Computer Science 61B - Summer 2001 - Olan - Midterm 2

Computer Science 61B - Summer 2001 - Olan - Midterm 2 - CS...

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Unformatted text preview: CS 61B Midterm II Summer 2001 CS 61B, Summer 2001 Midterm Exam II Professor Michael Olan Problem 1 (8 points - 1 pt each parts a.-e., 2 pts part f.) a. Consider the following proof: Suppose f(n) is O(g(n)) . From this we know that g(n) is bigOmega(f (n)) . Thus we can always conclude that when f(n) is O(g(n)) it must also be bigOmega(g(n)) . If you agree justify your answer. If not, give a counterexample. b. A certain sorting algorithm has estimated running time O(N^2) . Does this mean that it always takes longer to sort than an algorithm that is O(N log N) ? Explain your answer. c. What is the overall running time for each of the following algorithms: Algorithm 1 Algorithm 2 1. Read N data items into a Vector 2. Sort the Vector with tree sort 3. Search for a key k with binary search 1. Read N data items into a Vector 2. Search for a key k with linear search d. How would the estimates you calculated in part c. change if the search step is repeated N times? e. In lecture we saw a heapify method with run time bigTheta(N log N). However, it is possible to accomplish this in bigTheta(N) using a "bottom up" heapify method which builds subheaps from the leaves up to the root. Complete the method below so that it is as efficient as possible: protected void heapify( ) { int i; for (______________ ; ________________ ; _______________ ) { reHeapifyDown( i ); } } f. Dr. I.M. Daprof has a policy of assigning "A" grades to the top sqrt(N) students in a class of N students. Always pressed for time, he uses the most efficient algorithm he knows: Sort the gradebook in descending order by numeric score using the fastest sorting algorithm we have seen so far in CS 61B...
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Computer Science 61B - Summer 2001 - Olan - Midterm 2 - CS...

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