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COT 5405

COT 5405. Spring 2009 Feb 10, 2009. Problem 1. Find shortest path in following multi stage graph. Problem 2. A substring is palindromic if it is the same whether read left to right or right to left. For instance, ABRACADABRA, has two palindromic substring of length three (ACA and ADA).

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COT 5405

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  1. COT 5405 Spring 2009 Feb 10, 2009

  2. Problem 1 • Find shortest path in following multi stage graph

  3. Problem 2 • A substring is palindromic if it is the same whether read left to right or right to left. • For instance, ABRACADABRA, has two palindromic substring of length three (ACA and ADA). • Design an O(n2) time algorithm that takes a string of n letters and returns the (length of the) longest palindromic string.

  4. Problem 3 • You have to cut a wood stick into pieces. • Cost of one cut == the length of the stick being cut. • Only make one cut at a time. • It is easy to notice that different selections in the order of cutting can led to different prices. • For example, consider a stick of length 10 meters that has to be cut at 2, 4 and 7 meters from one end. • One can be cutting first at 2, then at 4, then at 7. This leads to a price of 10 + 8 + 6 = 24 because the first stick was of 10 meters, the resulting of 8 and the last one of 6. • Another choice could be cutting at 4, then at 2, then at 7. This would lead to a price of 10 + 4 + 6 = 20, which is a better price. • Find out the minimum cost for cutting a given stick.

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