Burrows–Wheeler transform

Burrows–Wheeler transform is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

This page uses content from Wikipedia. The original article was at Burrows–Wheeler_transform. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

The Burrows–Wheeler transform (BWT, also called block-sorting compression) rearranges a character string into runs of similar characters. This is useful for compression, since it tends to be easy to compress a string that has runs of repeated characters by techniques such as move-to-front transform and run-length encoding. More importantly, the transformation is reversible, without needing to store any additional data. The BWT is thus a "free" method of improving the efficiency of text compression algorithms, costing only some extra computation.

Source: Burrows–Wheeler transform

Go

Translation of: Python

<lang go>package main

import (

   "fmt"
   "sort"
   "strings"

)

const stx = "\002" const etx = "\003"

func bwt(s string) (string, error) {

   if strings.Index(s, stx) >= 0 || strings.Index(s, etx) >= 0 {
       return "", fmt.Errorf("String can't contain STX or ETX")
   }
   s = stx + s + etx
   le := len(s)
   table := make([]string, le)
   table[0] = s
   for i := 1; i < le; i++ {
       table[i] = s[i:] + s[:i]
   }
   sort.Strings(table)
   lastBytes := make([]byte, le)
   for i := 0; i < le; i++ {
       lastBytes[i] = table[i][le-1]
   }
   return string(lastBytes), nil

}

func ibwt(r string) string {

   le := len(r)
   table := make([]string, le)
   for range table {
       for i := 0; i < le; i++ {
           table[i] = r[i:i+1] + table[i]
       }
       sort.Strings(table)
   }
   for _, row := range table {
       if strings.HasSuffix(row, etx) {
           return row[1 : le-1]
       }
   }
   return ""

}

func makePrintable(s string) string {

   // substitute ^ for STX and | for ETX to print results
   t := strings.Replace(s, stx, "^", 1)
   return strings.Replace(t, etx, "|", 1)

}

func main() {

   tests := []string{
       "banana",
       "appellee",
       "dogwood",
       "TO BE OR NOT TO BE OR WANT TO BE OR NOT?",
       "SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES",
       "\002ABC\003",
   }
   for _, test := range tests {
       fmt.Println(makePrintable(test))
       fmt.Print(" --> ")
       t, err := bwt(test)
       if err != nil {
           fmt.Println("ERROR:", err)
       } else {
           fmt.Println(makePrintable(t))
       }
       r := ibwt(t)
       fmt.Println(" -->", r, "\n")
   }

}</lang>

Output:

banana
 --> |annb^aa
 --> banana 

appellee
 --> |e^elplepa
 --> appellee 

dogwood
 --> |do^oodwg
 --> dogwood 

TO BE OR NOT TO BE OR WANT TO BE OR NOT?
 --> |?OOORREEETTRTW   BBB  ATTT   NNOOONOO^   
 --> TO BE OR NOT TO BE OR WANT TO BE OR NOT? 

SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES
 --> |STEXYDST.E.IXXIIXXSSMPPS.B..EE.^.USFXDIIOIIIT
 --> SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES 

^ABC|
 --> ERROR: String can't contain STX or ETX
 -->  

Kotlin

Translation of: Python

<lang scala>// Version 1.2.60

const val STX = "\u0002" const val ETX = "\u0003"

fun bwt(s: String): String {

   if (s.contains(STX) || s.contains(ETX)) {
       throw RuntimeException("String can't contain STX or ETX")
   }
   val ss = STX + s + ETX
   val table = Array<String>(ss.length) { ss.substring(it) + ss.substring(0, it) }
   table.sort()
   return String(table.map { it[it.lastIndex] }.toCharArray())

}

fun ibwt(r: String): String {

   val len = r.length
   val table = Array<String>(len) { "" }
   repeat(len) {
       for (i in 0 until len) {
           table[i] = r[i].toString() + table[i]
       }
       table.sort()
   }
   for (row in table) {
       if (row.endsWith(ETX)) {
           return row.substring(1, len - 1)
       }
   }
   return ""

}

fun makePrintable(s: String): String {

   // substitute ^ for STX and | for ETX to print results
   return s.replace(STX, "^").replace(ETX, "|")

}

fun main(args: Array<String>) {

   val tests = listOf(
       "banana",
       "appellee",
       "dogwood",
       "TO BE OR NOT TO BE OR WANT TO BE OR NOT?",
       "SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES",
       "\u0002ABC\u0003"
   )
   for (test in tests) {
       println(makePrintable(test))
       print(" --> ")
       var t = ""
       try {
           t = bwt(test)
           println(makePrintable(t))
       }
       catch (ex: RuntimeException) {
           println("ERROR: " + ex.message)
       }
       val r = ibwt(t)
       println(" --> $r\n")
   }

}</lang>

Output:

banana
 --> |annb^aa
 --> banana

appellee
 --> |e^elplepa
 --> appellee

dogwood
 --> |do^oodwg
 --> dogwood

TO BE OR NOT TO BE OR WANT TO BE OR NOT?
 --> |?OOORREEETTRTW   BBB  ATTT   NNOOONOO^   
 --> TO BE OR NOT TO BE OR WANT TO BE OR NOT?

SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES
 --> |STEXYDST.E.IXXIIXXSSMPPS.B..EE.^.USFXDIIOIIIT
 --> SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES

^ABC|
 --> ERROR: String can't contain STX or ETX
 --> 

Perl 6

Works with: Rakudo version 2018.06

<lang perl6># STX and ETX can be any characters that don't appear

1. in the text as long as STX sorts before ETX.

constant \STX = '👍'; constant \ETX = '👎';

1. Burrows-Wheeler transform

sub transform (Str $s is copy) {

   die "String can't contain STX or ETX characters." if $s.contains: STX|ETX;
   $s = STX ~ $s ~ ETX;
   my $l = $s.chars;
   (^$l).map({ $s.comb.list.rotate: $_ }).sort[*;*-1].join

}

1. Burrows-Wheeler inverse transform

sub ɯɹoɟsuɐɹʇ (Str $s) {

   my @t =  xx my $l = $s.chars;
   @t = ($s.comb Z~ @t).sort for ^$l;
   @t.first( *.starts-with: STX ).substr(1, $l - 2)

}

1. TESTING

for |<BANANA dogwood SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES>,

   'TO BE OR NOT TO BE OR WANT TO BE OR NOT?', "Oops{STX}"
   -> $phrase {
   say 'Original:            ', $phrase;
   say 'Transformed:         ', transform $phrase;
   say 'Inverse transformed: ', ɯɹoɟsuɐɹʇ transform $phrase;
   say ;

}</lang>

Output:

Original:            BANANA
Transformed:         BNN👍AA👎A
Inverse transformed: BANANA

Original:            dogwood
Transformed:         👍ooodwg👎d
Inverse transformed: dogwood

Original:            SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES
Transformed:         TEXYDST.E.IXIXIXXSSMPPS.B..E.👍.UESFXDIIOIIIT👎S
Inverse transformed: SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES

Original:            TO BE OR NOT TO BE OR WANT TO BE OR NOT?
Transformed:         OOORREEETTRTW   BBB  ATTT   NNOOONOO👍   👎?
Inverse transformed: TO BE OR NOT TO BE OR WANT TO BE OR NOT?

Original:            Oops👍
String can't contain STX or ETX characters.
  in sub transform at bwt.p6 line 9
  in block <unit> at bwt.p6 line 27

Python

This Python implementation sacrifices speed for simplicity: the program is short, but takes more than the linear time that would be desired in a practical implementation.

Using the STX/ETX control codes to mark the start and end of the text, and using s[i:] + s[:i] to construct the ith rotation of s, the forward transform takes the last character of each of the sorted rows. The inverse transform repeatedly inserts r as the left column of the table and sorts the table. After the whole table is built, it returns the row that ends with ETX, minus the STX and ETX.

<lang Python> def bwt(s):

   """Apply Burrows-Wheeler transform to input string."""
   assert "\002" not in s and "\003" not in s, "Input string cannot contain STX and ETX characters"
   s = "\002" + s + "\003"  # Add start and end of text marker
   table = sorted(s[i:] + s[:i] for i in range(len(s)))  # Table of rotations of string
   last_column = [row[-1:] for row in table]  # Last characters of each row
   return "".join(last_column)  # Convert list of characters into string

def ibwt(r):

   """Apply inverse Burrows-Wheeler transform."""
   table = [""] * len(r)  # Make empty table
   for i in range(len(r)):
       table = sorted(r[i] + table[i] for i in range(len(r)))  # Add a column of r
   s = [row for row in table if row.endswith("\003")][0]  # Find the correct row (ending in ETX)
   return s.rstrip("\003").strip("\002")  # Get rid of start and end markers

</lang>

Sidef

Translation of: Python

<lang ruby>class BurrowsWheelerTransform (String L = "\002") {

   method encode(String s) {
       assert(!s.contains(L), "String cannot contain `#{L.dump}`")
       s = (L + s)
       s.len.of{|i| s.substr(i) + s.substr(0, i) }.sort.map{.last}.join
   }

   method decode(String s) {
       var t = s.len.of("")
       var c = s.chars
       { t = (c »+« t).sort } * s.len
       t.first { .begins_with(L) }.substr(L.len)
   }

}

var tests = [

   "banana", "appellee", "dogwood", "TOBEORNOTTOBEORTOBEORNOT"
   "SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES",

]

var bwt = BurrowsWheelerTransform(L: '$')

tests.each { |str|

   var enc = bwt.encode(str)
   var dec = bwt.decode(enc)
   say "BWT(#{dec.dump}) = #{enc.dump}"
   assert_eq(str, dec)

}</lang>

Output:

BWT("banana") = "annb$aa"
BWT("appellee") = "e$elplepa"
BWT("dogwood") = "do$oodwg"
BWT("TOBEORNOTTOBEORTOBEORNOT") = "TOOOBBBRRTTTEEENNOOOOR$TO"
BWT("SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES") = "STEXYDST.E.IXXIIXXSSMPPS.B..EE.$.USFXDIIOIIIT"

zkl

<lang zkl>class BurrowsWheelerTransform{

  fcn init(chr="$"){ var special=chr; }
  fcn encode(str){
     _assert_(not str.holds(special), "String cannot contain char \"%s\"".fmt(special) );
     str=str.append(special);
     str.len().pump(List().merge,'wrap(n){ String(str[n,*],str[0,n]) })
     .pump(String,T("get",-1));	// last char of each "permutation"
  }
  fcn decode(str){      
     table:=List.createLong(str.len(),"");	// ("",""..), mutable
     do(str.len()){

foreach n in (str.len()){ table[n]=str[n] + table[n] } table.sort();

     }   // --> ("$dogwood","d$dogwoo","dogwood$",...)
     table.filter1("%s*".fmt(special).glob)[1,*];  // str[0]==$, often first element
  }

}</lang> <lang zkl>BWT:=BurrowsWheelerTransform(); //BWT.encode("$"); // --> assert(bbb.zkl:25): String cannot contain char "$"

tests:=T(

   "banana", "appellee", "dogwood", "TO BE OR NOT TO BE OR WANT TO BE OR NOT?",
   "SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES",);

foreach test in (tests){

  enc:=BWT.encode(test);
  println("%s\n  -->%s\n  -->%s".fmt(test,enc,BWT.decode(enc)));

}</lang>

Output:

banana
  -->annb$aa
  -->banana
appellee
  -->e$elplepa
  -->appellee
dogwood
  -->do$oodwg
  -->dogwood
TO BE OR NOT TO BE OR WANT TO BE OR NOT?
  -->OOORREEETTR?TW   BBB  ATTT   NNOOONOO$   
  -->TO BE OR NOT TO BE OR WANT TO BE OR NOT?
SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES
  -->STEXYDST.E.IXXIIXXSSMPPS.B..EE.$.USFXDIIOIIIT
  -->SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES