.. _Huffman:

.. raw:: html

   <script>ODSA.SETTINGS.DISP_MOD_COMP = true;ODSA.SETTINGS.MODULE_NAME = "Huffman";ODSA.SETTINGS.MODULE_LONG_NAME = "Huffman Coding";ODSA.SETTINGS.MODULE_CHAPTER = "Binary Trees"; ODSA.SETTINGS.BUILD_DATE = "2020-08-23 13:21:52"; ODSA.SETTINGS.BUILD_CMAP = false;JSAV_OPTIONS['lang']='en';JSAV_EXERCISE_OPTIONS['code']='java';</script>


.. |--| unicode:: U+2013   .. en dash
.. |---| unicode:: U+2014  .. em dash, trimming surrounding whitespace
   :trim:



.. odsalink:: AV/Binary/huffmanCON.css
.. This file is part of the OpenDSA eTextbook project. See
.. http://opendsa.org for more details.
.. Copyright (c) 2012-2020 by the OpenDSA Project Contributors, and
.. distributed under an MIT open source license.

.. avmetadata::
   :author: Cliff Shaffer

.. odsalink:: DataStructures/huffman.css


==============
Huffman Coding
==============

Huffman Coding
--------------

Coding
~~~~~~
   * ASCII codes are fixed length (7 + 1 bits)
      * In general, $n$ bits can store $2^n$ codes
   * An alternative is variable-length coding

   * The relative frequencies for eight selected letters.

      .. math::

         \begin{array}{|c|cccccccc|}
         \hline
         \textrm Letter & C & D & E & K & L & M & U & Z\\
         \textrm Frequency & 32 & 42 & 120 & 7 & 42 & 24 & 37 & 2\\
         \hline
         \end{array}

Huffman Coding Trees
~~~~~~~~~~~~~~~~~~~~
   .. inlineav:: huffmanBuildCON ss
      :long_name: Huffman Coding Tree Slideshow: Build
      :output: show


Assigning Codes
~~~~~~~~~~~~~~~
   .. inlineav:: huffmanLabelCON ss 
      :long_name: Huffman Coding Tree Slideshow: Label Edges
      :output: show


Using Codes
~~~~~~~~~~~
   .. inlineav:: huffmanCodesCON ss 
      :long_name: Huffman Coding Tree Slideshow: Setting Codes
      :output: show


Decoding
~~~~~~~~
   .. inlineav:: huffmanDecodeCON ss
      :long_name: Huffman Coding Tree Slideshow: Decoding
      :output: show

.. odsascript:: DataStructures/huffman.js
.. odsascript:: AV/Binary/huffmanBuildCON.js
.. odsascript:: AV/Binary/huffmanLabelCON.js
.. odsascript:: AV/Binary/huffmanCodesCON.js
.. odsascript:: AV/Binary/huffmanDecodeCON.js