Hi. I've been practicing DP problems but until now I'd just seen problems with states like dp[i][j] = best choice using i first elements and with cost j.

But when I've tried this problem 425C - Сережа и две последовательности and after thinking a couple of days, I watched the tutorial and find a dp like dp[i][j] = best choice using "no more than" first i elements with j steps.

What call my attention was the part of the i parameter, because is not something fixed, if you could understand me. I know that maybe this could be some basic DP technique but I would like that you could suggest me problems with this type of dp.

Sorry for my english