Pattern Matching Algorithms 89-775-01 FINAL EXAM Instructor: Prof. Amihood Amir Summary: Pattern Matching Algorithms 89-775-01 FINAL EXAM MOED A Instructor: Prof. Amihood Amir Length of Exam: 2 hours Time: 12:00, February 16th, 2010 BOOKS AND NOTEBOOKS ARE ALLOWED!!! 1. The Point-Set Matching Problem is defined as follows. INPUT: Text T = t0, ..., tn, and pattern P = p0, ..., pm, pi, tj {0, 1}, i = 0, ..., m, j = 0, ..., n. OUTPUT: All locations i in T where ti+j = pj or ti+j = 1 and pj = 0, j = 0, ..., m. The text and pattern represent points on the line, where every 1 is a point. The idea is to find the text locations where every pattern point aligns with a text point. (We do not care if there are text points that do not align with pattern points.) text element. Example: If T = 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1 and P = 1, 0, 0 then there is a match in location 1 of the text, since the first location of the pattern matches the text, and there are no more 1's in the pattern. Similarly, there is a match in text locations 2, 5, 7 and 8. a) Write an algorithm that solves the Point-Set Matching Problem (explain the algo- rithm's idea, the tools you used, and give a high level description). b) What is the time complexity of your algorithm? Justify. Collections: Mathematics