03Fall - CSE 2320 Name _ Test 1 Fall 2003 Student ID # _...

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CSE 2320 Name ________________________________ Test 1 Fall 2003 Student ID # ___________________________ Multiple Choice. Write your answer to the LEFT of each problem. 4 points each 1. P ARTITION is useful in solving all of the following problems, except A. Finding the k smallest elements B. Q UICKSORT C. Selection D. Splitting an array for M ERGESORT 2. Which of the following sorts is not stable? A. I NSERTION -S ORT B. LSD R ADIX -S ORT C. M ERGESORT D. Q UICKSORT 3. Which of the following sorts is not based on key comparisons? A. I NSERTION -S ORT B. LSD R ADIX -S ORT C. M ERGESORT D. Q UICKSORT 4. Suppose the input to H EAPSORT is always a table of identical integers. The worst-case time will be A. Θ (1) B. Θ (n) C. Θ (n lg n) D. Θ (n 2 ) 5. Suppose the input to P ARTITION is always a set of identical integers. The worst-case time will be A. Θ (1) B. Θ (n) C. Θ (n lg n) D. Θ (n 2 ) 6. The time to multiply two n x n matrices is: A. Θ (n) B. Θ (n lg n) C. Θ (n 2 ) D. Θ (n 3 ) 7. f(n) = n lg n is in all of the following sets, except A. (lg n) B. Θ (log(n!)) C. O(1/n) D. O(n 2 ) 8. Which of the following best approximates H m – H n ? (m > n) A. H m-n B. 1/(m – n) C. ln(m / n) D. ln(m - n) 9. Which sort may be viewed as being an improvement on insertion sort? A. C OUNTING -S ORT B. H EAPSORT C. Q UICKSORT D. shellsort 10. Counting sort is often used as a part of which sorting algorithm? A. I NSERTION -S ORT B. LSD R ADIX -S ORT C. M ERGESORT D. Q UICKSORT Long Answer 1. Prove that if f ( n ) Î O g ( n ) ( ) then 1 f ( n ) Î W 1 g ( n ) ae è ç ö ø ÷. 10 points 2. Use the substitution method to show that T(n) = 2T(n/4) + n is in Θ (n). 15 points
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3. Use the recursion-tree method to show that T(n) = 2T(n/4) + n is in Θ (n). 15 points 4. Demonstrate P ARTITION on the following array. 10 points 9 3 6 2 7 4 1 8 0 5 5. Show the maxheap after performing H EAP -E XTRACT -M AX two times. 10 points 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 CSE 2320 Name ________________________________ Test 2 Fall 2003 Student ID # ___________________________ Multiple Choice. Write the letter of your answer to the LEFT of each problem. 4 points each Problems 1 and 2 refer to the following hash table whose keys are stored by linear probing using h(key) = key % 13. 0 1 2 3 4 5 6 7 8 9 10 11 12 122 110 20 86 87 62 94 1. 143 would be inserted into which slot of the given table? A. 0 B. 1 C. 2 D. 11 2. 136 would be inserted into which slot of the given table? A. 0 B. 4 C. 6 D. 11 Problems 3 and 4 refer to the following hash table whose keys are stored by double hashing using h 1 (key) = key % 13 and h 2 (key) = 1 + (key % 12). 0 1
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03Fall - CSE 2320 Name _ Test 1 Fall 2003 Student ID # _...

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