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# de Bruijn sequences

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).

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.

•   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.)

References

## 11l

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

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 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)
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
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 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
xthl ; Get sequence pointer
mov a,m ; Get digit
cpi 10 ; Valid digit?
jnc dinval ; If not, go do next 4-digit number
xthl ; Back to number
mov e,a
mvi d,0
dcr c ; More digits?
jnz dgtadd ; Then get digit
lxi d,val ; HL is now the current 4-digit number
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?
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)
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?
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]
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
jc dgtdiv
mvi a,'0'+10
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
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

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
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
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
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
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 [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.

Translation of: D

procedure De_Bruijn_Sequences is

function De_Bruijn (K, N : Positive) return String
is

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);
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

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#

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) {
}
} 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++

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

% 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
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
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
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

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

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

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) {
}
}
} 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

### Permutation-based

Straight-forward implementation of inverse Burrows—Wheeler transform [1] 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"

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

Translation of: Python
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

definitions. The C. verb computes the cycles. J's sort is not 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=: (/:[email protected]:groups -: [email protected]:[) NB. LENGTH verify_PINs SEQUENCE

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

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) {
}
}
} 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

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
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

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) {
}
} 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) {
} 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

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

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

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

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

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

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

# 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

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)))
(for ([j (in-range (add1 (vector-ref a (- t p))) k)])
(vector-set! a t j)
(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

(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';
}

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

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

/*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

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

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

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)
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

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")
}
}
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

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