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Exam2Grading - BCB 567/CprE 548 Fall 2007 Exam 2 Solutions...

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BCB 567/CprE 548 Fall 2007 Exam 2 Solutions 1. (a) This is true. Consider that LCP [ i ] = k . This means that suffix SA [ i ] and suffix SA [ i + 1] have a longest common prefix of length k . This implies that suffixes SA [ i ] + 1 and SA [ i + 1] + 1 have a longest common prefix of k - 1. This means that the range minimum in the LCP array between indexes INV [ SA [ i ] + 1] and INV [ SA [ i + 1] + 1] is k - 1. However, for this to be true, there must be some entry in the LCP array equal to k - 1. (b) The maximum zero entries in the LCP is equal to the alphabet size (if you consider the last entry of the LCP array) or alphabet size - 1 if you do not. Think about a dictionary and how many times the first letter changes. Grading Notes: Both Σ and Σ - 1 received full credit. Because the alphabet size can be at most N , the answers N or N - 1 received partial credit. (c) The minimum number of occurrences is 6. For each incoming suffix link, there exists some internal node with path label . Therefore, occurs at least twice. Because there are 3 suffix links, we have at least 3 × 2 = 6 occurrences. (d) i. No, counter example: ABC and ABCAB ii. No, counter example: ABC and ABCAB iii. Yes iv. No, counter example: ABC and ABCAB 2. (a) – (b) – (c) i. To find length 3 repeats in the look-up table, search for table entries with more than one index.
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