Problem Link - http://www.iarcs.org.in/inoi/2011/zco2011/zco2011-1b.php

The task is to find the maximum score you can get in the game. Such problems, based on games, where you have to simulate, predict the result, or obtain the maximum possible score always seem to puzzle me.

I can do it with recursion by considering two cases - first number picked or last number picked, each of which again branches into two states similarly, and so on... which finally can yield the max possible result.

But it's a very time-inefficient approach, since time increases exponentially, due to the large test cases.

What is the most pragmatic approach to the problem, and to such problems in general?