The shadow-paging scheme requires the page table to be copied. Suppose the page table is represented as a B+-tree.

a. Suggest how to share as many nodes as possible between the new copy and the shadow copy of the B+-tree, assuming that updates are made only to leaf entries, with no insertions or deletions.

b. Even with the above optimization, logging is much cheaper than a shadow copy scheme, for transactions that perform small updates. Explain why.