CSC 517: Algorithms Midterm Exam October 2006 - Prof. B. Rosenberg, Exams of Computer Science

Download CSC 517: Algorithms Midterm Exam October 2006 - Prof. B. Rosenberg and more Exams Computer Science in PDF only on Docsity! Burton Rosenberg CSC 517: Algorithms 1 Midterm October 9, 2006. 11:15–12:05 PM There are five problems each worth five points for a total of 25 points. Show all your work, partial credit will be awarded. Space is provided on the test for your work; if you use a blue book for additional workspace, sign it and return it with the test. No notes, no collaboration. Name: Problem Credit 1 2 3 4 5 Total CSC 517: Algorithms 4 3. Show the result of Build-Max-Heap when run on the following array. (Show several intermediate steps.) 13 16 14 15 1 8 7 3 9 10 CSC 517: Algorithms 5 4. Consider the following algorithm to see if all the values in an array are unique, for i = 1 to length(A) for j = 1 to length(A) if ( i!=j ) if A[i] == A[j] return false end for end for return true Give the run time of this algorithm, in terms of n = length(A). Justify your answer. Find another algorithm to accomplish the task of finding if all values in an array are unique, which is significantly faster than the algorithm presented above. CSC 517: Algorithms 6 5. When you are one year old, one candle is lit for your birthday. When you are two years old, two candles are lit. When three, three candles, and so forth. By your 80-th birthday, what is the total number of candles lit for all your birthdays combined, including the 80 candles for this birthday.