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Coins in a Line

Problem Description

There are A coins (Assume A is even) in a line.

Two players take turns to take a coin from one of the ends of the line until there are no more coins left.

The player with the larger amount of money wins, Assume that you go first.

Return the maximum amount of money you can win.

NOTE:

  • You can assume that opponent is clever and plays optimally.


  • Problem Constraints

    1 <= length(A) <= 500

    1 <= A[i] <= 105



    Input Format

    The first and the only argument of input contains an integer array A.



    Output Format

    Return an integer representing the maximum amount of money you can win.



    Example Input

    Input 1:

     A = [1, 2, 3, 4]
    

    Input 2:

     A = [5, 4, 8, 10]
    


    Example Output

    Output 1:

     6
    

    Output 2:

     15
    


    Example Explanation

    Explanation 1:

     You      : Pick 4
     Opponent : Pick 3
     You      : Pick 2
     Opponent : Pick 1

    Total money with you : 4 + 2 = 6

    Explanation 2:

     You      : Pick 10
     Opponent : Pick 8
     You      : Pick 5
     Opponent : Pick 4

    Total money with you : 10 + 5 = 15



    NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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