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ps3n2 - Problem 2 0 Construction of the Algorithm Let's...

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Problem 2 0) Construction of the Algorithm Let’s consider a function I such that I ( i ) = set of interesting loci covered by( a i , b i ) and let’s sort the set of restriction enzymes based on their I value and consider the n t h enzyme, then we know that we have two cases: either the enzyme n is within an optimal set O or it’s not. If enzyme n is not in the optimal set, then we can simply discard it and look at the smaller subset and find k other enzymes. However, if n is in the optimal set, then we add I(n) into our optimal set and look at the left over enzymes and find k-1 other enzymes to use. This gives us the following definition of the optimum set of enzymes OPT ( n, k ) = max cardinality ( OPT ( n - 1 , k ) , I ( n ) U OPT ( n - 1 , k - 1)) if n 6 = 0 , k 6 = 0 else 1) Algorithm 1. Create the I(i) table by going through all restriction enzymes and then iterating over all interesting loci to see which ones are part of I(i). 2. First, we construct a n by k array with all entries initialized to the empty set.
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