

APCS 2024-01 public archive version: m934。

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