Challenge: Greedy Algorithms

Task

We’ve been hired to store a sequence of $n$ books on shelves in a library. The order of the books is fixed by the cataloging system and cannot be changed; each shelf must store a contiguous interval of the given sequence of books. We are given two arrays $H[1 .. n]$ and $T[1 .. n]$, where $H[i]$ and $T[i]$ are respectively the height and thickness of the $i$th book in the sequence. All shelves in this library have the same length $L$; the total thickness of all books on any single shelf cannot exceed $L$. Suppose all the books have the same height $$ ...