de Bruijn sequences

From Rosetta Code
Task
De Bruijn sequences
You are encouraged to solve this task according to the task description, using any language you may know.

The sequences are named after the Dutch mathematician   Nicolaas Govert de Bruijn.


A note on Dutch capitalization:   Nicolaas' last name is   de Bruijn,   the   de   isn't normally capitalized unless it's the first word in a sentence.   Rosetta Code (more or less by default or by fiat) requires the first word in the task name to be capitalized.


In combinatorial mathematics,   a   de Bruijn sequence   of order   n   on a   size-k   alphabet (computer science)   A   is a cyclic sequence in which every possible   length-n   string (computer science, formal theory)   on   A   occurs exactly once as a contiguous substring.

Such a sequence is denoted by   B(k, n)   and has length   kn,   which is also the number of distinct substrings of length   n   on   A;    
de Bruijn sequences are therefore optimally short.

There are:

                         (k!)k(n-1)   ÷   kn

distinct de Bruijn sequences   B(k, n).


Task

For this Rosetta Code task,   a   de Bruijn   sequence is to be generated that can be used to shorten a brute-force attack on a   PIN-like   code lock that does not have an "enter" key and accepts the last   n   digits entered.


Note:   automated teller machines (ATMs)   used to work like this,   but their software has been updated to not allow a brute-force attack.


Example

A   digital door lock   with a 4-digit code would have B (10, 4) solutions,   with a length of   10,000   (digits).

Therefore, only at most     10,000 + 3     (as the solutions are cyclic or wrap-around)   presses are needed to open the lock.

Trying all 4-digit codes separately would require   4 × 10,000   or   40,000   presses.


Task requirements
  •   Generate a de Bruijn sequence for a 4-digit (decimal) PIN code.
  •   Show the length of the generated de Bruijn sequence.
  •   (There are many possible de Bruijn sequences that solve this task,   one solution is shown on the discussion page).
  •   Show the first and last   130   digits of the de Bruijn sequence.
  •   Verify that all four-digit (decimal)   1,000   PIN codes are contained within the de Bruijn sequence.
  •   0000, 0001, 0002, 0003,   ...   9996, 9997, 9998, 9999   (note the leading zeros).
  •   Reverse the de Bruijn sequence.
  •   Again, perform the (above) verification test.
  •   Replace the 4,444th digit with a period (.) in the original de Bruijn sequence.
  •   Perform the verification test (again).   There should be four PIN codes missing.


(The last requirement is to ensure that the verification tests performs correctly.   The verification processes should list any and all missing PIN codes.)

Show all output here, on this page.

Other tasks related to string operations:
Metrics
Counting
Remove/replace
Anagrams/Derangements/shuffling
Find/Search/Determine
Formatting
Song lyrics/poems/Mad Libs/phrases
Tokenize
Sequences


References



11l[edit]

Translation of: D
V digits = ‘0123456789’

F deBruijn(k, n)
   V alphabet = :digits[0 .< k]
   V a = [Byte(0)] * (k * n)
   [Byte] seq

   F db(Int t, Int p) -> N
      I t > @n
         I @n % p == 0
            @seq.extend(@a[1 .< p + 1])
      E
         @a[t] = @a[t - p]
         @db(t + 1, p)
         V j = @a[t - p] + 1
         L j < @k
            @a[t] = j [&] F'F
            @db(t + 1, t)
            j++

   db(1, 1)
   V buf = ‘’
   L(i) seq
      buf ‘’= alphabet[i]

   R buf‘’buf[0 .< n - 1]

F validate(db)
   V found = [0] * 10'000
   [String] errs

   L(i) 0 .< db.len - 3
      V s = db[i .< i + 4]
      I s.is_digit()
         found[Int(s)]++

   L(i) 10'000
      I found[i] == 0
         errs [+]= ‘    PIN number #04 missing’.format(i)
      E I found[i] > 1
         errs [+]= ‘    PIN number #04 occurs #. times’.format(i, found[i])

   I errs.empty
      print(‘  No errors found’)
   E
      V pl = I errs.len == 1 {‘’} E ‘s’
      print(‘  ’String(errs.len)‘ error’pl‘ found:’)
      L(err) errs
         print(err)

V db = deBruijn(10, 4)

print(‘The length of the de Bruijn sequence is ’db.len)
print("\nThe first 130 digits of the de Bruijn sequence are: "db[0.<130])
print("\nThe last 130 digits of the de Bruijn sequence are: "db[(len)-130..])

print("\nValidating the deBruijn sequence:")
validate(db)

print("\nValidating the reversed deBruijn sequence:")
validate(reversed(db))

db[4443] = ‘.’
print("\nValidating the overlaid deBruijn sequence:")
validate(db)
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the deBruijn sequence:
  No errors found

Validating the reversed deBruijn sequence:
  No errors found

Validating the overlaid deBruijn sequence:
  4 errors found:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

8080 Assembly[edit]

bdos:	equ	5	; BDOS entry point	
putch:	equ	2	; Write character to console
puts:	equ	9	; Write string to console
	org	100h
	lhld	bdos+1	; Put stack at highest usable address
	sphl
	;;;	Generate de_bruijn(10,4) ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	mvi	c,40	; Zero out a[]
	xra	a
	lxi	d,arr
zloop:	stax	d
	inx	d
	dcr	c
	jnz	zloop
	lxi	h,seq	; H = start of sequence
	lxi	b,0101h	; db(1,1)
	call	db_
	lxi	d,seq	; Allow wrap-around by appending first 3 digits
	mvi	c,3
wrap:	ldax	d	; get one of first digits
	mov	m,a	; store after last digit
	inx	d	; advance pointers
	inx	h
	dcr	c	; do this 3 times
	jnz	wrap
	push	h	; store end of data
	;;;	Print length ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	lxi	d,slen	; print "Length: "
	call	pstr
	lxi 	d,-seq	; calculate length (-seq+seqEnd)
	dad	d
	call	puthl	; print length
	call	pnl	; print newline
	;;;	Print first and last 130 digits ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	lxi	d,sfrst	; print "First 130: "
	call	pstr
	lxi 	h,seq	; print first 130 digits
	call	p130
	call	pnl	; print newline
	lxi	d,slast	; print "Last 130: "
	call	pstr
	pop	h	; Get end of sequence
	push	h
	lxi	d,-130	; 130th last digit 
	dad	d
	call	p130	; print last 130 digits
	call	pnl
	call	verify	; verify that all numbers are there
	;;;	Reverse and verify ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	lxi	d,srev	; Print "reversing..."
	call	pstr
	pop	h	; HL = address of last digit
	dcx	h
	push	h	; stack = address of last digit
	lxi	d,seq	; DE = address of first digit
	call	rvrs	; Reverse
	call	verify	; Verify that all numbers are there
	lxi	d,seq	; Then reverse again (restoring it)
	pop	h
	call	rvrs
	;;;	Replace 4444th digit with '.' and verify ;;;;;;;;;;;;;;;;;;;;;;
	lxi	d,s4444
	call	pstr
	mvi	a,'.'
	sta	seq+4444
	call	verify
	rst	0
	;;;	db(t,p); t,p in B,C; end of sequence in HL ;;;;;;;;;;;;;;;;;;;;
db_:	mov	a,b	; if t>n (n=4)
	cpi	5	; t >= n+1
	jc	dbelse
	mov	a,c	; 4%p==0, for p in {1,2,3,4}, is false iff p=3
	cpi	3
	rz		; stop if p=3, i.e. 4%p<>0
	lxi	d,arr+1	; copy P elements to seq forom arr[1..]
dbextn:	ldax	d	; take from a[]
	mov	m,a	; store in sequence
	inx	h	; advance pointers
	inx	d
	dcr	c	; and do this P times
	jnz	dbextn
	ret
dbelse:	mov	a,b	; t - p
	sub	c
	mvi	d,arr/256
	mov	e,a	; a[] is page-aligned for easier indexing
	ldax	d	; get a[t-p]
	mov	e,b	; store in a[t]
	stax	d
	push	b	; keep T and P 
	inr	b	; db(t+1, p)
	call	db_
	pop	b	; restore T and P
	mov	a,b	; get a[t-p]
	sub	c
	mvi	d,arr/256
	mov	e,a
	ldax	d	; j = a[t-p]
dbloop:	inr	a	; j++
	cpi	10	; reached K = 10?
	rnc		; then stop
	mvi	d,arr/256
	mov	e,b
	stax	d	; a[t] = j
	push	psw	; keep j
	push	b	; keep t and p
	mov	c,b
	inr	b
	call	db_	; db(t+1, t)
	pop	b	; restore t and p
	pop	psw	; restore j
	jmp	dbloop
	;;;	Verify that all numbers are there ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
verify:	lxi	d,sver	; print "Verifying... "
	call	pstr
	mvi	d,0	; Zero out the flag array
	lxi	b,10000	
	lxi	h,val
vzero:	mov	m,d
	inx	h
	dcx	b
	mov	a,b
	ora	c
	jnz	vzero
	lxi	h,seq	; Sequence pointer
donum:	push	h	; Store sequence pointer
	push	h	; Push two copies
	lxi	h,0	; Current 4-digit number
	mvi	c,4	; Number has 4 digits
dgtadd:	mov	d,h	; HL *= 10 
	mov	e,l
	dad	h
	dad	h
	dad	d
	dad	h
	xthl		; Get sequence pointer
	mov	a,m	; Get digit
	inx	h	; Advance pointer
	cpi	10	; Valid digit?
	jnc	dinval	; If not, go do next 4-digit number
	xthl		; Back to number
	mov	e,a
	mvi	d,0
	dad	d	; Add digit to number
	dcr	c	; More digits?
	jnz	dgtadd	; Then get digit
	lxi	d,val	; HL is now the current 4-digit number
	dad	d
	inr	m 	; val[HL]++ (we've seen it)
dinval:	pop	h	; Pointer to after last valid digit
	pop	h	; Pointer to start of current number
	inx	h	; Get 4-digit number that starts at next digit	
	mov	d,h	; Next pointer in DE
	mov	e,l
	lxi	b,-(seq+10000)	; Are we there yet?
	dad	b
	mov	a,h
	ora	l
	xchg		; Next pointer back in HL
	jnz	donum	; If not done, do next number. 
	lxi	h,val	; Done - get start of validation array
	mvi	b,0	; B will be set if one is missing
vnum:	mov	a,m	; Have we seen HL-val?
	ana	a 	
	jnz	vnext	; If so, do the next number
	push	h	; Otherwise, keep current address,
	lxi	d,-val	; Subtract val (to get the number)
	dad	d
	call	puthl	; Print this number as being missing
	mvi	b,1	; Set B,
	pop 	h	; and then restore the address
vnext:	inx	h	; Increment the number
	push	h
	lxi	d,-(val+10000)	; Are we there yet?
	dad	d
	mov	a,h
	ora	l
	pop	h
	jnz	vnum	; If not, check next number.
	dcr	b	; At the end, if B was not set,
	lxi	d,snone	; print "none missing",
	jnz	pstr
	lxi	d,smiss	; otherwise, print "missing"
	jmp	pstr
	;;;	Subroutines ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	;;;	reverse memory starting at DE and ending at HL
rvrs:	mov	b,m	; Load [HL]
	ldax	d	; Load [DE]
	mov	m,a	; [HL] = old [DE]
	mov	a,b
	stax	d	; [DE] = old [HL]
	inx	d	; Move bottom pointer upwards,
	dcx	h	; Move top pointer downwards,
	mov	a,d	; D<H = not there yet
	cmp	h
	jc	rvrs
	mov	a,e	; E<L = not there yet
	cmp	l
	jc	rvrs
	ret
	;;;	print number in HL, saving registers
puthl:	push	h	; save registers
	push	d
	push	b
	lxi	b,nbuf	; number buffer pointer
	push	b	; keep it on the stack
dgt:	lxi	b,-10
	lxi	d,-1
dgtdiv:	inx	d	; calculate digit
	dad	b
	jc	dgtdiv
	mvi	a,'0'+10
	add	l
	pop	h	; get pointer from stack
	dcx	h	; go to previous digit
	mov	m,a	; store digit
	push	h 	; put pointer back
	xchg		; are there any more digits?
	mov	a,h
	ora	l
	jnz	dgt	; if so, calculate next digit
	pop	d 	; otherwise, get pointer to first digit
	jmp	pstr_	; and print the resulting string	
	;;;	print 130 digits from the sequence, starting at HL
p130:	push	h
	push	d
	push	b
	mvi	b,130	; 130 digits
p130l:	mov	a,m	; get current digit
	adi 	'0'	; make ASCII
	inx	h	; advance pointer
	push	b	; save pointer and counter
	push	h
	mvi	c,putch	; print character
	mov	e,a
	call	bdos
	pop	h	; restore pointer and counter
	pop	b
	dcr	b	; one fewer character left
	jnz	p130l	; if characters left, print next
	jmp	rsreg	; otherwise, restore registers and return
	;;;	print newline
pnl:	lxi	d,snl
	;;;	print string in DE, saving registers
pstr:	push	h	; store registers
	push	d
	push 	b
pstr_:	mvi	c,puts	; print string using CP/M
	call	bdos
rsreg:	pop	b	; restore registers
	pop	d
	pop 	h
	ret
snl:	db	13,10,'$'
slen:	db	'Length: $'
sfrst:	db	'First 130: $'
slast:	db	'Last 130: $'
srev:	db	'Reversing...',13,10,'$'
s4444:	db	'Set seq[4444] to `.`...',13,10,'$'
sver:	db	'Verifying... $'
snone:	db	'none '
smiss:	db	'missing',13,10,'$'
	db	'00000'	; number output buffer
nbuf:	db	' $'
arr:	equ	($/256+1)*256	; Place to store a[] (page-aligned)
val:	equ	arr+40		; Place to store validation flags
seq:	equ	val+10000	; Place to store De Bruijn sequence
Output:
Length: 10003
First 130: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350
Last 130: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000
Verifying... none missing
Reversing...
Verifying... none missing
Set seq[4444] to `.`...
Verifying... 1459 4591 5914 8145 missing

8086 Assembly[edit]

putch:	equ	2	; Print character
puts:	equ	9	; Print string
	cpu	8086
	bits	16
section	.text
	org	100h
	;;;	Calculate de_bruijn(10, 4) ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	xor	ax,ax		; zero a[]
	mov	di,arr
	mov	cx,20		; 20 words = 40 bytes
	rep	stosw
	mov	di,seq		; start of sequence
	mov	dx,0101h	; db(1,1)
	call	db_
	mov	si,seq		; Add first 3 to end for wrapping
	mov	cx,3
	rep	movsb
	lea	bp,[di-1]	; Store pointer to last digit in BP
	;;;	Print length ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	mov	ah,puts		; Print "Length:"
	mov	dx,slen
	int	21h
	mov	ax,di		; Length = end - start
	sub	ax,seq
	call	putax		; Print length
	;;;	Print first and last 130 characters and verify ;;;;;;;;;;;;;;;;
	mov	ah,puts		; Print "First 130..."
	mov	dx,sfrst
	int	21h
	mov	si,seq		; print first 130 digits
	call	p130
	mov	ah,puts		; Print "Last 130..."
	mov	dx,slast
	int 	21h
	mov	si,di		; print last 130 digit 
	sub	si,130
	call	p130
	call	verify
	;;;;	Reverse the sequence and verify ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	mov	ah,puts		; Print "Reversing..."
	mov	dx,srev
	int	21h
	mov	si,seq		; SI = first digit in sequence
	mov	di,bp		; DI = last digit in sequence
	call	rvrs		; Reverse
	call	verify		; Verify
	mov	si,seq		; Reverse again, putting it back
	mov	di,bp
	call	rvrs
	;;;	Set seq[4444] to '.' and verify ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	mov	ah,puts		; Print "set seq[4444] to '.'"
	mov	dx,s4444
	int	21h
	mov	[seq+4444],byte '.'
	call	verify		; Verify
	ret
	;;;	db(t, p); t=dh p=dl, di=seq ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
db_:	cmp	dh,4		; t>n? (n=4)
	jbe	.els
	cmp	dl,3		; for p in {1,2,3,4}, 4%p==0 iff p=3
	je	.out
	mov	si,arr+1	; add DL=P bytes from a[1..] to sequence
	mov	cl,dl
	xor 	ch,ch
	rep	movsb
	jmp	.out
.els:	xor	bh,bh
	mov	bl,dh
	sub	bl,dl		; t - p
	mov	al,[arr+bx]	; al = a[t-p]
	mov	bl,dh		; t 
	mov	[arr+bx],al	; a[t] = al
	push	dx		; keep arguments
	inc	dh		; db(++t,p)
	call	db_			
	pop	dx		; restore arguments
	mov	bl,dh		; al = a[t-p]
	sub	bl,dl
	mov	al,[arr+bx]
.loop:	inc	al		; al++
	cmp	al,10		; when al>=k,
	jae	.out		; then stop.
	mov	bl,dh
	mov	[arr+bx],al	; a[t] = j
	push	ax		; keep state
	push	dx
	mov	dl,dh		; db(t+1, t)
	inc	dh
	call	db_
	pop	dx
	pop	ax
	jmp	.loop
.out:	ret
	;;;	Verify that all numbers are there ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
verify:	mov	ah,puts		; Print "verifying..."
	mov	dx,sver
	int	21h
	mov	di,val		; Zero validation array
	mov	cx,5000		; 10000 bytes = 5000 words
	xor	ax,ax
	rep	stosw
	mov	di,val
	mov	si,seq		; Pointer to start of sequence
	mov	cx,6409h	; CH=100 (multiplier), CL=9 (highest digit)
.num:	mov	ax,[si]		; Read first two digits
	cmp	ah,cl		; Check that they are valid
	ja	.inval
	cmp	al,cl
	ja	.inval
	xchg	al,ah		; High digit * 10 + low digit
	aad
	mul	ch		; Multiply by 100 (to add in next two)
	mov	bx,ax
	mov	ax,[si+2]	; Read last two digits
	cmp	ah,cl		; Check that they are valid
	ja	.inval
	cmp	al,cl
	ja	.inval
	xchg	al,ah		; High digit * 10 + low digit
	aad
	add	bx,ax		; BX = final 4-digit number
	inc	byte [di+bx]	; Mark this 4-digit number as seen
.inval:	inc	si		; Next digit
	cmp	si,seq+10000	; Are we at the end yet?
	jne	.num		; If not, do next number
	mov	si,val		; For each number < 10000, check if it's there
	xor	cl,cl		; Will be set if a number is missing
.test:	lodsb			; Do we have this number?
	test	al,al
	jnz	.tnext		; If so, try next number
	mov	ax,si		; Otherwise, print the missing number
	sub	ax,val
	call	putax
	mov	cl,1		; And set CL
.tnext:	cmp	si,val+10000	; Are we at the end yet?
	jne	.test
	test	cl,cl
	mov	dx,smiss	; Print "... missing"
	jnz	.print		; if CL is set
	mov	dx,snone	; or "none missing" otherwise.
.print:	mov	ah,puts
	int	21h
	ret
	;;;	Subroutines ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
	;;;	Print number in AX
putax:	push	ax		; Keep registers we're changing
	push	dx		
	push	bx
	push	di
	mov	di,numbuf	; Pointer to number buffer
	mov	bx,10		; Divisor
.digit:	xor	dx,dx		; Divide AX by 10
	div	bx
	add	dl,'0'		; Add '0' to remainder (digit)
	dec	di		; Store digit in buffer
	mov	[di],dl
	test	ax,ax		; Any more digits?
	jnz	.digit		; If so, do next digits
	mov	dx,di		; At the end, print the string
	mov	ah,puts
	int	21h
	pop	di		; Restore registers
	pop	bx
	pop	dx
	pop	ax
	ret 
	;;;	Print 130 digits starting at SI
p130:	mov	cx,130		; 130 characters
	mov	ah,putch	; Print characters
.loop:	lodsb			; Get digit
	add	al,'0'		; Make ASCII
	mov	dl,al		; Print digit
	int	21h
	loop 	.loop
	ret
	;;;	Reverse memory starting at SI and ending at DI
rvrs:	mov	al,[si]		; Load [SI],
	mov	ah,[di]		; Load [DI],
	mov	[di],al		; Set [DI] = old [SI]
	mov	[si],ah		; Set [SI] = old [DI]
	inc	si		; Increment bottom pointer
	dec	di		; Decrement top pointer
	cmp	si,di		; If SI >= DI, we're done
	jb	rvrs
	ret
section	.data
slen:	db	'Length: $'
sfrst:	db	13,10,'First 130: $'
slast:	db	13,10,'Last 130: $'
srev:	db	13,10,'Reversing... $'
s4444:	db	13,10,'Set seq[4444] to `.`...$'
sver:	db	13,10,'Verifying... $'
snone:	db	'none '
smiss:	db	'missing.$'
	db	'00000'
numbuf:	db	' $'
section	.bss
arr:	resb	40		; a[]
val:	resb	10000		; validation array
seq:	equ	$
Output:
Length: 10003
First 130: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350
Last 130: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000
Verifying... none missing.
Reversing...
Verifying... none missing.
Set seq[4444] to `.`...
Verifying... 1460 4592 5915 8146 missing.

Ada[edit]

Translation of: D
with Ada.Text_IO;              use Ada.Text_IO;
with Ada.Strings.Fixed;        use Ada.Strings;
with Ada.Strings.Unbounded;

procedure De_Bruijn_Sequences is

   function De_Bruijn (K, N : Positive) return String
   is
      use Ada.Strings.Unbounded;

      Alphabet : constant String := "0123456789";

      subtype Decimal is Integer range 0 .. 9;
      type Decimal_Array is array (Natural range <>) of Decimal;

      A   : Decimal_Array (0 .. K * N - 1) := (others => 0);
      Seq : Unbounded_String;

      procedure Db (T, P : Positive) is
      begin
         if T > N then
            if N mod P = 0 then
               for E of A (1 .. P) loop
                  Append (Seq, Alphabet (Alphabet'First + E));
               end loop;
            end if;
         else
            A (T) := A (T - P);
            Db (T + 1, P);
            for J in A (T - P) + 1 .. K - 1 loop
               A (T) := J;
               Db (T + 1, T);
            end loop;
         end if;
      end Db;

   begin
      Db (1, 1);
      return To_String (Seq) & Slice (Seq, 1, N - 1);
   end De_Bruijn;

   function Image (Value : Integer) return String
   is (Fixed.Trim (Value'Image, Left));

   function PIN_Image (Value : Integer) return String
   is (Fixed.Tail (Image (Value), Count => 4, Pad => '0'));

   procedure Validate (Db : String)
   is
      Found  : array (0 .. 9_999) of Natural := (others => 0);
      Errors : Natural := 0;
   begin

      --  Check all strings of 4 consecutive digits within 'db'
      --  to see if all 10,000 combinations occur without duplication.
      for A in Db'First .. Db'Last - 3 loop
         declare
            PIN : String renames Db (A .. A + 4 - 1);
         begin
            if (for all Char of PIN => Char in '0' .. '9') then
               declare
                  N : constant Integer := Integer'Value (PIN);
                  F : Natural renames Found (N);
               begin
                  F := F + 1;
               end;
            end if;
         end;
      end loop;

      for I in 0_000 .. 9_999 loop
         if Found (I) = 0 then
            Put_Line ("  PIN number " & PIN_Image (I) & " missing");
            Errors := Errors + 1;
         elsif Found (I) > 1 then
            Put_Line ("  PIN number " & PIN_Image (I) & " occurs "
                        & Image (Found (I)) & " times");
            Errors := Errors + 1;
         end if;
      end loop;

      case Errors is
         when 0 =>  Put_Line ("  No errors found");
         when 1 =>  Put_Line ("  1 error found");
         when others =>
            Put_Line ("  " & Image (Errors) & " errors found");
      end case;
   end Validate;

   function Backwards (S : String) return String is
      R : String (S'Range);
   begin
      for A in 0 .. S'Length - 1 loop
         R (R'Last - A) := S (S'First + A);
      end loop;
      return R;
   end Backwards;

   DB  : constant String := De_Bruijn (K => 10, N => 4);
   Rev : constant String := Backwards (DB);
   Ovl :          String := DB;
begin
   Put_Line ("The length of the de Bruijn sequence is " & DB'Length'Image);
   New_Line;

   Put_Line ("The first 130 digits of the de Bruijn sequence are: ");
   Put_Line ("  " & Fixed.Head (DB, 130));
   New_Line;

   Put_Line ("The last 130 digits of the de Bruijn sequence are: ");
   Put_Line ("  " & Fixed.Tail (DB, 130));
   New_Line;

   Put_Line ("Validating the deBruijn sequence:");
   Validate (DB);
   New_Line;

   Put_Line ("Validating the reversed deBruijn sequence:");
   Validate (Rev);
   New_Line;

   Ovl (4444) := '.';
   Put_Line ("Validating the overlaid deBruijn sequence:");
   Validate (Ovl);
   New_Line;
end De_Bruijn_Sequences;
Output:
The length of the de Bruijn sequence is  10003

The first 130 digits of the de Bruijn sequence are:
  0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are:
  6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the deBruijn sequence:
  No errors found

Validating the reversed deBruijn sequence:
  No errors found

Validating the overlaid deBruijn sequence:
  PIN number 1459 missing
  PIN number 4591 missing
  PIN number 5814 missing
  PIN number 8145 missing
  4 errors found

BASIC[edit]

10 DEFINT A-Z
20 K = 10: N = 4
30 DIM A(K*N), S(K^N+N), T(5), P(5), V(K^N\8)
40 GOSUB 200
50 PRINT "Length: ",S
60 PRINT "First 130:"
70 FOR I=0 TO 129: PRINT USING "#";S(I);: NEXT
80 PRINT: PRINT "Last 130:"
90 FOR I=S-130 TO S-1: PRINT USING "#";S(I);: NEXT
100 PRINT
110 GOSUB 600
120 PRINT "Reversing...": GOSUB 500: GOSUB 600: GOSUB 500
130 PRINT USING "Replacing 4444'th element (#):";S(4443)
140 S(4443) = -1 : REM 0-indexed, and using integers
150 GOSUB 600
160 END
200 REM Generate De Bruijn sequence given K and N
210 T(R) = 1: P(R) = 1
220 IF T(R) > N GOTO 380
230 A(T(R)) = A(T(R)-P(R))
240 R = R+1
250 T(R) = T(R-1)+1
260 P(R) = P(R-1)
270 GOSUB 220
280 R = R-1
290 FOR J = A(T(R)-P(R))+1 TO K-1
300 A(T(R)) = J
310 R = R+1
320 T(R) = T(R-1)+1
330 P(R) = T(R-1)
340 GOSUB 220
350 R = R-1
355 J = A(T(R))
360 NEXT
370 RETURN
380 IF N MOD P(R) THEN RETURN
390 FOR I = 1 TO P(R)
400 S(S) = A(I)
410 S = S+1
420 NEXT
430 RETURN
500 REM Reverse the sequence
510 FOR I=0 TO S\2
520 J = S(I)
530 S(I) = S(S-I)
540 S(S-I) = J
550 NEXT
560 RETURN
600 REM Validate the sequence (uses bit packing to save memory)
610 PRINT "Validating...";
620 FOR I=0 TO N-1: S(S+I)=S(I): NEXT
630 FOR I=0 TO K^N\8-1: V(I)=0: NEXT
640 FOR I=0 TO S
650 P=0
660 FOR J=0 TO N-1
662 D=S(I+J)
663 IF D<0 GOTO 690
665 P=K*P+D
669 NEXT J
670 X=P\8
680 V(X) = V(X) OR 2^(P AND 7)
690 NEXT I
700 M=1
710 FOR I=0 TO K^N\8-1
720 IF V(I)=255 GOTO 760
730 FOR J=0 TO 7
740 IF (V(I) AND 2^J)=0 THEN M=0: PRINT USING " ####";I*8+J;
750 NEXT
760 NEXT
770 IF M THEN PRINT " none";
780 PRINT " missing."
790 RETURN
Output:
Length:        10000
First 130:
00001000200030004000500060007000800090011001200130014001500160017001800190021002
20023002400250026002700280029003100320033003400350
Last 130:
89768986899696977697869796987698869896997699869997777877797788778977987799787879
78887889789878997979887989799879998888988998989999
Validating... none missing.
Reversing...
Validating... none missing.
Replacing 4444'th element (4):
Validating... 1459 4591 5814 8145 missing.

C#[edit]

Translation of: Kotlin
using System;
using System.Collections.Generic;
using System.Text;

namespace DeBruijn {
    class Program {
        const string digits = "0123456789";

        static string DeBruijn(int k, int n) {
            var alphabet = digits.Substring(0, k);
            var a = new byte[k * n];
            var seq = new List<byte>();
            void db(int t, int p) {
                if (t > n) {
                    if (n % p == 0) {
                        seq.AddRange(new ArraySegment<byte>(a, 1, p));
                    }
                } else {
                    a[t] = a[t - p];
                    db(t + 1, p);
                    var j = a[t - p] + 1;
                    while (j < k) {
                        a[t] = (byte)j;
                        db(t + 1, t);
                        j++;
                    }
                }
            }
            db(1, 1);
            var buf = new StringBuilder();
            foreach (var i in seq) {
                buf.Append(alphabet[i]);
            }
            var b = buf.ToString();
            return b + b.Substring(0, n - 1);
        }

        static bool AllDigits(string s) {
            foreach (var c in s) {
                if (c < '0' || '9' < c) {
                    return false;
                }
            }
            return true;
        }

        static void Validate(string db) {
            var le = db.Length;
            var found = new int[10_000];
            var errs = new List<string>();
            // Check all strings of 4 consecutive digits within 'db'
            // to see if all 10,000 combinations occur without duplication.
            for (int i = 0; i < le - 3; i++) {
                var s = db.Substring(i, 4);
                if (AllDigits(s)) {
                    int.TryParse(s, out int n);
                    found[n]++;
                }
            }
            for (int i = 0; i < 10_000; i++) {
                if (found[i] == 0) {
                    errs.Add(string.Format("    PIN number {0,4} missing", i));
                } else if (found[i] > 1) {
                    errs.Add(string.Format("    PIN number {0,4} occurs {1} times", i, found[i]));
                }
            }
            var lerr = errs.Count;
            if (lerr == 0) {
                Console.WriteLine("  No errors found");
            } else {
                var pl = lerr == 1 ? "" : "s";
                Console.WriteLine("  {0} error{1} found:", lerr, pl);
                errs.ForEach(Console.WriteLine);
            }
        }

        static string Reverse(string s) {
            char[] arr = s.ToCharArray();
            Array.Reverse(arr);
            return new string(arr);
        }

        static void Main() {
            var db = DeBruijn(10, 4);
            var le = db.Length;

            Console.WriteLine("The length of the de Bruijn sequence is {0}", le);
            Console.WriteLine("\nThe first 130 digits of the de Bruijn sequence are: {0}", db.Substring(0, 130));
            Console.WriteLine("\nThe last 130 digits of the de Bruijn sequence are: {0}", db.Substring(le - 130, 130));

            Console.WriteLine("\nValidating the deBruijn sequence:");
            Validate(db);

            Console.WriteLine("\nValidating the reversed deBruijn sequence:");
            Validate(Reverse(db));

            var bytes = db.ToCharArray();
            bytes[4443] = '.';
            db = new string(bytes);
            Console.WriteLine("\nValidating the overlaid deBruijn sequence:");
            Validate(db);
        }
    }
}
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the deBruijn sequence:
  No errors found

Validating the reversed deBruijn sequence:
  No errors found

Validating the overlaid deBruijn sequence:
  4 errors found:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

C++[edit]

Translation of: D
#include <algorithm>
#include <functional>
#include <iostream>
#include <iterator>
#include <string>
#include <sstream>
#include <vector>

typedef unsigned char byte;

std::string deBruijn(int k, int n) {
    std::vector<byte> a(k * n, 0);
    std::vector<byte> seq;

    std::function<void(int, int)> db;
    db = [&](int t, int p) {
        if (t > n) {
            if (n % p == 0) {
                for (int i = 1; i < p + 1; i++) {
                    seq.push_back(a[i]);
                }
            }
        } else {
            a[t] = a[t - p];
            db(t + 1, p);
            auto j = a[t - p] + 1;
            while (j < k) {
                a[t] = j & 0xFF;
                db(t + 1, t);
                j++;
            }
        }
    };

    db(1, 1);
    std::string buf;
    for (auto i : seq) {
        buf.push_back('0' + i);
    }
    return buf + buf.substr(0, n - 1);
}

bool allDigits(std::string s) {
    for (auto c : s) {
        if (c < '0' || '9' < c) {
            return false;
        }
    }
    return true;
}

void validate(std::string db) {
    auto le = db.size();
    std::vector<int> found(10000, 0);
    std::vector<std::string> errs;

    // Check all strings of 4 consecutive digits within 'db'
    // to see if all 10,000 combinations occur without duplication.
    for (size_t i = 0; i < le - 3; i++) {
        auto s = db.substr(i, 4);
        if (allDigits(s)) {
            auto n = stoi(s);
            found[n]++;
        }
    }

    for (int i = 0; i < 10000; i++) {
        if (found[i] == 0) {
            std::stringstream ss;
            ss << "    PIN number " << i << " missing";
            errs.push_back(ss.str());
        } else if (found[i] > 1) {
            std::stringstream ss;
            ss << "    PIN number " << i << " occurs " << found[i] << " times";
            errs.push_back(ss.str());
        }
    }

    if (errs.empty()) {
        std::cout << "  No errors found\n";
    } else {
        auto pl = (errs.size() == 1) ? "" : "s";
        std::cout << "  " << errs.size() << " error" << pl << " found:\n";
        for (auto e : errs) {
            std::cout << e << '\n';
        }
    }
}

int main() {
    std::ostream_iterator<byte> oi(std::cout, "");
    auto db = deBruijn(10, 4);

    std::cout << "The length of the de Bruijn sequence is " << db.size() << "\n\n";
    std::cout << "The first 130 digits of the de Bruijn sequence are: ";
    std::copy_n(db.cbegin(), 130, oi);
    std::cout << "\n\nThe last 130 digits of the de Bruijn sequence are: ";
    std::copy(db.cbegin() + (db.size() - 130), db.cend(), oi);
    std::cout << "\n";

    std::cout << "\nValidating the de Bruijn sequence:\n";
    validate(db);

    std::cout << "\nValidating the reversed de Bruijn sequence:\n";
    auto rdb = db;
    std::reverse(rdb.begin(), rdb.end());
    validate(rdb);

    auto by = db;
    by[4443] = '.';
    std::cout << "\nValidating the overlaid de Bruijn sequence:\n";
    validate(by);

    return 0;
}
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the de Bruijn sequence:
  No errors found

Validating the reversed de Bruijn sequence:
  No errors found

Validating the overlaid de Bruijn sequence:
  4 errors found:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

CLU[edit]

% Generate the De Bruijn sequence consisiting of N-digit numbers
de_bruijn = cluster is generate
    rep = null
    own k: int := 0
    own n: int := 0
    own a: array[int] := array[int]$[]
    own seq: array[int] := array[int]$[]
    
    generate = proc (k_, n_: int) returns (string)
        k := k_
        n := n_
        a := array[int]$fill(0, k*n, 0)
        seq := array[int]$[]
        db(1, 1)
        s: stream := stream$create_output()
        for i: int in array[int]$elements(seq) do
            stream$puts(s, int$unparse(i))
        end
        return(stream$get_contents(s))
    end generate
    
    db = proc (t, p: int)
        if t>n then 
            if n//p = 0 then
                for i: int in int$from_to(1, p) do
                    array[int]$addh(seq, a[i])
                end
            end
        else
            a[t] := a[t - p]
            db(t+1, p)
            for j: int in int$from_to(a[t - p] + 1, k-1) do
                a[t] := j
                db(t + 1, t)
            end
        end
    end db
end de_bruijn

% Reverse a string
reverse = proc (s: string) returns (string)
    r: array[char] := array[char]$predict(1, string$size(s))
    for c: char in string$chars(s) do
        array[char]$addl(r, c)
    end
    return(string$ac2s(r))
end reverse 

% Find all missing N-digit values
find_missing = proc (db: string, n: int) returns (sequence[string])
    db := db || string$substr(db, 1, n) % wrap
    missing: array[string] := array[string]$[]
    s: stream := stream$create_output()
    for i: int in int$from_to(0, 10**n-1) do
        %s: stream := stream$create_output()
        stream$reset(s)
        stream$putzero(s, int$unparse(i), n)
        val: string := stream$get_contents(s)
        if string$indexs(val, db) = 0 then
            array[string]$addh(missing, val)
        end
    end
    return(sequence[string]$a2s(missing))
end find_missing

% Report all missing values, or 'none'.
validate = proc (s: stream, db: string, n: int)
    stream$puts(s, "Validating...")
    missing: sequence[string] := find_missing(db, n)
    for v: string in sequence[string]$elements(missing) do
        stream$puts(s, " " || v)
    end
    if sequence[string]$size(missing) = 0 then
        stream$puts(s, " none")
    end
    stream$putl(s, " missing.")
end validate

start_up = proc ()
    po: stream := stream$primary_output()
    
    % Generate the De Bruijn sequence for 4-digit numbers
    db: string := de_bruijn$generate(10, 4)
    
    % Report length and first and last digits
    stream$putl(po, "Length: " || int$unparse(string$size(db)))
    stream$putl(po, "First 130 characters:")
    stream$putl(po, string$substr(db, 1, 130))
    stream$putl(po, "Last 130 characters:")
    stream$putl(po, string$substr(db, string$size(db)-130, 130))
    
    % See if there are any missing values in the sequence
    validate(po, db, 4)
    
    % Reverse and validate again
    stream$putl(po, "Reversing...")
    validate(po, reverse(db), 4)
    
    % Replace the 4444'th element with '.' and validate again
    stream$putl(po, "Setting the 4444'th character to '.'...")
    db := string$substr(db, 1, 4443) || "." || string$rest(db, 4445)
    validate(po, db, 4)
end start_up
Output:
Length: 10000
First 130 characters:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350
Last 130 characters:
6897689868996969776978697969876988698969976998699977778777977887789779877997878797888788978987899797988798979987999888898899898999
Validating... none missing.
Reversing...
Validating... none missing.
Setting the 4444'th character to '.'...
Validating... 1459 4591 5814 8145 missing.

D[edit]

Translation of: Kotlin
import std.array;
import std.conv;
import std.format;
import std.range;
import std.stdio;

immutable DIGITS = "0123456789";

string deBruijn(int k, int n) {
    auto alphabet = DIGITS[0..k];
    byte[] a;
    a.length = k * n;
    byte[] seq;

    void db(int t, int p) {
        if (t > n) {
            if (n % p == 0) {
                auto temp = a[1..p + 1];
                seq ~= temp;
            }
        } else {
            a[t] = a[t - p];
            db(t + 1, p);
            auto j = a[t - p] + 1;
            while (j < k) {
                a[t] = cast(byte)(j & 0xFF);
                db(t + 1, t);
                j++;
            }
        }
    }
    db(1, 1);
    string buf;
    foreach (i; seq) {
        buf ~= alphabet[i];
    }

    return buf ~ buf[0 .. n - 1];
}

bool allDigits(string s) {
    foreach (c; s) {
        if (c < '0' || '9' < c) {
            return false;
        }
    }
    return true;
}

void validate(string db) {
    auto le = db.length;
    int[10_000] found;
    string[] errs;
    // Check all strings of 4 consecutive digits within 'db'
    // to see if all 10,000 combinations occur without duplication.
    foreach (i; 0 .. le - 3) {
        auto s = db[i .. i + 4];
        if (allDigits(s)) {
            auto n = s.to!int;
            found[n]++;
        }
    }
    foreach (i; 0 .. 10_000) {
        if (found[i] == 0) {
            errs ~= format("    PIN number %04d missing", i);
        } else if (found[i] > 1) {
            errs ~= format("    PIN number %04d occurs %d times", i, found[i]);
        }
    }
    if (errs.empty) {
        writeln("  No errors found");
    } else {
        auto pl = (errs.length == 1) ? "" : "s";
        writeln("  ", errs.length, " error", pl, " found:");
        writefln("%-(%s\n%)", errs);
    }
}

void main() {
    auto db = deBruijn(10, 4);

    writeln("The length of the de Bruijn sequence is ", db.length);
    writeln("\nThe first 130 digits of the de Bruijn sequence are: ", db[0 .. 130]);
    writeln("\nThe last 130 digits of the de Bruijn sequence are: ", db[$ - 130 .. $]);

    writeln("\nValidating the deBruijn sequence:");
    validate(db);

    writeln("\nValidating the reversed deBruijn sequence:");
    validate(db.retro.to!string);

    auto by = db.dup;
    by[4443] = '.';
    db = by.idup;
    writeln("\nValidating the overlaid deBruijn sequence:");
    validate(db);
}
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the deBruijn sequence:
  No errors found

Validating the reversed deBruijn sequence:
  No errors found

Validating the overlaid deBruijn sequence:
  4 errors found:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

Go[edit]

package main

import (
    "bytes"
    "fmt"
    "strconv"
    "strings"
)

const digits = "0123456789"

func deBruijn(k, n int) string {
    alphabet := digits[0:k]
    a := make([]byte, k*n)
    var seq []byte
    var db func(int, int) // recursive closure
    db = func(t, p int) {
        if t > n {
            if n%p == 0 {
                seq = append(seq, a[1:p+1]...)
            }
        } else {
            a[t] = a[t-p]
            db(t+1, p)
            for j := int(a[t-p] + 1); j < k; j++ {
                a[t] = byte(j)
                db(t+1, t)
            }
        }
    }
    db(1, 1)
    var buf bytes.Buffer
    for _, i := range seq {
        buf.WriteByte(alphabet[i])
    }
    b := buf.String()
    return b + b[0:n-1] // as cyclic append first (n-1) digits
}

func allDigits(s string) bool {
    for _, b := range s {
        if b < '0' || b > '9' {
            return false
        }
    }
    return true
}

func validate(db string) {
    le := len(db)
    found := make([]int, 10000)
    var errs []string
    // Check all strings of 4 consecutive digits within 'db'
    // to see if all 10,000 combinations occur without duplication.
    for i := 0; i < le-3; i++ {
        s := db[i : i+4]
        if allDigits(s) {
            n, _ := strconv.Atoi(s)
            found[n]++
        }
    }
    for i := 0; i < 10000; i++ {
        if found[i] == 0 {
            errs = append(errs, fmt.Sprintf("    PIN number %04d missing", i))
        } else if found[i] > 1 {
            errs = append(errs, fmt.Sprintf("    PIN number %04d occurs %d times", i, found[i]))
        }
    }
    lerr := len(errs)
    if lerr == 0 {
        fmt.Println("  No errors found")
    } else {
        pl := "s"
        if lerr == 1 {
            pl = ""
        }
        fmt.Printf("  %d error%s found:\n", lerr, pl)
        fmt.Println(strings.Join(errs, "\n"))
    }
}

func reverse(s string) string {
    bytes := []byte(s)
    for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
        bytes[i], bytes[j] = bytes[j], bytes[i]
    }
    return string(bytes)
}

func main() {
    db := deBruijn(10, 4)
    le := len(db)
    fmt.Println("The length of the de Bruijn sequence is", le)
    fmt.Println("\nThe first 130 digits of the de Bruijn sequence are:")
    fmt.Println(db[0:130])
    fmt.Println("\nThe last 130 digits of the de Bruijn sequence are:")
    fmt.Println(db[le-130:])
    fmt.Println("\nValidating the de Bruijn sequence:")
    validate(db)

    fmt.Println("\nValidating the reversed de Bruijn sequence:")
    dbr := reverse(db)
    validate(dbr)

    bytes := []byte(db)
    bytes[4443] = '.'
    db = string(bytes)
    fmt.Println("\nValidating the overlaid de Bruijn sequence:")
    validate(db)
}
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are:
6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the de Bruijn sequence:
  No errors found

Validating the reversed de Bruijn sequence:
  No errors found

Validating the overlaid de Bruijn sequence:
  4 errors found:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

Groovy[edit]

Translation of: Java
import java.util.function.BiConsumer

class DeBruijn {
    interface Recursable<T, U> {
        void apply(T t, U u, Recursable<T, U> r);
    }

    static <T, U> BiConsumer<T, U> recurse(Recursable<T, U> f) {
        return { t, u -> f.apply(t, u, f) }
    }

    private static String deBruijn(int k, int n) {
        byte[] a = new byte[k * n]
        Arrays.fill(a, (byte) 0)

        List<Byte> seq = new ArrayList<>()

        BiConsumer<Integer, Integer> db = recurse({ int t, int p, f ->
            if (t > n) {
                if (n % p == 0) {
                    for (int i = 1; i < p + 1; ++i) {
                        seq.add(a[i])
                    }
                }
            } else {
                a[t] = a[t - p]
                f.apply(t + 1, p, f)
                int j = a[t - p] + 1
                while (j < k) {
                    a[t] = (byte) (j & 0xFF)
                    f.apply(t + 1, t, f)
                    j++
                }
            }
        })
        db.accept(1, 1)

        StringBuilder sb = new StringBuilder()
        for (Byte i : seq) {
            sb.append("0123456789".charAt(i))
        }

        sb.append(sb.subSequence(0, n - 1))
        return sb.toString()
    }

    private static boolean allDigits(String s) {
        for (int i = 0; i < s.length(); ++i) {
            char c = s.charAt(i)
            if (!Character.isDigit(c)) {
                return false
            }
        }
        return true
    }

    private static void validate(String db) {
        int le = db.length()
        int[] found = new int[10_000]
        Arrays.fill(found, 0)
        List<String> errs = new ArrayList<>()

        // Check all strings of 4 consecutive digits within 'db'
        // to see if all 10,000 combinations occur without duplication.
        for (int i = 0; i < le - 3; ++i) {
            String s = db.substring(i, i + 4)
            if (allDigits(s)) {
                int n = Integer.parseInt(s)
                found[n]++
            }
        }

        for (int i = 0; i < 10_000; ++i) {
            if (found[i] == 0) {
                errs.add(String.format("    PIN number %d is missing", i))
            } else if (found[i] > 1) {
                errs.add(String.format("    PIN number %d occurs %d times", i, found[i]))
            }
        }

        if (errs.isEmpty()) {
            System.out.println("    No errors found")
        } else {
            String pl = (errs.size() == 1) ? "" : "s"
            System.out.printf("  %d error%s found:\n", errs.size(), pl)
            errs.forEach(System.out.&println)
        }
    }

    static void main(String[] args) {
        String db = deBruijn(10, 4)

        System.out.printf("The length of the de Bruijn sequence is %d\n\n", db.length())
        System.out.printf("The first 130 digits of the de Bruijn sequence are: %s\n\n", db.substring(0, 130))
        System.out.printf("The last 130 digits of the de Bruijn sequence are: %s\n\n", db.substring(db.length() - 130))

        System.out.println("Validating the de Bruijn sequence:")
        validate(db)

        StringBuilder sb = new StringBuilder(db)
        String rdb = sb.reverse().toString()
        System.out.println()
        System.out.println("Validating the de Bruijn sequence:")
        validate(rdb)

        sb = new StringBuilder(db)
        sb.setCharAt(4443, '.' as char)
        System.out.println()
        System.out.println("Validating the overlaid de Bruijn sequence:")
        validate(sb.toString())
    }
}
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the de Bruijn sequence:
    No errors found

Validating the de Bruijn sequence:
    No errors found

Validating the overlaid de Bruijn sequence:
  4 errors found:
    PIN number 1459 is missing
    PIN number 4591 is missing
    PIN number 5814 is missing
    PIN number 8145 is missing

Haskell[edit]

Permutation-based[edit]

Straight-forward implementation of inverse Burrows—Wheeler transform [[wp:De_Bruijn_sequence#Construction|De_Bruijn_sequence#Construction] is reasonably efficient for the task (about a milliseconds for B(10,4) in GHCi).

import Data.List
import Data.Map ((!))
import qualified Data.Map as M

-- represents a permutation in a cycle notation
cycleForm :: [Int] -> [[Int]]
cycleForm p = unfoldr getCycle $ M.fromList $ zip [0..] p
  where
    getCycle p
      | M.null p = Nothing
      | otherwise = 
          let Just ((x,y), m) = M.minViewWithKey p
              c = if x == y then [] else takeWhile (/= x) (iterate (m !) y)
          in Just (c ++ [x], foldr M.delete m c)

-- the set of Lyndon words generated by inverse Burrows—Wheeler transform 
lyndonWords :: Ord a => [a] -> Int -> [[a]]
lyndonWords s n = map (ref !!) <$> cycleForm perm
  where
    ref = concat $ replicate (length s ^ (n - 1)) s
    perm = s >>= (`elemIndices` ref)

-- returns the de Bruijn sequence of order n for an alphabeth s
deBruijn :: Ord a => [a] -> Int -> [a]
deBruijn s n = let lw = concat $ lyndonWords n s
               in lw ++ take (n-1) lw
λ> cycleForm [1,4,3,2,0]
[[1,4,0],[3,2]]

λ> lyndonWords "ab" 3
["a","aab","abb","b"]

λ> deBruijn "ab" 3
"aaababbbaa"

The task.

import Control.Monad (replicateM)

main = do
  let symbols = ['0'..'9']
  let db = deBruijn symbols 4
  putStrLn $ "The length of de Bruijn sequence: " ++ show (length db)
  putStrLn $ "The first 130 symbols are:\n" ++ show (take 130 db)
  putStrLn $ "The last 130 symbols are:\n" ++ show (drop (length db - 130) db)

  let words = replicateM 4 symbols
  let validate db  = filter (not . (`isInfixOf` db)) words
  putStrLn $ "Words not in the sequence: " ++ unwords (validate db)

  let db' = a ++ ('.': tail b) where (a,b) = splitAt 4444 db
  putStrLn $ "Words not in the corrupted sequence: " ++ unwords (validate db')
λ> main
The length of de Bruijn sequence: 10003
The first 130 symbols are:
"0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350"
The last 130 symbols are:
"6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000"
Words not in the sequence: 
Words not in the corrupted sequence: 1459 4591 5914 8145

Array-based[edit]

Translation of: Python
import Control.Monad.State
import Data.Array (Array, listArray, (!), (//))
import qualified Data.Array as A

deBruijn :: [a] -> Int -> [a]
deBruijn s n =
  let
    k = length s
    
    db :: Int -> Int -> State (Array Int Int) [Int]    
    db t p =
      if t > n
      then 
        if n `mod` p == 0
        then get >>= \a -> return [ a ! k | k <- [1 .. p]]
        else return []
      else do
        a <- get
        x <- setArray t (a ! (t-p)) >> db (t+1) p
        a <- get
        y <- sequence [ setArray t j >> db (t+1) t
                      | j <- [a ! (t-p) + 1 .. k - 1] ]
        return $ x ++ concat y
        
    setArray i x = modify (// [(i, x)])
    
    seqn = db 1 1 `evalState` listArray (0, k*n-1) (repeat 0)
    
  in [ s !! i | i <- seqn ++ take (n-1) seqn ]

J[edit]

definitions. The C. verb computes the cycles. J's sort is a stable sort.

NB. implement inverse Burrows—Wheeler transform sequence method

repeat_alphabet=:  [: , [: i.&> (^ <:) # [
assert 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 -: 2 repeat_alphabet 4

de_bruijn=: ({~ ([: ; [: C. /:^:2))@:repeat_alphabet     NB. K de_bruijn N

pins=: #&10 #: [: i. 10&^   NB. pins y  generates all y digit PINs
groups=: [ ]\ ] , ({.~ <:)~    NB. length x infixes of sequence y cyclically extended by x-1
verify_PINs=: (/:~@:groups -: pins@:[)  NB. LENGTH verify_PINs SEQUENCE
Task
   NB. A is the sequence
   A=: 10 de_bruijn 4

   NB. tally A
   #A
10000
   
   NB. literally the first and final 130 digits
   Num_j_ {~ 130 ({. ,: ({.~ -)~) A
0000101001101111000210020102110202001210120112111202121200221022012211220222122220003100320030103110321030203120322030300131013201
9469956996699769986990799179927993799479957996799779987990899189928993899489958996899789988990999199929993999499959996999799989999

   NB. verifications.  seriously?
   4 verify_PINs A
1
   4 (verify_PINs |.) A
1
   4 verify_PINs (a.i.'.') (<: 4444)} A
0

Java[edit]

Translation of: C++
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.function.BiConsumer;

public class DeBruijn {
    public interface Recursable<T, U> {
        void apply(T t, U u, Recursable<T, U> r);
    }

    public static <T, U> BiConsumer<T, U> recurse(Recursable<T, U> f) {
        return (t, u) -> f.apply(t, u, f);
    }

    private static String deBruijn(int k, int n) {
        byte[] a = new byte[k * n];
        Arrays.fill(a, (byte) 0);

        List<Byte> seq = new ArrayList<>();

        BiConsumer<Integer, Integer> db = recurse((t, p, f) -> {
            if (t > n) {
                if (n % p == 0) {
                    for (int i = 1; i < p + 1; ++i) {
                        seq.add(a[i]);
                    }
                }
            } else {
                a[t] = a[t - p];
                f.apply(t + 1, p, f);
                int j = a[t - p] + 1;
                while (j < k) {
                    a[t] = (byte) (j & 0xFF);
                    f.apply(t + 1, t, f);
                    j++;
                }
            }
        });
        db.accept(1, 1);

        StringBuilder sb = new StringBuilder();
        for (Byte i : seq) {
            sb.append("0123456789".charAt(i));
        }

        sb.append(sb.subSequence(0, n - 1));
        return sb.toString();
    }

    private static boolean allDigits(String s) {
        for (int i = 0; i < s.length(); ++i) {
            char c = s.charAt(i);
            if (!Character.isDigit(c)) {
                return false;
            }
        }
        return true;
    }

    private static void validate(String db) {
        int le = db.length();
        int[] found = new int[10_000];
        Arrays.fill(found, 0);
        List<String> errs = new ArrayList<>();

        // Check all strings of 4 consecutive digits within 'db'
        // to see if all 10,000 combinations occur without duplication.
        for (int i = 0; i < le - 3; ++i) {
            String s = db.substring(i, i + 4);
            if (allDigits(s)) {
                int n = Integer.parseInt(s);
                found[n]++;
            }
        }

        for (int i = 0; i < 10_000; ++i) {
            if (found[i] == 0) {
                errs.add(String.format("    PIN number %d is missing", i));
            } else if (found[i] > 1) {
                errs.add(String.format("    PIN number %d occurs %d times", i, found[i]));
            }
        }

        if (errs.isEmpty()) {
            System.out.println("    No errors found");
        } else {
            String pl = (errs.size() == 1) ? "" : "s";
            System.out.printf("  %d error%s found:\n", errs.size(), pl);
            errs.forEach(System.out::println);
        }
    }

    public static void main(String[] args) {
        String db = deBruijn(10, 4);

        System.out.printf("The length of the de Bruijn sequence is %d\n\n", db.length());
        System.out.printf("The first 130 digits of the de Bruijn sequence are: %s\n\n", db.substring(0, 130));
        System.out.printf("The last 130 digits of the de Bruijn sequence are: %s\n\n", db.substring(db.length() - 130));

        System.out.println("Validating the de Bruijn sequence:");
        validate(db);

        StringBuilder sb = new StringBuilder(db);
        String rdb = sb.reverse().toString();
        System.out.println();
        System.out.println("Validating the de Bruijn sequence:");
        validate(rdb);

        sb = new StringBuilder(db);
        sb.setCharAt(4443, '.');
        System.out.println();
        System.out.println("Validating the overlaid de Bruijn sequence:");
        validate(sb.toString());
    }
}
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the de Bruijn sequence:
    No errors found

Validating the de Bruijn sequence:
    No errors found

Validating the overlaid de Bruijn sequence:
  4 errors found:
    PIN number 1459 is missing
    PIN number 4591 is missing
    PIN number 5814 is missing
    PIN number 8145 is missing

Julia[edit]

function debruijn(k::Integer, n::Integer)
    alphabet = b"0123456789abcdefghijklmnopqrstuvwxyz"[1:k]
    a = zeros(UInt8, k * n)
    seq = UInt8[]

    function db(t, p)
        if t > n
            if n % p == 0
                append!(seq, a[2:p+1])
            end
        else
            a[t + 1] = a[t - p + 1]
            db(t + 1, p)
            for j in a[t-p+1]+1:k-1
                a[t + 1] = j
                db(t + 1, t)
            end
        end
    end

    db(1, 1)
    return String([alphabet[i + 1] for i in vcat(seq, seq[1:n-1])])
end

function verifyallPIN(str, k, n, deltaposition=0)
    if deltaposition != 0
        str = str[1:deltaposition-1] * "." * str[deltaposition+1:end]
    end
    result = true
    for i in 1:k^n-1
        pin = string(i, pad=n)
        if !occursin(pin, str)
            println("PIN $pin does not occur in the sequence.")
            result = false
        end
    end
    println("The sequence does ", result ? "" : "not ", "contain all PINs.")
end

const s = debruijn(10, 4)
println("The length of the sequence is $(length(s)). The first 130 digits are:\n",
    s[1:130], "\nand the last 130 digits are:\n", s[end-130:end])
print("Testing sequence: "), verifyallPIN(s, 10, 4)
print("Testing the reversed sequence: "), verifyallPIN(reverse(s), 10, 4)
println("\nAfter replacing 4444th digit with \'.\':"), verifyallPIN(s, 10, 4, 4444)
Output:
The length of the sequence is 10003. The first 130 digits are:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350
and the last 130 digits are:
76898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000
Testing sequence: The sequence does contain all PINs.
Testing the reversed sequence: The sequence does contain all PINs.

After replacing 4444th digit with '.':
PIN 1459 does not occur in the sequence.
PIN 4591 does not occur in the sequence.
PIN 5814 does not occur in the sequence.
PIN 8145 does not occur in the sequence.
The sequence does not contain all PINs.

Kotlin[edit]

Translation of: Go
const val digits = "0123456789"

fun deBruijn(k: Int, n: Int): String {
    val alphabet = digits.substring(0, k)
    val a = ByteArray(k * n)
    val seq = mutableListOf<Byte>()
    fun db(t: Int, p: Int) {
        if (t > n) {
            if (n % p == 0) {
                seq.addAll(a.sliceArray(1..p).asList())
            }
        } else {
            a[t] = a[t - p]
            db(t + 1, p)
            var j = a[t - p] + 1
            while (j < k) {
                a[t] = j.toByte()
                db(t + 1, t)
                j++
            }
        }
    }
    db(1, 1)
    val buf = StringBuilder()
    for (i in seq) {
        buf.append(alphabet[i.toInt()])
    }
    val b = buf.toString()
    return b + b.subSequence(0, n - 1)
}

fun allDigits(s: String): Boolean {
    for (c in s) {
        if (c < '0' || '9' < c) {
            return false
        }
    }
    return true
}

fun validate(db: String) {
    val le = db.length
    val found = MutableList(10_000) { 0 }
    val errs = mutableListOf<String>()
    // Check all strings of 4 consecutive digits within 'db'
    // to see if all 10,000 combinations occur without duplication.
    for (i in 0 until le - 3) {
        val s = db.substring(i, i + 4)
        if (allDigits(s)) {
            val n = s.toInt()
            found[n]++
        }
    }
    for (i in 0 until 10_000) {
        if (found[i] == 0) {
            errs.add("    PIN number %04d missing".format(i))
        } else if (found[i] > 1) {
            errs.add("    PIN number %04d occurs %d times".format(i, found[i]))
        }
    }
    val lerr = errs.size
    if (lerr == 0) {
        println("  No errors found")
    } else {
        val pl = if (lerr == 1) {
            ""
        } else {
            "s"
        }
        println("  $lerr error$pl found:")
        println(errs.joinToString("\n"))
    }
}

fun main() {
    var db = deBruijn(10, 4)
    val le = db.length

    println("The length of the de Bruijn sequence is $le")
    println("\nThe first 130 digits of the de Bruijn sequence are: ${db.subSequence(0, 130)}")
    println("\nThe last 130 digits of the de Bruijn sequence are: ${db.subSequence(le - 130, le)}")

    println("\nValidating the deBruijn sequence:")
    validate(db)

    println("\nValidating the reversed deBruijn sequence:")
    validate(db.reversed())

    val bytes = db.toCharArray()
    bytes[4443] = '.'
    db = String(bytes)
    println("\nValidating the overlaid deBruijn sequence:")
    validate(db)
}
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the deBruijn sequence:
  No errors found

Validating the reversed deBruijn sequence:
  No errors found

Validating the overlaid deBruijn sequence:
  4 errors found:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

Lua[edit]

Translation of: C++
function tprint(tbl)
    for i,v in pairs(tbl) do
        print(v)
    end
end

function deBruijn(k, n)
    local a = {}
    for i=1, k*n do
        table.insert(a, 0)
    end

    local seq = {}
    function db(t, p)
        if t > n then
            if n % p == 0 then
                for i=1, p do
                    table.insert(seq, a[i + 1])
                end
            end
        else
            a[t + 1] = a[t - p + 1]
            db(t + 1, p)

            local j = a[t - p + 1] + 1
            while j < k do
                a[t + 1] = j % 256
                db(t + 1, t)
                j = j + 1
            end
        end
    end

    db(1, 1)

    local buf = ""
    for i,v in pairs(seq) do
        buf = buf .. tostring(v)
    end
    return buf .. buf:sub(1, n - 1)
end

function allDigits(s)
    return s:match('[0-9]+') == s
end

function validate(db)
    local le = string.len(db)
    local found = {}
    local errs = {}

    for i=1, 10000 do
        table.insert(found, 0)
    end

    -- Check all strings of 4 consecutive digits within 'db'
    -- to see if all 10,000 combinations occur without duplication.
    for i=1, le - 3 do
        local s = db:sub(i, i + 3)
        if allDigits(s) then
            local n = tonumber(s)
            found[n + 1] = found[n + 1] + 1
        end
    end

    local count = 0
    for i=1, 10000 do
        if found[i] == 0 then
            table.insert(errs, "    PIN number " .. (i - 1) .. " missing")
            count = count + 1
        elseif found[i] > 1 then
            table.insert(errs, "    PIN number " .. (i - 1) .. " occurs " .. found[i] .. " times")
            count = count + 1
        end
    end

    if count == 0 then
        print("  No errors found")
    else
        tprint(errs)
    end
end

function main()
    local db = deBruijn(10,4)

    print("The length of the de Bruijn sequence is " .. string.len(db))
    print()

    io.write("The first 130 digits of the de Bruijn sequence are: ")
    print(db:sub(0, 130))
    print()

    io.write("The last 130 digits of the de Bruijn sequence are: ")
    print(db:sub(-130))
    print()

    print("Validating the de Bruijn sequence:")
    validate(db)
    print()

    print("Validating the reversed de Bruijn sequence:")
    validate(db:reverse())
    print()

    db = db:sub(1,4443) .. "." .. db:sub(4445)
    print("Validating the overlaid de Bruijn sequence:")
    validate(db)
    print()
end

main()
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the de Bruijn sequence:
  No errors found

Validating the reversed de Bruijn sequence:
  No errors found

Validating the overlaid de Bruijn sequence:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

Mathematica/Wolfram Language[edit]

seq = DeBruijnSequence[Range[0, 9], 4];
seq = seq~Join~Take[seq, 3];
Length[seq]
{seq[[;; 130]], seq[[-130 ;;]]}
Complement[
 StringDrop[ToString[NumberForm[#, 4, NumberPadding -> {"0", "0"}]], 
    1] & /@ Range[0, 9999], 
 Union[StringJoin /@ Partition[ToString /@ seq, 4, 1]]]
seq = Reverse[seq];
Complement[
 StringDrop[ToString[NumberForm[#, 4, NumberPadding -> {"0", "0"}]], 
    1] & /@ Range[0, 9999], 
 Union[StringJoin /@ Partition[ToString /@ seq, 4, 1]]]
seq[[4444]] = ".";
Complement[
 StringDrop[ToString[NumberForm[#, 4, NumberPadding -> {"0", "0"}]], 
    1] & /@ Range[0, 9999], 
 Union[StringJoin /@ Partition[ToString /@ seq, 4, 1]]]
Output:
10003
{{0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 4, 0, 0, 0, 5, 0, 0,
   0, 6, 0, 0, 0, 7, 0, 0, 0, 8, 0, 0, 0, 9, 0, 0, 1, 1, 0, 0, 1, 2, 
  0, 0, 1, 3, 0, 0, 1, 4, 0, 0, 1, 5, 0, 0, 1, 6, 0, 0, 1, 7, 0, 0, 1,
   8, 0, 0, 1, 9, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 3, 0, 0, 2, 4, 0, 
  0, 2, 5, 0, 0, 2, 6, 0, 0, 2, 7, 0, 0, 2, 8, 0, 0, 2, 9, 0, 0, 3, 1,
   0, 0, 3, 2, 0, 0, 3, 3, 0, 0, 3, 4, 0, 0, 3, 5, 0}, {6, 8, 9, 8, 6,
   8, 9, 9, 6, 9, 6, 9, 7, 7, 6, 9, 7, 8, 6, 9, 7, 9, 6, 9, 8, 7, 6, 
  9, 8, 8, 6, 9, 8, 9, 6, 9, 9, 7, 6, 9, 9, 8, 6, 9, 9, 9, 7, 7, 7, 7,
   8, 7, 7, 7, 9, 7, 7, 8, 8, 7, 7, 8, 9, 7, 7, 9, 8, 7, 7, 9, 9, 7, 
  8, 7, 8, 7, 9, 7, 8, 8, 8, 7, 8, 8, 9, 7, 8, 9, 8, 7, 8, 9, 9, 7, 9,
   7, 9, 8, 8, 7, 9, 8, 9, 7, 9, 9, 8, 7, 9, 9, 9, 8, 8, 8, 8, 9, 8, 
  8, 9, 9, 8, 9, 8, 9, 9, 9, 9, 0, 0, 0}}
{}
{}
{"1478", "4781", "7813", "8137"}

Nim[edit]

Translation of: D
import algorithm, parseutils, strformat, strutils

const Digits = "0123456789"

#---------------------------------------------------------------------------------------------------

func deBruijn(k, n: int): string =
  let alphabet = Digits[0..<k]
  var a = newSeq[byte](k * n)
  var sequence: seq[byte]

  #.................................................................................................

  func db(t, p: int) =
    if t > n:
      if n mod p == 0:
        sequence &= a[1..p]
    else:
      a[t] = a[t - p]
      db(t + 1, p)
      var j = a[t - p] + 1
      while j < k.uint:
        a[t] = j
        db(t + 1, t)
        inc j

    #...............................................................................................

  db(1, 1)
  for i in sequence:
    result &= alphabet[i]
  result &= result[0..(n-2)]

#---------------------------------------------------------------------------------------------------

proc validate(db: string) =

  var found: array[10_000, int]
  var errs: seq[string]

  ## Check all strings of 4 consecutive digits within 'db'
  ## to see if all 10,000 combinations occur without duplication.
  for i in 0..(db.len - 4):
    let s = db[i..(i+3)]
    var n: int
    if s.parseInt(n) == 4:
      inc found[n]

  for n, count in found:
    if count == 0:
      errs &= fmt"    PIN number {n:04d} missing"
    elif count > 1:
      errs &= fmt"    PIN number {n:04d} occurs {count} times"

  if errs.len == 0:
    echo "  No errors found"
  else:
    let plural = if errs.len == 1: "" else: "s"
    echo fmt"  {errs.len} error{plural} found"
    for err in errs: echo err

#———————————————————————————————————————————————————————————————————————————————————————————————————

var db = deBruijn(10, 4)

echo fmt"The length of the de Bruijn sequence is {db.len}"
echo ""
echo fmt"The first 130 digits of the de Bruijn sequence are: {db[0..129]}"
echo ""
echo fmt"The last 130 digits of the de Bruijn sequence are: {db[^130..^1]}"
echo ""

echo "Validating the deBruijn sequence:"
db.validate()
echo ""
echo "Validating the reversed deBruijn sequence:"
reversed(db).join().validate()
echo ""

db[4443] = '.'
echo "Validating the overlaid deBruijn sequence:"
db.validate()
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the deBruijn sequence:
  No errors found

Validating the reversed deBruijn sequence:
  No errors found

Validating the overlaid deBruijn sequence:
  4 errors found
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

Pascal[edit]

A console application in Free Pascal, created with the Lazarus IDE.

For a given word length n, constructs a de Bruijn sequence by concatenating, in lexicographic order, all the Lyndon words whose length divides n. (See Wikipedia article "de Bruijn sequence", section "Construction".)

program deBruijnSequence;
uses SysUtils;

// Create a de Bruijn sequence for the given word length and alphabet.
function deBruijn( const n : integer; // word length
                   const alphabet : string) : string;
var
  d, k, m, s, t, seqLen : integer;
  w : array of integer;
begin
  k := Length( alphabet);
  // de Bruijn sequence will have length k^n
  seqLen := 1;
  for t := 1 to n do seqLen := seqLen*k;
  SetLength( result, seqLen);
  d := 0; // index into de Bruijn sequence (will be pre-inc'd)
  // Work through Lyndon words of length <= n, in lexicographic order.
  SetLength( w, n); // w holds array of indices into the alphabet
  w[0] := 1; // first Lyndon word
  m := 1; // m = length of Lyndon word
  repeat
    // If m divides n, append the current Lyndon word to the output
    if (m = n) or (m = 1) or (n mod m = 0) then begin
      for t := 0 to m - 1 do begin
        inc(d);
        result[d] := alphabet[w[t]];
      end;
    end;
    // Get next Lyndon word using Duval's algorithm:
    // (1) Fill w with repetitions of current word
    s := 0; t := m;
    while (t < n) do begin
      w[t] := w[s];
      inc(t);  inc(s);
      if s = m then s := 0;
    end;
    // (2) Repeatedly delete highest index k from end of w, if present
    m := n;
    while (m > 0) and (w[m - 1] = k) do dec(m);
    // (3) If word is now null, stop; else increment end value
    if m > 0 then inc( w[m - 1]);
  until m = 0;
  Assert( d = seqLen); // check that the sequence is exactly filled in
end;

// Check a de Bruijn sequence, assuming that its alphabet consists
//  of the digits '0'..'9' (in any order);
procedure CheckDecimal( const n : integer; // word length
                        const deB : string);
var
  count : array of integer;
  j, L, pin, nrErrors : integer;
  wrap : string;
begin
  L := Length( deB);
  // The de Bruijn sequence is cyclic; make an array to handle wrapround.
  SetLength( wrap, 2*n - 2);
  for j := 1 to n - 1 do wrap[j] := deB[L + j - n  + 1];
  for j := n to 2*n - 2 do wrap[j] := deB[j - n + 1];
  // Count occurrences of each PIN.
  // PIN = -1 if character is not a decimal digit.
  SetLength( count, L);
  for j := 0 to L - 1 do count[L] := 0;
  for j := 1 to L - n + 1 do begin
    pin := SysUtils.StrToIntDef( Copy( deB, j, n), -1);
    if pin >= 0 then inc( count[pin]);
  end;
  for j := 1 to n - 1 do begin
    pin := SysUtils.StrToIntDef( Copy( wrap, j, n), -1);
    if pin >= 0 then inc( count[pin]);
  end;
  // Check that all counts are 1
  nrErrors := 0;
  for j := 0 to L - 1 do begin
    if count[j] <> 1 then begin
      inc( nrErrors);
      WriteLn( SysUtils.Format( '  PIN %d has count %d', [j, count[j]]));
    end;
  end;
  WriteLn( SysUtils.Format( '  Number of errors = %d', [nrErrors]));
 end;

// Main routine
var
  deB, rev : string;
  L, j : integer;
begin
   deB := deBruijn( 4, '0123456789');
//   deB := deBruijn( 4, '7368290514'); // any permutation would do
   L := Length( deB);
   WriteLn( SysUtils.Format( 'Length of de Bruijn sequence = %d', [L]));
   if L >= 260 then begin
     WriteLn;
     WriteLn( 'First and last 130 characters are:');
     WriteLn( Copy( deB, 1, 65));
     WriteLn( Copy( deb, 66, 65));
     WriteLn( '...');
     WriteLn( Copy( deB, L - 129, 65));
     WriteLn( Copy( deB, L - 64, 65));
   end;
   WriteLn;
   WriteLn( 'Checking de Bruijn sequence:');
   CheckDecimal( 4, deB);
   // Check reversed sequence
   SetLength( rev, L);
   for j := 1 to L do rev[j] := deB[L + 1 - j];
   WriteLn( 'Checking reversed sequence:');
   CheckDecimal( 4, rev);
   // Check sequence with '.' instad of decimal digit
   if L >= 4444 then begin
     deB[4444] := '.';
     WriteLn( 'Checking vandalized sequence:');
     CheckDecimal( 4, deB);
   end;
end.
Output:
Length of de Bruijn sequence = 10000

First and last 130 characters are:
00001000200030004000500060007000800090011001200130014001500160017
00180019002100220023002400250026002700280029003100320033003400350
...
89768986899696977697869796987698869896997699869997777877797788778
97798779978787978887889789878997979887989799879998888988998989999

Checking de Bruijn sequence:
  Number of errors = 0
Checking reversed sequence:
  Number of errors = 0
Checking vandalized sequence:
  PIN 1459 has count 0
  PIN 4591 has count 0
  PIN 5814 has count 0
  PIN 8145 has count 0
  Number of errors = 4

Perl[edit]

Translation of: Raku
use strict;
use warnings;
use feature 'say';

my $seq;
for my $x (0..99) {
    my $a = sprintf '%02d', $x;
    next if substr($a,1,1) < substr($a,0,1);
    $seq .= (substr($a,0,1) == substr($a,1,1)) ? substr($a,0,1) : $a;
    for ($a+1 .. 99) {
        next if substr(sprintf('%02d', $_), 1,1) <= substr($a,0,1);
        $seq .= sprintf "%s%02d", $a, $_;
    }
}
$seq .= '000';

sub check {
    my($seq) = @_;
    my %chk;
    for (0.. -1 + length $seq) { $chk{substr($seq, $_, 4)}++ }
    say 'Missing: ' . join ' ', grep { ! $chk{ sprintf('%04d',$_) } } 0..9999;
    say 'Extra:   ' . join ' ', sort grep { $chk{$_} > 1 } keys %chk;
}

my $n = 130;
say "de Bruijn sequence length: " . length $seq;
say "\nFirst $n characters:\n" . substr($seq, 0, $n );
say "\nLast $n characters:\n"  . substr($seq, -$n, $n);
say "\nIncorrect 4 digit PINs in this sequence:";
check $seq;

say "\nIncorrect 4 digit PINs in the reversed sequence:";
check(reverse $seq);

say "\nReplacing the 4444th digit, '@{[substr($seq,4443,1)]}', with '5'";
substr $seq, 4443, 1, 5;
say "Incorrect 4 digit PINs in the revised sequence:";
check $seq;
Output:
de Bruijn sequence length: 10003

First 130 characters:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

Last 130 characters:
6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Incorrect 4 digit PINs in this sequence:
Missing:
Extra:

Incorrect 4 digit PINs in the reversed sequence:
Missing:
Extra:

Replacing the 4444th digit, '4', with '5'
Incorrect 4 digit PINs in the revised sequence:
Missing: 1459 4591 5814 8145
Extra:   1559 5591 5815 8155

Phix[edit]

Translation of: zkl
Translation of: Go
string deBruijn = ""
for n=0 to 99 do
    string a = sprintf("%02d",n)
    integer a1 = a[1],
            a2 = a[2]
    if a2>=a1 then
        deBruijn &= iff(a1=a2?a1:a)
        for m=n+1 to 99 do
            string ms = sprintf("%02d",m)
            if ms[2]>a1 then
                deBruijn &= a&ms
            end if
        end for
   end if
end for
deBruijn &= "000"
printf(1,"de Bruijn sequence length: %d\n\n",length(deBruijn))
printf(1,"First 130 characters:\n%s\n\n",deBruijn[1..130])
printf(1,"Last 130 characters:\n%s\n\n",deBruijn[-130..-1])
 
function check(string text)
    sequence res = {}
    sequence found = repeat(0,10000)
    integer k
    for i=1 to length(text)-3 do
        k = to_integer(text[i..i+3],-1)+1
        if k!=0 then found[k] += 1 end if
    end for
    for i=1 to 10000 do
        k = found[i]
        if k!=1 then
            string e = sprintf("Pin number %04d ",i-1)
            e &= iff(k=0?"missing":sprintf("occurs %d times",k))
            res = append(res,e)
        end if
    end for
    k = length(res)
    if k=0 then
        res = "No errors found"
    else
        string s = iff(k=1?"":"s")
        res = sprintf("%d error%s found:\n ",{k,s})&join(res,"\n ")
    end if
    return res
end function
 
printf(1,"Missing 4 digit PINs in this sequence: %s\n", check(deBruijn))
printf(1,"Missing 4 digit PINs in the reversed sequence: %s\n",check(reverse(deBruijn)))
printf(1,"4444th digit in the sequence: %c (setting it to .)\n", deBruijn[4444])
deBruijn[4444] = '.'
printf(1,"Re-running checks: %s\n",check(deBruijn))
Output:
de Bruijn sequence length: 10003

First 130 characters:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

Last 130 characters:
6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Missing 4 digit PINs in this sequence: No errors found
Missing 4 digit PINs in the reversed sequence: No errors found
4444th digit in the sequence: 4 (setting it to .)
Re-running checks: 4 errors found:
 Pin number 1459 missing
 Pin number 4591 missing
 Pin number 5814 missing
 Pin number 8145 missing

Python[edit]

# from https://en.wikipedia.org/wiki/De_Bruijn_sequence

def de_bruijn(k, n):
    """
    de Bruijn sequence for alphabet k
    and subsequences of length n.
    """
    try:
        # let's see if k can be cast to an integer;
        # if so, make our alphabet a list
        _ = int(k)
        alphabet = list(map(str, range(k)))

    except (ValueError, TypeError):
        alphabet = k
        k = len(k)

    a = [0] * k * n
    sequence = []

    def db(t, p):
        if t > n:
            if n % p == 0:
                sequence.extend(a[1:p + 1])
        else:
            a[t] = a[t - p]
            db(t + 1, p)
            for j in range(a[t - p] + 1, k):
                a[t] = j
                db(t + 1, t)
    db(1, 1)
    return "".join(alphabet[i] for i in sequence)
    
def validate(db):
    """
    
    Check that all 10,000 combinations of 0-9 are present in 
    De Bruijn string db.
    
    Validating the reversed deBruijn sequence:
      No errors found
    
    Validating the overlaid deBruijn sequence:
      4 errors found:
        PIN number 1459 missing
        PIN number 4591 missing
        PIN number 5814 missing
        PIN number 8145 missing
    
    """
    
    dbwithwrap = db+db[0:3]
    
    digits = '0123456789'
    
    errorstrings = []
    
    for d1 in digits:
        for d2 in digits:
            for d3 in digits:
                for d4 in digits:
                    teststring = d1+d2+d3+d4
                    if teststring not in dbwithwrap:
                        errorstrings.append(teststring)
                        
    if len(errorstrings) > 0:
        print("  "+str(len(errorstrings))+" errors found:")
        for e in errorstrings:
            print("  PIN number "+e+"  missing")
    else:
        print("  No errors found")

db = de_bruijn(10, 4)

print(" ")
print("The length of the de Bruijn sequence is ", str(len(db)))
print(" ")
print("The first 130 digits of the de Bruijn sequence are: "+db[0:130])
print(" ")
print("The last 130 digits of the de Bruijn sequence are: "+db[-130:])
print(" ")
print("Validating the deBruijn sequence:")
validate(db)
dbreversed = db[::-1]
print(" ")
print("Validating the reversed deBruijn sequence:")
validate(dbreversed)
dboverlaid = db[0:4443]+'.'+db[4444:]
print(" ")
print("Validating the overlaid deBruijn sequence:")
validate(dboverlaid)
Output:
The length of the de Bruijn sequence is  10000
 
The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350
 
The last 130 digits of the de Bruijn sequence are: 8976898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999
 
Validating the deBruijn sequence:
  No errors found
 
Validating the reversed deBruijn sequence:
  No errors found
 
Validating the overlaid deBruijn sequence:
  4 errors found:
  PIN number 1459  missing
  PIN number 4591  missing
  PIN number 5814  missing
  PIN number 8145  missing

Racket[edit]

Translation of: Go
#lang racket
 
(define (de-bruijn k n)
  (define a (make-vector (* k n) 0))
  (define seq '())
  (define (db t p)
    (cond
      [(> t n) (when (= (modulo n p) 0)
                 (set! seq (cons (call-with-values
                                  (thunk (vector->values a 1 (add1 p)))
                                  list)
                                 seq)))]
      [else (vector-set! a t (vector-ref a (- t p)))
            (db (add1 t) p)
            (for ([j (in-range (add1 (vector-ref a (- t p))) k)])
              (vector-set! a t j)
              (db (add1 t) t))]))
  (db 1 1)
  (define seq* (append* (reverse seq)))
  (append seq* (take seq* (sub1 n))))

(define seq (de-bruijn 10 4))
(printf "The length of the de Bruijn sequence is ~a\n\n" (length seq))
(printf "The first 130 digits of the de Bruijn sequence are:\n~a\n\n"
        (take seq 130))
(printf "The last 130 digits of the de Bruijn sequence are:\n~a\n\n"
        (take-right seq 130))

(define (validate name seq)
  (printf "Validating the ~ade Bruijn sequence:\n" name)
  (define expected (for/set ([i (in-range 0 10000)]) i))
  (define actual (for/set ([a (in-list seq)]
                           [b (in-list (rest seq))]
                           [c (in-list (rest (rest seq)))]
                           [d (in-list (rest (rest (rest seq))))])
                   (+ (* 1000 a) (* 100 b) (* 10 c) d)))
  (define diff (set-subtract expected actual))
  (cond
    [(set-empty? diff) (printf "  No errors found\n")]
    [else (for ([n (in-set diff)])
            (printf "  ~a is missing\n" (~a n #:width 4 #:pad-string "0")))])
  (newline))

(validate "" seq)
(validate "reversed " (reverse seq))
(validate "overlaid " (list-update seq 4443 add1))
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are:
(0 0 0 0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 9 0 0 1 1 0 0 1 2 0 0 1 3 0 0 1 4 0 0 1 5 0 0 1 6 0 0 1 7 0 0 1 8 0 0 1 9 0 0 2 1 0 0 2 2 0 0 2 3 0 0 2 4 0 0 2 5 0 0 2 6 0 0 2 7 0 0 2 8 0 0 2 9 0 0 3 1 0 0 3 2 0 0 3 3 0 0 3 4 0 0 3 5 0)

The last 130 digits of the de Bruijn sequence are:
(6 8 9 8 6 8 9 9 6 9 6 9 7 7 6 9 7 8 6 9 7 9 6 9 8 7 6 9 8 8 6 9 8 9 6 9 9 7 6 9 9 8 6 9 9 9 7 7 7 7 8 7 7 7 9 7 7 8 8 7 7 8 9 7 7 9 8 7 7 9 9 7 8 7 8 7 9 7 8 8 8 7 8 8 9 7 8 9 8 7 8 9 9 7 9 7 9 8 8 7 9 8 9 7 9 9 8 7 9 9 9 8 8 8 8 9 8 8 9 9 8 9 8 9 9 9 9 0 0 0)

Validating the de Bruijn sequence:
  No errors found

Validating the reversed de Bruijn sequence:
  No errors found

Validating the overlaid de Bruijn sequence:
  1459 is missing
  4591 is missing
  8145 is missing
  5814 is missing

Raku[edit]

(formerly Perl 6)

Works with: Rakudo version 2019.07.1

Deviates very slightly from the task spec. Generates a randomized de Bruijn sequence and replaces the 4444th digit with a the digit plus 1 mod 10 rather than a '.', mostly so it can demonstrate detection of extra PINs as well as missing ones.

# Generate the sequence
my $seq;

for ^100 {
    my $a = .fmt: '%02d';
    next if $a.substr(1,1) < $a.substr(0,1);
    $seq ~= ($a.substr(0,1) == $a.substr(1,1)) ?? $a.substr(0,1) !! $a;
    for +$a ^..^ 100 {
        next if .fmt('%02d').substr(1,1) <= $a.substr(0,1);
        $seq ~= sprintf "%s%02d", $a, $_ ;
    }
}

$seq = $seq.comb.list.rotate((^10000).pick).join;

$seq ~= $seq.substr(0,3);

sub check ($seq) {
    my %chk;
    for ^($seq.chars) { %chk{$seq.substr( $_, 4 )}++ }
    put 'Missing: ', (^9999).grep( { not %chk{ .fmt: '%04d' } } ).fmt: '%04d';
    put 'Extra:   ', %chk.grep( *.value > 1 )».key.sort.fmt: '%04d';
}

## The Task
put "de Bruijn sequence length: " ~ $seq.chars;

put "\nFirst 130 characters:\n" ~ $seq.substr( 0, 130 );

put "\nLast 130 characters:\n" ~ $seq.substr( * - 130 );

put "\nIncorrect 4 digit PINs in this sequence:";
check $seq;

put "\nIncorrect 4 digit PINs in the reversed sequence:";
check $seq.flip;

my $digit = $seq.substr(4443,1);
put "\nReplacing the 4444th digit, ($digit) with { ($digit += 1) %= 10 }";
put "Incorrect 4 digit PINs in the revised sequence:";
$seq.substr-rw(4443,1) = $digit;
check $seq;
Sample output:
de Bruijn sequence length: 10003

First 130 characters:
4558455945654566456745684569457545764577457845794585458645874588458945954596459745984599464647464846494655465646574658465946654666

Last 130 characters:
5445644574458445944654466446744684469447544764477447844794485448644874488448944954496449744984499454546454745484549455545564557455

Incorrect 4 digit PINs in this sequence:
Missing: 
Extra:   

Incorrect 4 digit PINs in the reversed sequence:
Missing: 
Extra:   

Replacing the 4444th digit, (1) with 2
Incorrect 4 digit PINs in the revised sequence:
Missing: 0961 1096 6109 9610
Extra:   0962 2096 6209 9620

REXX[edit]

The   de Bruijn   sequence generated by these REXX programs are identical to the sequence shown on the   discussion   page   (1st topic).

hard-coded node to be removed[edit]

/*REXX pgm calculates the  de Bruijn  sequence for all pin numbers  (4 digit decimals). */
$=                                               /*initialize the  de Bruijn  sequence. */
#=10;   lastNode= (#-2)(#-2)(#-1)(#-2)           /*this number is formed when this # ···*/
                                                 /*  ··· is skipped near the cycle end. */
  do j=0  for 10;  $= $ || j;  jj= j || j        /*compose the left half of the numbers.*/
                                                 /* [↓]     "  right  "   "  "     "    */
                                do k=jj+1  to 99;      z= jj || right(k, 2, 0)
                                if z==lastNode  then iterate    /*the last node skipped.*/
                                if pos(z, $)\==0  then iterate  /*# in sequence? Skip it*/
                                $= $ || z        /* ◄─────────────────────────────────┐ */
                                end   /*k*/      /*append a number to the sequence──◄─┘ */

     do r= jj  to (j || 9);  b= right(r, 2, 0)   /*compose the left half of the numbers.*/
     if b==jj  then iterate
     $= $ || right(b, 2, 0)                      /* [↓]     "  right  "   "  "     "    */
                                do k= b+1  to 99;      z= right(b, 2, 0) || right(k, 2, 0)
                                if pos(z, $)\==0  then iterate  /*# in sequence? Skip it*/
                                $= $ || z        /* ◄─────────────────────────────────┐ */
                                end   /*k*/      /*append a number to the sequence──◄─┘ */
     end   /*r*/
  end      /*j*/
                      @deB= 'de Bruijn sequence' /*literal used in some SAY instructions*/
$= $ || left($, 3)        /*append 000*/         /*simulate "wrap-around" de Bruijn seq.*/
       say 'length of the' @deB " is " length($) /*display the length of  de Bruijn seq.*/
say;   say 'first 130 digits of the' @deB":"     /*display the title for the next line. */
       say left($, 130)                          /*display 130 left-most digits of seq. */
say;   say ' last 130 digits of the' @deB":"     /*display the title for the next line. */
       say right($, 130)                         /*display 130 right-most digits of seq.*/
say                                              /*display a blank line.                */
call val $                                       /*call the  VAL  sub for verification. */
               @deB= 'reversed'   @deB           /*next,  we'll check on a reversed seq.*/
$$= reverse($)                                   /*do what a mirror does,  reversify it.*/
call val $$                                      /*call the  VAL  sub for verification. */
$= overlay(., $, 4444)                           /*replace 4,444th digit with a period. */
               @deB= 'overlaid' subword(@deB, 2) /* [↑] this'll cause a validation barf.*/
call val $                                       /*call the  VAL  sub for verification. */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
val: parse arg $$$;    e= 0;    _= copies('─',8) /*count of errors (missing PINs) so far*/
     say;      say _ 'validating the'    @deB"." /*display what's happening in the pgm. */
         do pin=0  for 1e4; pin4= right(pin,4,0) /* [↓]  maybe add leading zeros to pin.*/
         if pos(pin4, $$$)\==0  then iterate     /*Was number found?  Just as expected. */
         say 'PIN number '      pin       " wasn't found in"         @deb'.'
         e= e + 1                                /*bump the counter for number of errors*/
         end   /*pin*/                           /* [↑]  validate all 10,000 pin numbers*/
     if e==0  then e= 'No'                       /*Gooder English (sic) the error count.*/
     say _   e   'errors found.'                 /*display the number of errors found.  */
     return
output:
length of the de Bruijn sequence  is  10003

first 130 digits of the de Bruijn sequence:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

 last 130 digits of the de Bruijn sequence:
6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000


──────── validating the de Bruijn sequence.
──────── No errors found.

──────── validating the reversed de Bruijn sequence.
──────── No errors found.

──────── validating the overlaid de Bruijn sequence.
PIN number  1459  wasn't found in overlaid de Bruijn sequence.
PIN number  4591  wasn't found in overlaid de Bruijn sequence.
PIN number  5814  wasn't found in overlaid de Bruijn sequence.
PIN number  8145  wasn't found in overlaid de Bruijn sequence.
──────── 4 errors found.

programmatically removing of a node[edit]

Programming note:   instead of hardcoding the   lastNode   (that is elided from the sequence),   the 5th to the last node could simply be deleted.

This method slightly bloats the program and slows execution.

/*REXX pgm calculates the  de Bruijn  sequence for all pin numbers  (4 digit decimals). */
$=                                               /*initialize the  de Bruijn  sequence. */
   do j=0  for 10;  $= $ j;   jj= j || j          /*compose the left half of the numbers.*/
  $$= space($, 0)                                /* [↓]     "  right  "   "  "     "    */
                                do k=jj+1  to 99;      z= jj || right(k, 2, 0)
                                if pos(z, $$)\==0  then iterate /*# in sequence? Skip it*/
                                $= $ z           /* ◄─────────────────────────────────┐ */
                                end   /*k*/      /*append a number to the sequence──◄─┘ */
  $$= space($, 0)
     do r= jj  to (j || 9);  b= right(r, 2, 0)   /*compose the left half of the numbers.*/
     if b==jj  then iterate
     $= $ right(b, 2, 0)                         /* [↓]     "  right  "   "  "     "    */
     $$= space($, 0);           do k= b+1  to 99;      z= right(b, 2, 0) || right(k, 2, 0)
                                if pos(z, $$)\==0  then iterate /*# in sequence? Skip it*/
                                $= $ z           /* ◄─────────────────────────────────┐ */
                                end   /*k*/      /*append a number to the sequence──◄─┘ */
     $$= space($, 0)
     end   /*r*/
  end      /*j*/

$= delword($, words($)-4, 1)                     /*delete 5th from the last word in $.  */
$= space($, 0)
                      @deB= 'de Bruijn sequence' /*literal used in some SAY instructions*/
$= $ || left($, 3)        /*append 000*/         /*simulate "wrap-around" de Bruijn seq.*/
       say 'length of the' @deB " is " length($) /*display the length of  de Bruijn seq.*/
say;   say 'first 130 digits of the' @deB":"     /*display the title for the next line. */
       say left($, 130)                          /*display 130 left-most digits of seq. */
say;   say ' last 130 digits of the' @deB":"     /*display the title for the next line. */
       say right($, 130)                         /*display 130 right-most digits of seq.*/
call val $                                       /*call the  VAL  sub for verification. */
               @deB= 'reversed'   @deB           /*next,  we'll check on a reversed seq.*/
$r= reverse($)                                   /*do what a mirror does,  reversify it.*/
call val $r                                      /*call the  VAL  sub for verification. */
$= overlay(., $, 4444)                           /*replace 4,444th digit with a period. */
               @deB= 'overlaid' subword(@deB, 2) /* [↑] this'll cause a validation barf.*/
call val $                                       /*call the  VAL  sub for verification. */
exit                                             /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
val: parse arg $$$;    e= 0;    _= copies('─',8) /*count of errors (missing PINs) so far*/
     say;      say _ 'validating the'    @deB"." /*display what's happening in the pgm. */
         do pin=0  for 1e4; pin4= right(pin,4,0) /* [↓]  maybe add leading zeros to pin.*/
         if pos(pin4, $$$)\==0  then iterate     /*Was number found?  Just as expected. */
         say 'PIN number '      pin       " wasn't found in"         @deb'.'
         e= e + 1                                /*bump the counter for number of errors*/
         end   /*pin*/                           /* [↑]  validate all 10,000 pin numbers*/
     if e==0  then e= 'No'                       /*Gooder English (sic) the error count.*/
     say _   e   'errors found.'                 /*display the number of errors found.  */
     return
output   is identical to the 1st REXX version.

Ruby[edit]

Translation of: D
def deBruijn(k, n)
    alphabet = "0123456789"
    @a = Array.new(k * n, 0)
    @seq = []

    def db(k, n, t, p)
        if t > n then
            if n % p == 0 then
                temp = @a[1 .. p]
                @seq.concat temp
            end
        else
            @a[t] = @a[t - p]
            db(k, n, t + 1, p)
            j = @a[t - p] + 1
            while j < k do
                @a[t] = j # & 0xFF
                db(k, n, t + 1, t)
                j = j + 1
            end
        end
    end
    db(k, n, 1, 1)

    buf = ""
    for i in @seq
        buf <<= alphabet[i]
    end
    return buf + buf[0 .. n-2]
end

def validate(db)
    le = db.length
    found = Array.new(10000, 0)
    errs = []
    # Check all strings of 4 consecutive digits within 'db'
    # to see if all 10,000 combinations occur without duplication.
    for i in 0 .. le-4
        s = db[i .. i+3]
        if s.scan(/\D/).empty? then
            found[s.to_i] += 1
        end
    end
    for i in 0 .. found.length - 1
        if found[i] == 0 then
            errs <<= ("    PIN number %04d missing" % [i])
        elsif found[i] > 1 then
            errs <<= ("    PIN number %04d occurs %d times" % [i, found[i]])
        end
    end
    if errs.length == 0 then
        print "  No errors found\n"
    else
        pl = (errs.length == 1) ? "" : "s"
        print "  ", errs.length, " error", pl, " found:\n"
        for err in errs
            print err, "\n"
        end
    end
end

db = deBruijn(10, 4)
print "The length of the de Bruijn sequence is ", db.length, "\n\n"
print "The first 130 digits of the de Bruijn sequence are: ", db[0 .. 129], "\n\n"
print "The last 130 digits of the de Bruijn sequence are: ", db[-130 .. db.length], "\n\n"

print "Validating the de Bruijn sequence:\n"
validate(db)
print "\n"

db[4443] = '.'
print "Validating the overlaid de Bruijn sequence:\n"
validate(db)
Output:
The length of the de Bruijn sequence is 10003

The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the de Bruijn sequence:
  No errors found

Validating the overlaid de Bruijn sequence:
  4 errors found:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

Visual Basic .NET[edit]

Translation of: C#
Imports System.Text

Module Module1

    ReadOnly DIGITS As String = "0123456789"

    Function DeBruijn(k As Integer, n As Integer) As String
        Dim alphabet = DIGITS.Substring(0, k)
        Dim a(k * n) As Byte
        Dim seq As New List(Of Byte)
        Dim db As Action(Of Integer, Integer) = Sub(t As Integer, p As Integer)
                                                    If t > n Then
                                                        If n Mod p = 0 Then
                                                            Dim seg = New ArraySegment(Of Byte)(a, 1, p)
                                                            seq.AddRange(seg)
                                                        End If
                                                    Else
                                                        a(t) = a(t - p)
                                                        db(t + 1, p)
                                                        Dim j = a(t - p) + 1
                                                        While j < k
                                                            a(t) = j
                                                            db(t + 1, t)
                                                            j += 1
                                                        End While
                                                    End If
                                                End Sub
        db(1, 1)
        Dim buf As New StringBuilder
        For Each i In seq
            buf.Append(alphabet(i))
        Next
        Dim b = buf.ToString
        Return b + b.Substring(0, n - 1)
    End Function

    Function AllDigits(s As String) As Boolean
        For Each c In s
            If c < "0" OrElse "9" < c Then
                Return False
            End If
        Next
        Return True
    End Function

    Sub Validate(db As String)
        Dim le = db.Length
        Dim found(10000) As Integer
        Dim errs As New List(Of String)
        ' Check all strings of 4 consecutive digits within 'db'
        ' to see if all 10,000 combinations occur without duplication.
        For i = 1 To le - 3
            Dim s = db.Substring(i - 1, 4)
            If (AllDigits(s)) Then
                Dim n As Integer = Nothing
                Integer.TryParse(s, n)
                found(n) += 1
            End If
        Next
        For i = 1 To 10000
            If found(i - 1) = 0 Then
                errs.Add(String.Format("    PIN number {0,4} missing", i - 1))
            ElseIf found(i - 1) > 1 Then
                errs.Add(String.Format("    PIN number {0,4} occurs {1} times", i - 1, found(i - 1)))
            End If
        Next
        Dim lerr = errs.Count
        If lerr = 0 Then
            Console.WriteLine("  No errors found")
        Else
            Dim pl = If(lerr = 1, "", "s")
            Console.WriteLine("  {0} error{1} found:", lerr, pl)
            errs.ForEach(Sub(x) Console.WriteLine(x))
        End If
    End Sub

    Function Reverse(s As String) As String
        Dim arr = s.ToCharArray
        Array.Reverse(arr)
        Return New String(arr)
    End Function

    Sub Main()
        Dim db = DeBruijn(10, 4)
        Dim le = db.Length

        Console.WriteLine("The length of the de Bruijn sequence is {0}", le)
        Console.WriteLine(vbNewLine + "The first 130 digits of the de Bruijn sequence are: {0}", db.Substring(0, 130))
        Console.WriteLine(vbNewLine + "The last 130 digits of the de Bruijn sequence are: {0}", db.Substring(le - 130, 130))

        Console.WriteLine(vbNewLine + "Validating the deBruijn sequence:")
        Validate(db)

        Console.WriteLine(vbNewLine + "Validating the reversed deBruijn sequence:")
        Validate(Reverse(db))

        Dim bytes = db.ToCharArray
        bytes(4443) = "."
        db = New String(bytes)
        Console.WriteLine(vbNewLine + "Validating the overlaid deBruijn sequence:")
        Validate(db)
    End Sub

End Module
Output:
The first 130 digits of the de Bruijn sequence are: 0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

The last 130 digits of the de Bruijn sequence are: 6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Validating the deBruijn sequence:
  No errors found

Validating the reversed deBruijn sequence:
  No errors found

Validating the overlaid deBruijn sequence:
  4 errors found:
    PIN number 1459 missing
    PIN number 4591 missing
    PIN number 5814 missing
    PIN number 8145 missing

Wren[edit]

Translation of: Phix
Library: Wren-fmt
Library: Wren-str
import "/fmt" for Fmt
import "/str" for Str
 
var deBruijn = ""
for (n in 0..99) {
    var a = Fmt.rjust(2, n, "0")
    var a1 = a[0].bytes[0]
    var a2 = a[1].bytes[0]
    if (a2 >= a1) {
        deBruijn = deBruijn + ((a1 == a2) ? String.fromByte(a1): a)
        var m = n + 1
        while (m <= 99) {
            var ms = Fmt.rjust(2, m, "0")
            if (ms[1].bytes[0] > a1) deBruijn = deBruijn + a + ms
            m = m + 1
        }
    }
}
 
deBruijn = deBruijn + "000"
System.print("de Bruijn sequence length: %(deBruijn.count)\n")
System.print("First 130 characters:\n%(deBruijn[0...130])\n")
System.print("Last 130 characters:\n%(deBruijn[-130..-1])\n")
  
var check = Fn.new { |text|
    var res = []
    var found = List.filled(10000, 0)
    var k = 0
    for (i in 0...(text.count-3)) {
        var s = text[i..i+3]
        if (Str.allDigits(s)) {
            k = Num.fromString(s)
            found[k] = found[k] + 1
        }
    }
    for (i in 0...10000) {
        k = found[i]
        if (k != 1) {
            var e = "  Pin number %(Fmt.dz(4, i)) "
            e = e + ((k == 0) ? "missing" : "occurs %(k) times")
            res.add(e)
        }
    }
    k = res.count
    if (k == 0) {
        res = "No errors found"
    } else {
        var s = (k == 1) ? "" : "s"
        res = "%(k) error%(s) found:\n" + res.join("\n")
    }
    return res
}
 
System.print("Missing 4 digit PINs in this sequence: %(check.call(deBruijn))")
System.print("Missing 4 digit PINs in the reversed sequence: %(check.call(deBruijn[-1..0]))")
 
System.print("\n4,444th digit in the sequence: '%(deBruijn[4443])' (setting it to '.')")
deBruijn = deBruijn[0..4442] + "." + deBruijn[4444..-1]
System.print("Re-running checks: %(check.call(deBruijn))")
Output:
de Bruijn sequence length: 10003

First 130 characters:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

Last 130 characters:
6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Missing 4 digit PINs in this sequence: No errors found
Missing 4 digit PINs in the reversed sequence: No errors found

4,444th digit in the sequence: '4' (setting it to '.')
Re-running checks: 4 errors found:
  Pin number 1459 missing
  Pin number 4591 missing
  Pin number 5814 missing
  Pin number 8145 missing

zkl[edit]

Translation of: Raku
dbSeq:=Data();	// a byte/character buffer
foreach n in (100){
   a,a01,a11 := "%02d".fmt(n), a[0,1], a[1,1];
   if(a11<a01) continue;
   dbSeq.append( if(a01==a11) a01 else a );
   foreach m in ([n+1 .. 99]){
      if("%02d".fmt(m)[1,1] <= a01) continue;
      dbSeq.append("%s%02d".fmt(a,m));
   }
}
dbSeq.append("000");
seqText:=dbSeq.text;
println("de Bruijn sequence length: ",dbSeq.len());

println("\nFirst 130 characters:\n",seqText[0,130]);
println("\nLast 130 characters:\n", seqText[-130,*]);

fcn chk(seqText){
   chk:=Dictionary();
   foreach n in ([0..seqText.len()-1]){ chk[seqText[n,4]]=True }
   (9999).pump(List,"%04d".fmt,'wrap(k){ if(chk.holds(k)) Void.Skip else k })
}
println("\nMissing 4 digit PINs in this sequence: ", chk(seqText).concat(" "));
print("Missing 4 digit PINs in the reversed sequence: ",chk(seqText.reverse()).concat(" "));

println("\n4444th digit in the sequence: ", seqText[4443]);
dbSeq[4443]=".";
println("Setting the 4444th digit and reruning checks: ",chk(dbSeq.text).concat(" "));
Output:
de Bruijn sequence length: 10003

First 130 characters:
0000100020003000400050006000700080009001100120013001400150016001700180019002100220023002400250026002700280029003100320033003400350

Last 130 characters:
6898689969697769786979698769886989699769986999777787779778877897798779978787978887889789878997979887989799879998888988998989999000

Missing 4 digit PINs in this sequence: 
Missing 4 digit PINs in the reversed sequence: 
4444th digit in the sequence: 4
Setting the 4444th digit and reruning checks: 1459 4591 5814 8145