06Summer - CSE 2320 Name _ Test 1 Summer 2006 Last 4 Digits...

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CSE 2320 Name ____________________________________ Test 1 Summer 2006 Last 4 Digits of Student ID # __________________ Multiple Choice. Write your answer to the LEFT of each problem. 3 points each 1. The time to multiply two n x n matrices is: A. Θ n ( ) B. Θ n log n ( ) C. Θ n 2 ae è ç ö ø ÷ D. Θ n 3 ae è ç ö ø ÷ 2. For which of the following sorts does the decision tree model not apply? A. Counting B. Insertion C. M ERGE -S ORT D. Q UICKSORT 3. Which of the following sorts is not stable? A. H EAPSORT B. Insertion C. LSD Radix Sort D. M ERGE -S ORT 4. As n approaches , H n H 2 n approaches? A. 1 B. 2 C. ln n D. n ! 5. The function n + log n is in which set? A. n log n ( ) B. Θ log n ( ) C. Θ n ( ) D. Θ n log n ( ) 6. Which of the following expressions corresponds to the time needed for LSD Radix Sort? A. Θ ( d + k + n ) B. Θ ( d ( k + n )) C. Θ ( k + n ) D. Θ ( dkn ) 7. Suppose a binary search is to be performed on a table with 50 elements. The maximum number of elements that could be examined (probes) is: A. 4 B. 5 C. 6 D. 7 8. f n ( ) = n lg n is in all of the following sets, except A. log n ( ) B. Θ log n ! ( ) ( C. Ο 1 n ( ) D. Ο n 2 ae è ç ö ø ÷ 9. The expected time for Q UICKSORT for n keys is in which set? (All n ! input permutations are equally likely.) A. Θ log n ( B. Θ n ( ) C. Θ n log n ( D. Θ n 2 ae è ç ö ø ÷ 10. What is the value of 2 k k =0 t å ? A. 2 k B. 2 t C. 2 t +1 - 1 D. 2 t 11. Suppose that you have correctly determined some c and n o to prove that f n ( ) Î O g n ( ) ( ) . Which of the following is not necessarily true? A. c may be decreased B. c may be increased C. n o may be increased D. g n ( ) Î W f n ( ) ( ) 12. Suppose you are using the substitution method to establish a Θ bound on a recurrence T n ( ) and you already know that T n ( ) Î W n ( ) and T n ( ) Î O n 3 ae è ç ö ø ÷ . Which of the following cannot be shown as an improvement? A. T n ( ) Î O lg n ( ) B. T n ( ) Î O n ( ) C. T n ( ) Î W n 2 ae è ç ö ø ÷ D. T n ( ) Î W n 3 ae è ç ö ø ÷ 13. Suppose the 201 priorities in a maxheap are unique. Which of the following subscripts may not store the minimum? A. 100 B. 101 C. 199 D. 200 14. Suppose a minheap that can hold m records is used to produce sorted subfiles for an external mergesort. If the large input file is randomly ordered, the expected number of records in a subfile is:
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A. m B. 2 m C. m ln m D. m 2 15. Which of the following will not be true regarding the decision tree for insertion sort for sorting n input values? A. Every path from the root to a leaf will have Ο n log n ( ) decisions. B. The height of the tree is n log n ( ). C. There will be a path from the root to a leaf with n 2 ae è ç ö ø ÷ decisions. D. There will be n ! leaves. Long Answer 1. Suppose an int array a contains m zeroes followed by n ones, where m and n are unknown. The size of the array is given to you as p , i.e. p==m+n . Give C code for a binary search to determine m in Ο log p ( ) time. 15 points 2. Use the substitution method to show that T n ( ) = 3 T n 3 ( ) + n 2 is in Θ n 2 ae è ç ö ø ÷ . 10 points 3. Use the recursion-tree method to show that T n ( ) = 3 T n 3 ( ) + n 2 is in Θ n 2 ae è ç ö ø ÷ . 10 points 4. Show the result after P ARTITION manipulates the following subarray. 10 points 3 1 6 9 8 5 7 0 2 4 5.
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06Summer - CSE 2320 Name _ Test 1 Summer 2006 Last 4 Digits...

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