Play optimally?

#1

Will both players choose max value from first or last or will they focus on achieving a greater sum than the other ?

#2

Going for maximum number on each turn is Greedy Approach while aiming for a maximum total is the Optimal Approach. While the Greedy Approach might work for some testcases , it will not work for all of the them

Try this testcase :
4
2 3 7 4

Using the greedy technque ,
Player 1 picks 4
Player 2 picks 7
Player 1 picks 3
Player 2 picks 2

Player 1 Score = 4 + 3 = 7
Player 2 Score = 7 + 2 = 9

Since our goal was to make sure that Player 1 wins, the greedy technique fails

If we were not inclined to use the greedy technique and had played optimally like this
Player 1 picks 2 (Even though its lesser of 2 & 4)
Player 2 picks 4
Player 1 picks 7
Player 2 picks 3

Player 1 Score = 2 + 7 = 9
Player 2 Score = 4 + 3 = 7

Player 1 wins.

#3

I hope I’ve cleared your doubt. I ask you to please rate your experience here
Your feedback is very important. It helps us improve our platform and hence provide you
the learning experience you deserve.

On the off chance, you still have some questions or not find the answers satisfactory, you may reopen
the doubt.