Final Examination Semester 1 / Year 2011

Transcription

1 Southern College Kolej Selatan 南方学院 Final Examination Semester 1 / Year 2011 COURSE : DATA STRUCTURE AND ALGORITHM COURSE CODE : PROG2103 TIME : 2 1/2 HOURS DEPARTMENT : COMPUTER SCIENCE LECTURER : SO YONG QUAY Student s ID: Batch No: Notes to candidates: 1) The question paper consists of 6 pages and 16 questions. 2) There are two parts in this paper. Students are required to answer all questions. 3) Return the question paper with your answer booklet.

2 Part A: Multiple Choice (2 marks for each correct answer) 1. What is the running time for deleting a specified element in a linked list? a) O(1) b) O(logn) c) O(n/2) d) O(n) 2. Use the binary search to find a target value in an array of 475 items. What is the fewest number of comparisons the search will require? a) 475 b) 10 c) 9 d) 1 3. What is Big O estimation for t (n) = ( n ) / (n + 3) + 6 log 2 n? a) 1 b) n c) n 2 d) log 2 n 4. Determine which of the following array have the heap property. a. b. c. d The disadvantage of a mergesort is that a) it is not recursive. b) it uses more memory. c) although faster than the insertion sort, it is much slower than quicksort. d) it is complicated to implement. 1 / 6

3 6. If the last row of the heap s level is 10, the heap has maximum nodes. (a) 1023 (b) 1024 (c) 2047 (d) If an array has 532 elements, then Knuth s Shellsort would start with an interval of (a) 40 (b) 121 (c) 364 (d) If a tree is represented by an array, the parent node of a node at index n has an index of? (a) 2*n + 1 (b) (n - 1) / 2 (c) n / (d) n- 1 / 2 9. Partition is a) putting all elements larger than a certain value on one end of the array. b) dividing an array in half. c) partially sorting parts of an array. d) sorting each half of an array separately. 10. The biggest node in a minimum heap is a. always a left child. b. always a right child. c. always on the bottom row. d. always a root. Part B: Answer all Questions 11. a) Explain the quick sort algorithm and what is complexity time of quick sort? (8 marks) b) Given the following list of values. Perform a Quick Sort using the last value in the list as the pivot value in each pass. (10 marks) (Use the following table format for your answer.) 2 / 6

4 Index Pass No a) Explain how to find the inorder successor in binary tree. (5 marks) b) Discuss the complexity time of the deletion a node in binary tree and use Big-O notation to show your final answer. (5 marks) c) Use Binary Tree to arrange the following number series. (5 marks) 24, 91, 15, 3, 14, 19, 17, 83, 90, 33, 19, 9, 59 d) Use 12c) binary tree, If the root node 24 is deleted, which node as the replacement node? Redraw the new binary search tree. (5 marks) 13. Analyze the following program and use the Big O notation to show its complexity time. a) Assume that there are n elements stored in the array. (8 marks) private void recsort(long[] workspace, int lowerbound, int upperbound) if(lowerbound == upperbound) return; else int mid = (lowerbound+upperbound) / 2; recsort(workspace, lowerbound, mid); recsort(workspace, mid+1, upperbound); 3 / 6

5 conquer(workspace, lowerbound, mid+1, upperbound); private void conquer(long[] workspace, int lowptr, int highptr, int upperbound) int j = 0 int lowerbound = lowptr; int mid = highptr-1; int n = upperbound-lowerbound+1; while(lowptr <= mid && highptr <= upperbound) if( thearray[lowptr] < thearray[highptr] ) workspace[j++] = thearray[lowptr++]; else workspace[j++] = thearray[highptr++]; while(lowptr <= mid) workspace[j++] = thearray[lowptr++]; while(highptr <= upperbound) workspace[j++] = thearray[highptr++]; for(j=0; j<n; j++) thearray[lowerbound+j] = workspace[j]; b) (4 marks) int sum = 0; for (int j = 0; j < m; j++) for (int i = 0; i < n; i++) sum += calculation(); public static int calculation() int subsum = 0, n; for (int j = 1; j <= n; j++) for (int i =1; i<=n; i++) subsum += i + j; return subsum; 4 / 6

6 14. Use the heapsort to sort the following heap values: Heap: (A heap is implemented as an array; use the following table format for your answer.) (10 marks) Index Pass No Original heap a) Explain the dynamic programming and divide-and-conquer algorithm in computer science. (8 marks) b) Discuss the advantages and disadvantages of dynamic programming and divideand-conquer algorithm. (6 marks) 16. Use the following graph to show the order of visiting the vertices by depth-first search and breadth-first search.(assume that the vertices are selected in alphabetical order and the starting vertex is A) (6 marks) 5 / 6

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