I have faced this problem in my unofficial national team selection test and i have been trying to solve it for days to no avail... Hope someone could help me :(

Given an integer array of length n (n <= 100000). Alberto and Brendaly play a game on it. On each turn the player picks a number from one of the 2 ends of the sequence. Alberto goes first. Both players wants to maximize their total score by the end of the game. If they both play optimally, whats the total score Alberto gets? all elements in array are not larger than 1e9.

Thank you!