Given a symbol table of a ''zero-indexed'' array of all possible input symbols
[[wp:Move-to-front transform|this algorithm]] reversibly transforms a sequence
of input symbols into an array of output numbers (indices).<br>
The transform in many cases acts to give frequently repeated input symbols
lower indices which is [[wp:Move-to-front_transform#Use_in_practical_data_compression_algorithms| useful in some compression algorithms]].

;Encoding algorithm:
<pre>
    for each symbol of the input sequence:
        output the index of the symbol in the symbol table
        move that symbol to the front of the symbol table
</pre>

;Decoding algorithm:
<pre>
    # Using the same starting symbol table
    for each index of the input sequence:
        output the symbol at that index of the symbol table
        move that symbol to the front of the symbol table
</pre>

;Example:
Encoding the string of character symbols 'broood' using a symbol table of
the characters 'a'-to-'z'

{| class="wikitable" border="1"
|-
! Input
! Output
! SymbolTable
|-
| '''b'''roood
| 1
| 'abcdefghijklmnopqrstuvwxyz'
|-
| b'''r'''oood
| 1 17
| 'bacdefghijklmnopqrstuvwxyz'
|-
| br'''o'''ood
| 1 17 15
| 'rbacdefghijklmnopqstuvwxyz'
|-
| bro'''o'''od
| 1 17 15 0
| 'orbacdefghijklmnpqstuvwxyz'
|-
| broo'''o'''d
| 1 17 15 0 0
| 'orbacdefghijklmnpqstuvwxyz'
|-
| brooo'''d'''
| 1 17 15 0 0 5
| 'orbacdefghijklmnpqstuvwxyz'
|}

Decoding the indices back to the original symbol order:
{| class="wikitable" border="1"
|-
! Input
! Output
! SymbolTable
|-
|  '''1''' 17 15 0 0 5
| b
| 'abcdefghijklmnopqrstuvwxyz'
|-
| 1 '''17''' 15 0 0 5
| br
| 'bacdefghijklmnopqrstuvwxyz'
|-
| 1 17 '''15''' 0 0 5
| bro
| 'rbacdefghijklmnopqstuvwxyz'
|-
| 1 17 15 '''0''' 0 5
| broo
| 'orbacdefghijklmnpqstuvwxyz'
|-
| 1 17 15 0 '''0''' 5
| brooo
| 'orbacdefghijklmnpqstuvwxyz'
|-
| 1 17 15 0 0 '''5'''
| broood
| 'orbacdefghijklmnpqstuvwxyz'
|}

;Task:
* Encode and decode the following three strings of characters using the symbol table of the characters 'a'-to-'z' as above.
* Show the strings and their encoding here.
* Add a check to ensure that the decoded string is the same as the original.

<br>
The strings are:

   <big> broood       </big>
   <big> bananaaa     </big>
   <big> hiphophiphop </big>

(Note the spellings.)
<br><br>