Computer Science 170 - Spring 1993 - Blum - Midterm 1

Computer Science 170 - Spring 1993 - Blum - Midterm 1 -...

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CS170, Midterm, Spring 1993 CS170 Spring 1993 Midterm Professor M. Blum CLOSED BOOK. CALCULATORS ALLOWED. You have two hours to complete this exam. ****DO ANY TWO OF THE THREE PROBLEMS. (Try to do all three if you can.)**** Problem #1 (Find An Element Above the Median) Give upper and lower bounds on the number of comparisons to solve the following problems: INPUT: An array A=[a 1 ...a N ] of real numbers. N = even integer. The array is NOT sorted. OUTPUT: An element a 1 contained in A that is greater than the MEDIAN, where the median is the biggest element in the bottom half. EXAMPLE: A = [1, 5, 3, 6]; MEDIAN = 3; RETURN 5 or 6. Use the decision tree model of computation. (Each comparison counts 1 step.) Make your bounds as tight as you can make them, but no tighter. Problem #2 (Celebrity Problem) DEFINITION: A celebrity is someone whom everyone knows, but who knows no one (else). THE PROBLEM: You are to determine if a party of N persons, N >= 2, has a celebrity by asking questions of the form "Do you know that person over there?" STEPS: Each question counts one step. All other computations are free.
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Computer Science 170 - Spring 1993 - Blum - Midterm 1 -...

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