quiz2-s2011

# quiz2-s2011 - 6.006 Spring 2011 Quiz 2 Introduction to...

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Introduction to Algorithms April 13, 2011 Massachusetts Institute of Technology 6.006 Spring 2011 Professors Erik Demaine, Piotr Indyk, and Manolis Kellis Quiz 2 Quiz 2 Do not open this quiz booklet until directed to do so. Read all the instructions on this page. When the quiz begins, write your name on every page of this quiz booklet. You have 120 minutes to earn 120 points. Do not spend too much time on any one problem. Read them all through ﬁrst, and attack them in the order that allows you to make the most progress. This quiz booklet contains 19 pages, including this one. Two extra sheets of scratch paper are attached. Please detach them before turning in your quiz at the end of the exam period. This quiz is closed book. You may use one handwritten, 8 1 2 00 × 11 00 or A4 crib sheets (both sides). No calculators or programmable devices are permitted. No cell phones or other communications devices are permitted. Write your solutions in the space provided. If you need more space, write on the back of the sheet containing the problem. Pages may be separated for grading. Do not waste time and paper rederiving facts that we have studied. It is sufﬁcient to cite known results. Show your work, as partial credit will be given. You will be graded not only on the correct- ness of your answer, but also on the clarity with which you express it. Be neat. Good luck! Problem Parts Points Grade Grader Problem Parts Points Grade Grader 1 8 24 6 10 2 6 24 7 10 3 4 12 8 10 4 10 9 10 5 10 Total 120 Name: Athena username: Recitation: Nick WF10 Nick WF11 Tianren WF12 David WF1 Joe WF2 Joe WF3a Michael WF3b

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6.006 Quiz 2 Name 2 Problem 1. True or false [24 points] (8 parts) For each of the following questions, circle either T (True) or F (False). Explain your choice. (Your explanation is worth more than your choice of true or false.) (a) T F Instead of using counting sort to sort digits in the radix sort algorithm, we can use any valid sorting algorithm and radix sort will still sort correctly. (b) T F The depth of a breadth-ﬁrst search tree on an undirected graph G = ( V,E ) from an arbitrary vertex v V is the diameter of the graph G . (The diameter d of a graph is the smallest d such that every pair of vertices s and t have δ ( s,t ) d .)
6.006 Quiz 2 Name 3 (c) T F Every directed acyclic graph has exactly one topological ordering. has valid topological orderings [ a,b,c ] or [ a,c,b ] . As another example, G = ( V,E ) = ( { a,b } , {} ) has valid topological orderings [ a,b ] or [ b,c ] .

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quiz2-s2011 - 6.006 Spring 2011 Quiz 2 Introduction to...

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