Alignment with gap penalties. The alignment algorithm of Exercise 6.26 helps to identify DNA sequences that are close to one another. The discrepancies between these closely matched sequences are often caused by errors in DNA replication. However, a closer look at the biological replication process reveals that the scoring function we considered earlier has a qualitative problem: nature often inserts or removes entire substrings of nucleotides (creating long gaps), rather than editing just one position at a time. Therefore, the penalty for a gap of length 10 should not be 10 times the penalty for a gap of length 1, but something significantly smaller.
Repeat Exercise 6.26, but this time use a modified scoring function in which the penalty for a gap of length k is c0 + c1 k, where c0 and c1 are given constants (and c0 is larger than c1).
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