Advanced · Module 16 · Lesson 4 of 4
Huffman coding
Huffman coding gives frequent symbols short bit codes and rare ones long codes, with no code a prefix of another. Repeatedly merging the two rarest subtrees in a heap builds the provably shortest such code.
By the end you can
- Explain prefix-free codes and why they can be decoded without separators
- Build a Huffman tree with a min-heap, read off the codes and compute the encoded size
- Explain why merging the two rarest symbols is optimal, and where Huffman coding is used
Builds on Scheduling and intervals, Top-k and merging streams.
01 · A question first
Text is usually stored with a fixed number of bits per character, but in English the letter e is more than a hundred times as common as z. Giving common letters short codes saves space, but how do you choose codes so that a stream of bits can still be split back into letters unambiguously, and the total is as short as possible?
Make a guess before you read on.
02 · The idea
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What's inside
- Variable-length codes
- Huffman's algorithm
- Why the greedy merge is optimal
- Huffman in the real world
- Limits
- Pseudocode & Multi-Language Implementations (C++, Java, Python)
- Complexity Derivation, Edge Cases & Common Mistakes
03 · Practice
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