SEQUENCE ALIGNMENT (and many other similar problems) can be resolved with dynamic programming in O(mn) time.

E.g. 

AGARSARF_GSSAGRGGGGEPEGRPGPFNG
|:|||:.. |:::|.|||||||||:|:.||
ASARSGSSAGGGGGGGGGGEPEGRSGSSNG

For this we construct a MATRIX of OPTIMAL SCORING



The computation of each optimum is usually described as:

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