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Given strings s1 and s2 of lengths m and n respectively, a minimum cover of s1 by s2 is a decomposition s1 = w1w2 .... wk, where each wi is a non-empty substring of s2 and k is minimized. Eg., given s1 = accgtatct and s2 = cgtactcatc, there are several covers of s1 by s2 possible, two of which are:
(i) cover1: s1 = w1w2w3w4 (where w1 = ac, w2 = cgt, w3 = atc, w4 = t) , and
(ii) cover2: s1 = w1w2w3w4w5 (where w1 = ac, w2 = c, w3 = gt, w4 = atc, w5 = t).
However, only cover1 is a minimal cover. Give an algorithm to compute a minimum cover (if one exists) in O (m + n) time and space. If a minimum cover does not exist your algorithm should state so and terminate within the same time and space bounds. Give a brief justification of why you think your algorithm is correct - meaning, how it guarantees finding the minimial cover (if one exists).
Implement the Prim's algorithm with array data structure as described in slide 12 of the file 04mst.ppt. Your program should have a runtime complexity of O(n2) and should be as eff
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Why is this correct/when is this the right idea
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