Hi, I am having difficutlties with this CSES problem "Book Shop". Firstly I implemented it recursively, but it gave me TLE. (Link). I've also been trying to get into iterative dp, so I tried it too and it worked! (Link)

However, I don't understand why recursive approach doesn't pass. Maybe I have implemented it poorly?

Also, it seems that there is an approach with $$$O(x)$$$ space complexity, but I have no clue how it works.