Stax, 27 25 23 18 bytes

«╥╦.ê§┘h!@ÆEÿ☺╜╫♥B

Run and debug it

Output is separated by newlines. This is a completely different algorithm that what I had before. I think there's still some golfing potential. I'll try to improve and annotate it later.

Stax, 27 25 23 18 bytes

«╥╦.ê§┘h!@ÆEÿ☺╜╫♥B

Run and debug it

Output is separated by newlines.

This program operates on adjacent pairs in the array, and determines whether there should be a split between them using this procedure.

Consider some arbitrary input [... w x y z ...]. Here is how to determine if there should be a split between x and y.

• If x == y, then yes.
• If x > y, then iff z >= x.
• If y > x, then iff w >= y.

The summing is left as an exercise.

Stax, 27 25 23 19 bytes

æ`9fDÇ←¡ñV°▀╖╛AK♂â▐

Run and debug it

Output is separated by newlines. This is a completely different algorithm that what I had before. I think there's still some golfing potential. I'll try to improve and annotate it later.

Stax, 27 25 23 18 bytes

«╥╦.ê§┘h!@ÆEÿ☺╜╫♥B

Run and debug it

Output is separated by newlines. This is a completely different algorithm that what I had before. I think there's still some golfing potential. I'll try to improve and annotate it later.

Stax, 27 25 23 bytes

âr╩iÄ╟Ö4⌡&3x░pσôâ↑▒☻i1☼

Run and debug it

Output is separated by newlines. This is a completely different algorithm that what I had before. I think there's still some golfing potential. I'll try to improve and annotate it later.

Stax, 27 25 23 19 bytes

æ`9fDÇ←¡ñV°▀╖╛AK♂â▐

Run and debug it

Output is separated by newlines. This is a completely different algorithm that what I had before. I think there's still some golfing potential. I'll try to improve and annotate it later.