hw7 - Cs445 - Homework #7 (optinal) Dynamic programming,...

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Cs445 — Homework #7 (optinal) Dynamic programming, Stable marriage, and Approximation algorithm If you choose to submit this homework, its grade would replace yout Due: 5/9/2005 at 11:59pm (deadline is Frm). If you are not in Tucson at this date, you may submit via email to Rohit. 1. Show how to reduce the space requirement of ±loyd-Warshall algorithm to O ( n 2 ). 2. How can you use ±loyd-Warshall algorithm to Fnd if the graph contains negative cycles ? 3. Generate a sequence of 5 matrices A 1 ,A 2 ,A 3 ,A 4 ,A 5 , and show how to optimally compute the number of multiplication operations need to compute the product A 1 · A 2 · A 3 · A 4 · A 5 . The smallest matrix has 5 rows, and the largest matrix has at least 100 rows. 4. Apply the LCS algorithms on the sequences X = pp HHelloWWord pp and Y = HeloWorld pp . Show the LCS table, and explain how do do you reconstruct the LCS ( X,Y ) 5. In the stable marriage algorithm (a) describes an input where during there algorithm Θ(
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hw7 - Cs445 - Homework #7 (optinal) Dynamic programming,...

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