Solve a problem using top$-$down and bottom$-$up approaches of Dynamic Programming

technique

DNA sequence is made of characters A$,$ C$,$ G and T$,$ which represent nucleotides. A sample

DNA string can be given as $$ACCGTTTAAAG$.$ Finding similarities between two DNA

sequences is a critical computation problem that is solved in bioinformatics.

Given two DNA strings find the length of the longest common string alignment between

them $($it need not be continuous$).$ Assume empty string does not match with anything.

Example: DNA string$1$: ATAGTTCCGTCAAA ; DNA string$2$: GTGTTCCCGTCAAA