Maximizing the Gap Symbols of an Optimal Alignment solved by 275

Adjusting Alignment Parameters

As we change the parameters contributing to alignment score, the nature of alignments achieving the maximum score may change. One feature of maximum-score alignments worthy of consideration is the number and size of their gaps. In this problem, we would like to determine the maximum number of possible gaps in any optimal alignment based solely on the parameter values chosen.

Problem

For the computation of an alignment score generalizing the edit alignment score, let $m$ denote the score assigned to matched symbols, $d$ denote the score assigned to mismatched non-gap symbols, and $g$ denote the score assigned a symbol matched to a gap symbol '-' (i.e., $g$ is a linear gap penalty).

Given: Two DNA strings $s$ and $t$ in FASTA format (each of length at most 5000 bp).

Return: The maximum number of gap symbols that can appear in any maximum score alignment of $s$ and $t$ with score parameters satisfying $m > 0$, $d < 0$, and $g < 0$.

Sample Dataset

>Rosalind_92
AACGTA
>Rosalind_47
ACACCTA

Sample Output

3