Optimal game strategy problem

#1

is my logic correct??

#2

You are close but your conditions for selecting are not right. This is how you need to do it.

ll optimalGame(ll i,ll j){
   if(i > j){
       return 0;
   }

   // Consider both the possibilities. You can pick either the first or the last coin.
   // Since the opponent plays optimally , we would get the minimum of the remaining coins for each choice.
   ll pickFirst = coins[i] + min( optimalGame(i+2,j) , optimalGame(i+1,j-1) ) ;
   ll pickLast = coins[j] + min( optimalGame(i,j-2) , optimalGame(i+1,j-1) ) ;

   // Pick the max of two as your final result
   ll ans = max(pickFirst,pickLast);

   return ans;
}


int main() {
   int n;
   cin >> n;   

   for(int i=0;i<n;i++){
       cin >> coins[i];
   }

   cout << optimalGame(0,n-1);

   return 0;
}