visual-cs

Algorithm Visualizations

Huffman Coding

An optimal prefix-free compression algorithm that assigns shorter bit strings to more frequent symbols. Build the Huffman tree step-by-step, inspect codes, and see live compression statistics.

Priority Queue (min-heap) — Step 0

Press Build to start

Char	Freq	Code	Bits	Contribution

Encoded bits will appear here…

Algorithm Steps

Count frequencies of each symbol in the input.

Create leaf nodes for each symbol and insert into a min-heap.

Extract two minimums, merge into an internal node with combined frequency.

Repeat until one node remains — the Huffman root.

Assign codes: traverse left → 0, right → 1.

Complexity

Build treeO(n log n)

EncodeO(m)

SpaceO(n)

n = unique charsm = input length

Key Properties

🌿

Prefix-free — no code is a prefix of another; decoding is unambiguous.

⚖️

Optimal — minimizes expected code length for a given symbol frequency distribution.

🔢

Greedy — always merges the two least-frequent nodes first.

📦

Lossless — the original data can be fully recovered from the encoded bitstream.