Analysis of lee215’s solution Lee already explained fairly well how to get the 1D dp. I just want to expound a little bit because there is a heavy dose of intuition that I believe is very beneficial for other problems. Intuition One of the first things that one tries when playing with this problem is figuring out when the second finger comes into the picture. I applaud the earlier posts in assuming a special starting position for both fingers, so that there is nothing special about when it transitions from one finger to two fingers.