Computer Science 170 - Spring 1994 - Blum - Final

# Computer Science 170 - Spring 1994 - Blum - Final - CS 170...

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CS 170, FINAL EXAM, Spring 1994 CS 170, Spring 1994 Final Examination Professor Manuel Blum This is a CLOSED BOOK exam. Calculators ARE permitted. Do at least 4 of the following 5 problems. If you do all 5, your grade will be the sum of your best 4 grades. Try to do all 5 problems. PUT ALL YOUR ANSWERS IN YOUR BLUE BOOK. Problem #1a (5 pts) Is n log 2 n = 2 log 2 2 n ? If not, is it < or >? Problem #1b (5 pts) (i) Find a MAX FLOW in this network: (ii) Find a min cut in the above network. Problem #1c (5 pts) file:///C|/Documents%20and%20Settings/Jason%20Raft. ..%20Spring%201994%20-%20Blum%20-%20Final%20Exam.htm (1 of 5)1/27/2007 5:30:46 PM

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CS 170, FINAL EXAM, Spring 1994 You are given a fair coin. How would you use it to simulate a toss of a (6-sided) die? Problem #1d (5 pts) Give an algorithm to multiply 2 complex numbers a+ib and c+id using just 3 real multiplications. INPUT: 4 real numbers a,b and c,d (denoting a+ib and c+id) OUTPUT: ac-bd, ad+bc (denoting (ac-bd) + i(ad+bc)) Problem #2a (10 pts) Give an efficient algorithm to determine whether 2 given points P 1 = (x 1 ,y 1 ) and P 2 = (x 2 ,y 2 ) lie on the same side of a given line, y = ax+b. Here a,b are rational numbers.
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Computer Science 170 - Spring 1994 - Blum - Final - CS 170...

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