Maximum Sum of Non-adjacent Elements in 1D array

Question

Given an array of integers, find a maximum sum of non-adjacent elements. For example, inputs [1, 0, 3, 9, 2,-1] should return 10 (1 + 9).

Answer 1

Let BEST_SUM(i) be the maximum sum of non-adjacent elements at positions <= i.

When i<0,   BEST_SUM(i) = 0
Otherwise:  BEST_SUM(i) = max( BEST_SUM(i-1), BEST_SUM(i-2)+a[i] )

BEST_SUM(a.length-1) is your answer.

NOTE: This is the max sum of non-adjacent elements, like you asked for. Looking at your code it looks like you may mean the best sum of two non-adjacent elements. The would be different, and easier.