[Verse 1]
Started with a problem, data compression on my mind
Files too heavy, bandwidth wasted, gotta optimize my grind
David Huffman had the vision back in fifty-two
Variable length encoding, let me break it down for you
Count the frequency of each symbol in your text
Most common gets the shortest code, that's what comes up next
Build a tree from bottom up, merge the smallest two
Priority queue keeps it sorted, that's the move we do
[Chorus]
Huffman codes, never the same length
Frequent symbols get the shortest strength
Prefix property, no code's a start
Of another code, that's the smart part
Huffman codes, optimal and tight
Binary tree built from left to right
Frequent symbols get the shortest strength
That's how we compress with Huffman codes
[Verse 2]
Take your symbols, count them up, put frequencies in nodes
Smallest values at the front, that's how the algorithm goes
Create internal nodes by merging pairs of leaves
Zero goes left, one goes right, building what we need
Keep combining till you got a single root on top
Read the path from root to leaf, that's where the codes stop
Longer paths for rare symbols, shorter for the frequent
This greedy method guarantees the result's efficient
[Chorus]
Huffman codes, never the same length
Frequent symbols get the shortest strength
Prefix property, no code's a start
Of another code, that's the smart part
Huffman codes, optimal and tight
Binary tree built from left to right
Frequent symbols get the shortest strength
That's how we compress with Huffman codes
[Bridge]
Decoding's easy when you got the tree
Follow each bit till you reach a leaf
No ambiguity in what you read
Prefix-free codes are all you need
From JPEG to ZIP files everywhere
Huffman's legacy is in the air
[Verse 3]
Real world applications got this algorithm paid
Text compression, image formats, everywhere it's made
The beauty's in the mathematics, provably optimal
When symbols are independent, results are just phenomenal
Time complexity's O of n log n to build the tree
Space complexity linear, memory stays free
Adaptive versions modify as new data flows
Static or dynamic, Huffman coding always knows
[Outro]
From the bottom to the top, merge the frequencies
Build the tree, extract the codes, compress with expertise
Huffman coding in your toolkit, data structure mastery
Variable length perfection, that's the legacy