No test case are passing
Optimal Game strategy 1
hi @Legendankit , your code fails for the cases like
4
8 15 3 7
where the answer should be 22 but your code produces 15.
why it is failing , in this question both players are playing optimally (Playing optimally means that both players will have insight into all possible next moves and will play in such a way to maximize their chance of winning without making a mistake.) so nimit will choose the coin that will result in less value left for piyush and you are not covering all the cases .
let me share you my approach :-
we would need an optimal solution for this. At each instance we would need to consider two possibilities that we can pick the first as well as the last element of the remaining array. Both these possibilities give rise to two more possibilities depending on the other player. Since the second player plays optimally and try to minimise our score. So overall we have two possibilities at each instance.
For the first possibility , where we could pick the first element , the other player will pick the next element from the side that would minimise our total score.
Similarly , for the second possibility , where we can pick the last element , the other player would still pick the next element from the side that would minimise our total score.
We entertain both these cases and take the maximum result of the two and return that result.
We take two pointer variables , say āiā and ājā which each represent the starting and the ending point of the remaining array currently in consideration. We work till the two pointers cross each other
In case of any doubt feel free to ask 
If you got the answer then mark your doubt as resolved
Still all the test cases are not passing
have you checked above code i have shared , you need to use dp to optimize this further as n is large and cant be solved by recursion alone i will leave this for you to do it