[Verse 1]
Two sequences sprawled across my screen tonight
String one holds "ABCDGH", string two "AEDFHR"
Need to excavate the buried treasure hiding
Longest common thread that weaves through both
Dynamic programming table spreads like chess
Grid dimensions match the lengths plus one
Each cell holds secrets of the choice behind
Bottom-up construction reveals the pattern
[Chorus]
LCS, decode the mystery
Table builds the history
If letters match, diagonal plus one
If different, take the maximum fun
Memoize to optimize the grind
Trace back the path you'll always find
Common subsequence crystallized
Through the matrix memorized
[Verse 2]
Position i and j mark coordinates clean
Compare characters at each intersection
Match found? Grab diagonal value, add one more
Mismatch means choose left or up, whichever's greater
Fill the grid from zero to the boundary edge
Final cell contains the golden answer length
But length alone won't satisfy the hunger
Reconstruction backward tells the story whole
[Chorus]
LCS, decode the mystery
Table builds the history
If letters match, diagonal plus one
If different, take the maximum fun
Memoize to optimize the grind
Trace back the path you'll always find
Common subsequence crystallized
Through the matrix memorized
[Bridge]
Start from bottom right corner of success
When values match, diagonal retreat
Add that character to result string growing
When unequal, follow larger neighbor's beat
Time complexity quadratic in the worst
Space can shrink to linear with technique
Applications bloom in diff tools and DNA
Edit distance cousin shares the same mystique
[Verse 3]
Recursive solution spawns exponential doom
Overlapping subproblems cry for rescue
Tabulation saves computed values fresh
Top-down memoization caches recursive calls
From biology to version control systems
Plagiarism detection, file comparison tools
Algorithm foundation proves its worth
Substring consecutive, subsequence scattered free
[Chorus]
LCS, decode the mystery
Table builds the history
If letters match, diagonal plus one
If different, take the maximum fun
Memoize to optimize the grind
Trace back the path you'll always find
Common subsequence crystallized
Through the matrix memorized
[Outro]
Matrix holds the wisdom of shared symbols
Trace the breadcrumbs backward to the source
Longest common subsequence decoded
Dynamic programming shows its force