Customer $($customer$\_$id$,$ c$\_$name, city$)$

Hotel $($hotel$\_$id$,$ h$\_$name, city, stars$)$

Reservation $($hotel$\_$id$,$ customer$\_$id$,$ cost$)$

and the following query:

Find names of all $5-$star hotels which are reserved by customers from

Minneapolis, with a reservation cost of at least $$1000.$

a$.$ The table below gives an example tree $($Tree $A)$ for the evaluation plan for the above query. Give two other possible equivalent trees for the given one.

$\backslash$table$[[,,],[,,],[$Tree: A$,,]]$

b$.)$ Given the statistics that $90\%$ of the reservation costs are more than $$1000,$ the customers' city is uniformly distributed in $3$ cities and $25\%$ of the hotels are $5$ stars. Which Tree would you choose to be the most efficient and why? Explain also why the other two trees are not efficient enough.