- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Huffman Algorithm for t-ary Trees in Data Structure
A simple algorithm
- A collection of n initial Huffman trees is prepared, each of which is a single leaf node. Keep the n trees onto a priority queue organized by weight (frequency).
- Remove or delete the first two trees (the ones with smallest weight). Combine these two trees to create a new tree whose root is associated with the two trees as children, and whose weight is the sum of the weights of the two children trees.
- Keep this new tree into the priority queue.
- Repeat steps 2-3 until and unless all of the partial Huffman trees have been joined into one.
It's a greedy algorithm: at each iteration, the algorithm creates a "greedy" decision to merge the two subtrees with smallest weight. Is it possible for algorithm to give the desired result?
- Lemma: Let x and y be the two lowest frequent characters. There is an optimal code tree in which x and y are siblings whose depth is minimum as any other leaf nodes in the tree.
- Theorem: Huffman codes are treated as optimal prefix-free binary codes (The greedy algorithm constructs the Huffman tree with the minimum external path weight for a given set of letters).
Advertisements