Let $c_1,c_2,...,c_{100}$ be the position of the books. We make the graph with vertices $c_i$ and a directed edge fron $c_i$ to $c_j$ if in the position $c_i$ we have the book $j$. We can see now that our glaph is a union of circles and every time we can delete at most two edges(we can delete three only if we have a circle o legt $3$).So if we star from a big circle of legt $100$ we need at least $50$ moves. With $50$ moves it is trivial that we can do it.