In a state−$-$of−$-$the−$-$art genetics laboratory, scientists are analyzing DNA sequences from various organisms. They are investigating the correlation between two specific DNA sequences obtained from separate species. These sequences are represented by strings ofnucleotides ($($A,$,$ C,$,$ G,$,$ T).$).$ The objective is to align these sequences by converting one into the other using the fewest possible operations. Permitted operations include insertion ($($adding a nucleotide),$),$ deletion ($($removing a nucleotide),$),$ or substitution ($($changing one nucleotide to another).$).$ Insertions and deletions are of the same cost, while substitutions incur a cost three times higher than them.

Propose adynamic programming algorithm to determine the sequence of operations with the minimum cost required to align these DNA sequences while ensuring similarity between the sequences. Explain your algorithm in detail. Give the pseudo code and analyze the time complexity ($($Big−$-$Oh notation)$)$ of your proposed algorithm.