Find the longest sequence length whose sum is divisible by 3

Question

I have an exercise that needs to be done with O(n) time complexity, however, I can only solve it with an O(n^2) solution.

You have an array and you need to count the

Answer 1

You apply dynamic programming. For every position you compute 3 values:

• The longest sequence ending in that position which has sum s = 0 mod 3
• The longest sequence ending in that position which has sum s = 1 mod 3
• The longest sequence ending in that position which has sum s = 2 mod 3

So given this value for position i you can easily compute the new ones for position i+1.