Problem $3.$ Database medians. You are working as a programmer for UMass administration,

and they ask you to determine the median GPA for all students. However, student GPAs are stored

in two different databases, one for in$-$state students and one for out$-$of$-$state students. Assume there

are n students of each type, so there are $2$n students total. You$$d like to determine the median of

this set of $2$n values, which we will define here to be the nth smallest value.

However, security is very tight, so the only way you can access these values is through queries to

the databases. In a single query, you can specify a value k to one of the two databases, and the

chosen database will return the kth smallest value that it contains. Since queries are expensive,

you would like to compute the median using as few queries as possible.

Give an algorithm that finds the median value using at most O$($log n$)$ queries.