Give a recurrence that describes the storage of the quadtree data structure as

described in this picture $($in the worst case$).$ Please :

$(1)$ explain the worst case, $(2)$ give the recurrence, $(3)$ explain what your $$n$$ is$,$ and $(4)$

annotate or explain how you chose the parts of the recurrence.

b$.$ Solve the recurrence from $($a$)$ using whatever method you$$d like $($and clearly state

what method you are using$).$

c$.$Explain using the solution from $($b$)$ if this is better or worse than the storing all

the pixels in a grid of ints. You must choose better or worse, if you believe they are in the

same space complexity class, you must still argue that one is better$/$worse than the other