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Problem 3 . Database medians. You are working as a programmer for UMass administration, and they ask you to determine the median GPA for all
Problem 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 instate students and one for outofstate students. Assume there
are n students of each type, so there are n students total. Youd like to determine the median of
this set of 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 Olog n queries.
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