Huffman coding

A simple way of reducing the size of a block of data is to replace the most common words with shorter ones that are not already used in the data. It is possible to reconstruct the original data using a dictionary that lists the short words and the longer words they replace.

The problem is to decide which codes to use, David A. Huffman found the optimal way of generating codes that guarantees the shortest possible output.

Count the number of times each word occurs in the data, this will be a histogram

do
  Find the two active nodes with the lowest count, these are the parents
  Create a new child node and link it to each of the two parent nodes, let it contain the sum of the two parents
  Mark the two parent nodes as as inactive
loop until only one active node remains

We will now have a binary tree structure.

Example

"Hello World"

Histogram:
'H' 1
'e' 1
'l' 3
'o' 2
'W' 1
'r' 1
'd' 1
' ' 1

1 1 1 1 1 1 2 3
\ / \ / \ / | |
 2   2   2  | |
  \ /     \ / |
   4       4  |
    \       \ /
     \	      7
      \     / 
       \   /
         11