The Lempel-Ziv-Welch Algorithm
			~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Notation
~~~~~~~~
 Each string W in the table is represented by a pair (C,K), where K is the
 last character in W and C is the location in the table of the prefix of W
 that contains all but the last character.  By convention, the null string is
 at location EMPTY; and the components of the pair in location I are denoted
 by PREF(I) and CHAR(I).

Compression
~~~~~~~~~~~
 Initialize the string table to contain the pair (EMPTY,K) for each char K

 C = EMPTY
 While ((K = getchar()) != EOF)
     If the pair (C,K) is in the table
     Then
	 Set C = code associated with the pair (C,K) in the table
     Else
	 Output code C
	 Insert the pair (C,K) into the table
	 Set C = code associated with the pair (EMPTY,K) in the table

 Output code C (if C != EMPTY)

Decompression
~~~~~~~~~~~~~
 Initialize the string table to contain the pair (EMPTY,K) for each char K

 // Version where strings are inserted  | // Version where strings are inserted
 // in table with UNKNOWN CHAR fields   | // only after CHAR field is known
					|
 While ((newC = C = getcode()) != EOF)  | oldC = EMPTY
     If CHAR(C) == UNKNOWN              | While ((newC = C = getcode()) != EOF)
     Then                               |     If C is an unknown code
	 Push finalK onto Kstack        |     Then
	 C = PREF(C)                    |         Push finalK onto Kstack
					|         C = oldC
     While PREF(C) != EMPTY             |
	 Push CHAR(C) onto Kstack       |     While PREF(C) != EMPTY
	 C = PREF(C)                    |         Push CHAR(C) onto Kstack
					|         C = PREF(C)
     finalK = CHAR(C)                   |
     putchar(finalK)                    |     finalK = CHAR(C)
					|     putchar(finalK)
     While Kstack is nonempty           |
	 Pop K off Kstack               |     While Kstack is nonempty
	 putchar(K)                     |         Pop K off Kstack
					|         putchar(K)
     If the CHAR field of the last code |
       assigned is UNKNOWN              |     If oldC != EMPTY
	 Replace it by finalK           |         Insert the pair (oldC,finalK)
     Insert the pair (newC,UNKNOWN)     |           into the table
       into the table                   |     oldC = newC

Example (with EMPTY = 0)
~~~~~~~~~~~~~~~~~~~~~~~~
  Message:      a  b  a  b  c  b  a  b  a  b  a  a  a  a  a  a  a  ...
  Encoding:     1  2     4  3     5        8  1    10       11     ...

  String Table:
    C PREF CHAR String    C PREF CHAR String    C PREF CHAR String    ...
    1   0    a   a        5   2    a   ba       9   8    a   baba
    2   0    b   b        6   4    c   abc     10   1    a   aa
    3   0    c   c        7   3    b   cb      11  10    a   aaa
    4   1    b   ab       8   5    b   bab     12  11    a   aaaa

								CS-323-08/13/19