[Verse 1]
Two strings sitting on my desk tonight
Subsequence hunting, gotta find what's right
Not substring rules, we can skip and hop
Pick letters out, but order never stops
Dynamic programming table in my mind
Bottom-up approach, solutions we'll find
If characters match, diagonal plus one
If they differ, take the max that's done
[Chorus]
L-C-S, longest common thread
Matrix building, fill it square by square instead
When they match go diagonal, add one more
When they don't, take maximum from before
Trace it back to find the actual string
L-C-S, that's the algorithm king
[Verse 2]
Initialize borders with zeros clean
First row and column, empty sequence scene
Work through each cell with decision making
Character comparison, no shortcuts taking
Three directions matter when we trace back
Diagonal means match, stay on track
Left or up when values came from there
Reconstruct the answer with focused care
[Chorus]
L-C-S, longest common thread
Matrix building, fill it square by square instead
When they match go diagonal, add one more
When they don't, take maximum from before
Trace it back to find the actual string
L-C-S, that's the algorithm king
[Bridge]
Time complexity quadratic, space the same
Optimization possible, change the game
Rolling arrays save memory when needed
Recursive memoization, elegance succeeded
ABCDGH and AEDFHR as examples
Four letters match, the pattern's so simple
[Verse 3]
Bottom-right corner holds the final count
Backtrack through choices, every step amounts
Build the sequence working in reverse
Character by character, none adverse
Applications everywhere you look around
DNA sequencing, differences profound
Version control and plagiarism detection
L-C-S provides the right direction
[Outro]
From empty strings to full comparison
Dynamic programming, perfect companion
Matrix filled with optimal solutions
L-C-S resolves string contributions