Also, your local alignment doesn't need to end at the end of either sequence, so you don't need to start your traceback in the bottom-right corner; you can start it in the cell with the highest score.

Global sequence alignment tries to find the best alignment between an entire sequence S1 and another entire sequence S2. Consider these two DNA sequences.

This process is composed of such sections as recognition of target template, alignment between query sequence and target sequence, modeling, evaluation of structure rationality.