Physics Sheldon Cooper Decided Give String Theory Favor Re Dr M Wortunately Grant Funded P Q43784572
The Physics Sheldon Cooper has decided to give up on String Theory in favor of re- Dr M wortunately, his grant-funded position at Caltech is dependent on his d i Sering Theory, she must search elsewhere. He applies and receives offers from MT HardWhile money is no object to Sheldon, he wants to ensure he’s paid fairly and that is r eals the median salary among the two schools’ Physics departments. There when you to find the median salary across the two departments. Each school mantains a database of all of the salaries for that particular school, but there is no central database. Each school has given you the ability to access their particular data by executing queries. For each query, you provide a particular database with a value k such that 1 <ksn, and the database returns to you the smallest salary in that school’s Physics department You may assume that each school has exactly n physicists (i.e. 2n total physicists across both school), every salary is unique (.e. no two physicists, regardless of school, have the same salary), and we define the median as the highest salary across both schools. 1. Design an algorithm that finds the median salary across both schools in O(log(n)) total queries. 2. State the complete recurrence for your algorithm. You may put your f(n) in big-theta nota- tion. Show that the solution for your recurrence is (log(n)). 3. Prove that your algorithm above finds the correct answer. Hint: Do induction on the size of the input. Show transcribed image text The Physics Sheldon Cooper has decided to give up on String Theory in favor of re- Dr M wortunately, his grant-funded position at Caltech is dependent on his d i Sering Theory, she must search elsewhere. He applies and receives offers from MT HardWhile money is no object to Sheldon, he wants to ensure he’s paid fairly and that is r eals the median salary among the two schools’ Physics departments. There when you to find the median salary across the two departments. Each school mantains a database of all of the salaries for that particular school, but there is no central database. Each school has given you the ability to access their particular data by executing queries. For each query, you provide a particular database with a value k such that 1
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