1. 授課教授：李錫智 Data Structures -4 th exam-

2. 1.[10] Suppose we have a text and a pattern shown in Fig.1. You apply the brute-force pattern matching algorithm to search for the first occurrence of the pattern in the text. How many comparisons between two characters are performed before you get the answer?

3. Ans: 27 Textabacaabadcabacabaabb 123456 abacab 7 abacab 89 abacab 10 abacab 1112 abacab 13141516 abacab 17 abacab 1819 abacab 20 abacab 21 abacab 222324252627 abacab

4. 2.[10] Consider again the text and the pattern shown in Fig.1. You apply the Boyer-Moore algorithm to search for the first occurrence of the pattern in the text. A.[5] What is the last-occurrence function L, i.e., what are the values of L(a), L(b), L(c), and L(d)? B.[5] How many comparisons between two characters in the text and the pattern, respectively, are performed before you get the answer?

5. Ans: A. L(a)=4, L(b)=5, L(c)=3, L(d)=-1 B. Textabacaabadcabacabaabb 1 abacab 432 abacab 5 abacab 6 abacab 7 abacab 1312111098 abacab

6. 3.[5] Draw a standard trie for the following set of strings: {abab, baba, aaccc, bcbc, ccaaa, ccab, bbaacc, cbcc, cbca, abaaa} Ans:

7. 4.[5] Draw a compressed trie for the following set of strings: {abab, baba, aaccc, bcbc, ccaaa, ccab, bbaacc, cbcc, cbca, abaaa} Ans:

8. 5.[10] List the BFS traversal sequence, starting from node 8, for the graph in Fig.2. When several nodes are acceptable, select first the node with the smallest number. Ans: 8, 5, 6, 10, 2, 3, 7, 9, 1, 4

9. 6.[10] List the DFS traversal sequence, starting from node 8, for the graph in Fig.2. When several nodes are acceptable, select first the node with the smallest number. Ans: 8, 5, 2, 1, 3, 4, 9, 6, 7, 10

10. 7.[10] Find the minimum spanning tree for Fig.3 using the Prim- Jarnik algorithm, starting with the node J. Please draw the intermediate result each time a new node and a new edge are added.

11. Ans: (1)(2) (3) (4)

12. Ans: (5) (6) (7) (8)

13. 8.[10] Find the minimum spanning tree for Fig.3 using Kruskal’s algorithm. Please draw the intermediate result each time a new edge is added.

14. Ans: (1)(2) (3)(4)

15. Ans: (5) (6) (7)

16. 9.[10] Consider again the text and the pattern shown in Fig.1. You apply the KMP algorithm to search for the first occurrence of the pattern in the text. A.[5] What is the failure function F, i.e., what are the values of F(0), F(1), F(2), F(3), F(4), and F(5)? B.[5] How many comparisons between two characters in the text and the pattern, respectively, are performed before you get the answer?

17. Ans: A. F(0)=0, F(1)=0, F(2)=1, F(3)=0, F(4)=1, F(5)=2 B. Textabacaabadcabacabaabb 123456 abacab 7 abacab 891011 abacab 12 abacab 13 abacab 14 abacab 151617181920 abacab

18. 10.[10] Suppose you want to transmit the string “dogs do not spot hot pots or cats” with Huffman encoding. Note that there is a blank between a pair of two words, and blanks should also be transmitted. A.[5] What are the codes for the involved characters? B.[ 5]What is the string of bits transmitted for this communication along the communication channel?

19. Ans: A. B. 01011000001001111010110110100010001110110001100011100001110001 1100011000101111100100111000001000000001011 acghnrdpsto_ 111111224577 acghnrdpsto_ 0000000000010000100000110100001001010100010110011011 PS. _ 代表 space

20. 11.[10] Find the shortest paths from node E to all the nodes in Fig.4. Please show the updated shortest distances each time a node is assured of its final answer.

21. Ans: (1)(2) (3)(4)

22. Ans: (5)(6) (7)

23. 12.[10] Find the minimum spanning tree for Fig.3 using Baruvka’s algorithm as shown below. Please draw T 1 each time statement 4 is encountered. 1) Algorithm BaruvkaMST(G) 2) T 1  V {just the vertices of G} 3) T 2  V {just the vertices of G} 4) while T 1 has fewer than n-1 edges do \\ n is the number of vertices in G 5) for each connected component C in T 1 do 6) Let edge e be the smallest-weight edge of all the edges between C and the other connected components in T 1 7) if e is not already in T 2 then 8) Add edge e to T 2 9) T 1  T 2 10) return T 1

24. 12. 1) Algorithm BaruvkaMST(G) 2) T 1  V {just the vertices of G} 3) T 2  V {just the vertices of G} 4) while T 1 has fewer than n-1 edges do \\ n is the number of vertices in G 5) for each connected component C in T 1 do 6) Let edge e be the smallest-weight edge of all the edges between C and the other connected components in T 1 7) if e is not already in T 2 then 8) Add edge e to T 2 9) T 1  T 2 10) return T 1

25. Ans: (1) (2) (3)