Lesson 199
Huffman Coding & Compression
Optimal Prefix Codes · The Entropy Limit
1:00How the greedy Huffman tree assigns optimal prefix-free codes — giving frequent symbols fewer bits — and why you can never compress everything.
By the end, you can
- Explain why giving frequent symbols shorter codes reduces total message size.
- Describe the prefix-free property and why it is necessary for unambiguous decoding.
- Trace the greedy Huffman merge sequence for a small frequency table.
- Read Huffman codes off a binary tree (left = 0, right = 1) and decode a bit stream.
- Compute the total bits used by a Huffman encoding and compare it to a fixed-length baseline.
- State the O(n log n) complexity of Huffman tree construction and identify the role of the min-heap.
- Relate Huffman's average code length to Shannon entropy and explain why L lands in [H, H+1).
- Distinguish lossless from lossy compression and give examples of each.
- Explain using the pigeonhole principle why no lossless compressor can shorten every file.
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