# midterm1(1) - CS 473 Midterm 1 Questions Version 1 Spring...

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CS 473 Midterm 1 Questions — Version 1 Spring 2010 This exam lasts 120 minutes. Write your answers in the separate answer booklet. Please return this question sheet with your answers. 1. Each of these ten questions has one of the following five answers: A : Θ( 1 ) B : Θ( log n ) C : Θ( n ) D : Θ( n log n ) E : Θ( n 2 ) Choose the correct answer for each question. Each correct answer is worth + 1 point; each incorrect answer is worth - 1 / 2 point; and each “I don’t know" is worth + 1 / 4 point. Negative scores will be recorded as 0. (a) What is 3 n + n 3 ? (b) What is n X i = 1 i n ? (c) What is s n X i = 1 i ? (d) How many bits are required to write the number n ! (the factorial of n ) in binary? (e) What is the solution to the recurrence E ( n ) = E ( n - 3 ) + 17 n ? (f) What is the solution to the recurrence F ( n ) = 2 F ( n / 4 ) + 6 n ? (g) What is the solution to the recurrence G ( n ) = 9 G ( n / 9 ) + 9 n ? (h) What is the worst-case running time of quicksort? (i) Let X [ 1.. n ,1.. n ] be a fixed array of numbers. Consider the following recursive function: WTF ( i , j ) =

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