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by Harlan

Huffman Coding is a common form of data compression where none of the original
data gets lost.  It begins by analyzing a string of data to determine which
pieces occur with the highest frequencies.  These frequencies and pieces are
used to construct a binary tree.  It is the °»path°… from root node to the
leaf with this data that forms its encoding.  The following example should
explain things:

	Data:  ABRRKBAARAA (11 bytes)
	
	Frequency counts:
	A  5
	R  3
	B  2
	K  1
	
	In Huffman Tree form, with frequency weights in parentheses:
	     ARBK (11)
	    /    \  
	   0      1
	  /        \
	A (5)      RBK (6)
	          /   \
	         0     1
	        /       \
	      R (3)     BK (3)
	                / \
	               0   1
	              /     \
	            B (2)   K (1)
	
	The encoding for each character is simply the path to that character:
	A    0
	R   10
	B  110
	K  111
	
	Here is the original data encoded:
	01101010 11111000 1000 (fits in 3 bytes)

We have compressed the original information by 80%!

A key point to note is that every character encoding has a unique prefix,
corresponding to the unique path to that character within the tree.  If this
were not so, then decoding would be impossible due to ambiguity.

The quiz this time is to write a program to implement a compression program
using Huffman encoding.

	Extra Credit:
	Perform the actual encoding using your tree.  You may encounter one issue
	during the decompression/decoding phase.  Your encoded string may not be a
	multiple of 8.  This means that when you compress your encoding into a
	binary number, padding 0°«s get added.  Then, upon decompression, you may
	see extra characters.  To counter this, one solution is to add your own
	padding of 1 extra character every time.  And then simply strip it off
	once you have decoded.
	
	You may also wish to provide a way to serialize the Huffman Tree so it
	can be shared among copies of your program.
	
	./huffman_encode.rb I want this message to get encoded!
	
	Encoded:
	11111111 11111110 11111111 11101111 10111111
	01100110 11111111 11110111 11111111 11011100
	11111111 11010111 01110111 11011110 10011011
	11111100 11110101 10010111 11101111 11111011
	11111101 11111101 01111111 01111111 11111110
	Encoded Bytes:
	25
	
	Original:
	I want this message to get encoded!
	Original Bytes:
	35
	
	Compressed:  28%