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Huffman / Data Compression Ladder

This lane is for the first time a greedy problem is really about optimal merge trees and weighted code depth, not about a left-to-right feasibility scan.

Who This Is For

Use this lane if:

  • Greedy overview already feels familiar
  • heaps do not scare you anymore
  • you want the classical Huffman route itself, not one industrial compression format

This lane is intentionally narrow:

Warm-Up

  • explain why every merge increases weighted path length by the merged weight
  • explain why the two smallest weights can be merged first in some optimal tree
  • explain why multiple code assignments may exist under ties even when the optimal cost is fixed

Target skill:

  • recognize when the real lesson is optimal merge / prefix code, not just use a priority queue

Core

  • min-heap over current subtree weights
  • deterministic tie-break for reproducible code assignment
  • merge-sum view of the objective
  • leaf-depth DFS for explicit codewords
  • exact flagship rep: Huffman Coding Benchmark

Target skill:

  • trust the heap-based Huffman route and know exactly what it does and does not try to cover

Stretch

  • compare against Prefix Constraints so merge-greedy and scan-greedy stay separate
  • compare against Heaps And Ordered Sets so PQ mechanics and optimality proof do not blur together
  • reopen full data-compression context only after the coding tree itself feels automatic

Target skill:

  • separate optimal prefix code construction from the rest of the repo's greedy family

Retrieval Layer

Repo Anchors And Compare Points

Exit Criteria

You are ready to move on when:

  • you can justify the two-smallest merge step
  • you can compute the answer both as merge sums and as weighted leaf depths
  • you know why this lane is not a production compression-engine lane

External Practice