Maximum Sum from Coins in a line

In this game, which we will call the coins-in-a-line game, an even num­ber, n, of coins, of var­i­ous denom­i­na­tions from var­i­ous coun­tries, are placed in a line. Two play­ers, who we will call Alice and Bob, take turns remov­ing one of the coins from either end of the remain­ing line of coins. That is, when it is a player’s turn, he or she removes the coin at the left or right end of the line of coins and adds that coin to his or her col­lec­tion. The player who removes a set of coins with larger total value than the other player wins, where we assume that both Alice and Bob know the value of each coin.

http://algorithms.tutorialhorizon.com/dynamic-programming-coin-in-a-line-game-problem/

http://www.geeksforgeeks.org/dynamic-programming-set-31-optimal-strategy-for-a-game/