Self-describing numbers

From Rosetta Code
This task has been clarified. Its programming examples are in need of review to ensure that they still fit the requirements of the task.
Task
Self-describing numbers
You are encouraged to solve this task according to the task description, using any language you may know.

There are several so-called "self-describing" or "self-descriptive" integers.

An integer is said to be "self-describing" if it has the property that, when digit positions are labeled 0 to N-1, the digit in each position is equal to the number of times that that digit appears in the number.

For example,   2020   is a four-digit self describing number:

  •   position   0   has value   2   and there are two 0s in the number;
  •   position   1   has value   0   and there are no 1s in the number;
  •   position   2   has value   2   and there are two 2s;
  •   position   3   has value   0   and there are zero 3s.


Self-describing numbers < 100.000.000  are:     1210,   2020,   21200,   3211000,   42101000.


Task Description
  1. Write a function/routine/method/... that will check whether a given positive integer is self-describing.
  2. As an optional stretch goal - generate and display the set of self-describing numbers.


Related tasks



Ada[edit]

with Ada.Text_IO; use Ada.Text_IO;
procedure SelfDesc is
subtype Desc_Int is Long_Integer range 0 .. 10**10-1;
 
function isDesc (innum : Desc_Int) return Boolean is
subtype S_Int is Natural range 0 .. 10;
type S_Int_Arr is array (0 .. 9) of S_Int;
ref, cnt : S_Int_Arr := (others => 0);
n, digit : S_Int := 0; num : Desc_Int := innum;
begin
loop
digit := S_Int (num mod 10);
ref (9 - n) := digit; cnt (digit) := cnt (digit) + 1;
num := num / 10; exit when num = 0; n := n + 1;
end loop;
return ref (9 - n .. 9) = cnt (0 .. n);
end isDesc;
 
begin
for i in Desc_Int range 1 .. 100_000_000 loop
if isDesc (i) then
Put_Line (Desc_Int'Image (i));
end if;
end loop;
end SelfDesc;
Output:
1210
2020
21200
3211000
42101000

ALGOL 68[edit]

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 2.6.win32
BEGIN
 
# return TRUE if number is self describing, FALSE otherwise #
OP SELFDESCRIBING = ( INT number )BOOL:
BEGIN
 
[10]INT counts := ( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 );
INT n := number;
INT digits := 0;
 
# count the occurances of each digit #
WHILE
n /= 0
DO
digits +:= 1;
counts[ ( n MOD 10 ) + 1 ] +:= 1;
n OVERAB 10
OD;
 
# construct the number that the counts would describe, #
# if the number was self describing #
 
INT described number := 0;
FOR i TO digits
DO
described number *:= 10;
described number +:= counts[ i ]
OD;
 
# if the described number is the input number, #
# it is self describing #
( number = described number )
END; # SELFDESCRIBING #
 
main: (
 
FOR i TO 100 000 000
DO
IF SELFDESCRIBING i
THEN
print( ( i, " is self describing", newline ) )
FI
OD
)
 
END
Output:
      +1210 is self describing
      +2020 is self describing
     +21200 is self describing
   +3211000 is self describing
  +42101000 is self describing

AutoHotkey[edit]

Uses CountSubString: Count occurrences of a substring#AutoHotkey

; The following directives and commands speed up execution:
#NoEnv
SetBatchlines -1
ListLines Off
Process, Priority,, high
 
MsgBox % 2020 ": " IsSelfDescribing(2020) "`n" 1337 ": " IsSelfDescribing(1337) "`n" 1210 ": " IsSelfDescribing(1210)
Loop 100000000
If IsSelfDescribing(A_Index)
list .= A_Index "`n"
MsgBox % "Self-describing numbers < 100000000 :`n" . list
 
CountSubstring(fullstring, substring){
StringReplace, junk, fullstring, %substring%, , UseErrorLevel
return errorlevel
}
 
IsSelfDescribing(number){
Loop Parse, number
If Not CountSubString(number, A_Index-1) = A_LoopField
return false
return true
}

Output:

---------------------------
Self.ahk
---------------------------
Self-describing numbers < 100000000 :
1210
2020
21200
3211000
42101000

---------------------------
OK   
---------------------------

AWK[edit]

# syntax: GAWK -f SELF-DESCRIBING_NUMBERS.AWK
BEGIN {
for (n=1; n<=100000000; n++) {
if (is_self_describing(n)) {
print(n)
}
}
exit(0)
}
function is_self_describing(n, i) {
for (i=1; i<=length(n); i++) {
if (substr(n,i,1) != gsub(i-1,"&",n)) {
return(0)
}
}
return(1)
}

output:

1210
2020
21200
3211000
42101000

BASIC[edit]

DIM x, r, b, c, n, m AS INTEGER
DIM a, d AS STRING
DIM v(10), w(10) AS INTEGER
CLS
FOR x = 1 TO 5000000
a$ = LTRIM$(STR$(x))
b = LEN(a$)
FOR c = 1 TO b
d$ = MID$(a$, c, 1)
v(VAL(d$)) = v(VAL(d$)) + 1
w(c - 1) = VAL(d$)
NEXT c
r = 0
FOR n = 0 TO 10
IF v(n) = w(n) THEN r = r + 1
v(n) = 0
w(n) = 0
NEXT n
IF r = 11 THEN PRINT x; " Yes,is autodescriptive number"
NEXT x
PRINT
PRINT "End"
SLEEP
END

BBC BASIC[edit]

      FOR N = 1 TO 5E7
IF FNselfdescribing(N) PRINT N
NEXT
END
 
DEF FNselfdescribing(N%)
LOCAL D%(), I%, L%, O%
DIM D%(9)
O% = N%
L% = LOG(N%)
WHILE N%
I% = N% MOD 10
D%(I%) += 10^(L%-I%)
N% DIV=10
ENDWHILE
= O% = SUM(D%())

Output:

      1210
      2020
     21200
   3211000
  42101000

Befunge[edit]

Translation of: ALGOL 68

Although we simply list the conforming numbers - nothing more.

Be aware, though, that even with a fast interpreter, it's going to be a very long time before you see the full set of results.

>1+9:0>\#06#:p#-:#1_$v
?v6:%+55:\+1\<<<\0:::<
#>g1+\6p55+/:#^_001p\v
^[email protected]#!`<<v\+g6g10*+55\<
>:*:*:*^>>:01g1+:01p`|
^_\#\:#+.#5\#5,#$:<-$<
Output:
1210
2020
21200
3211000
42101000

C[edit]

Using integers instead of strings.

#include <stdio.h>
 
inline int self_desc(unsigned long long xx)
{
register unsigned int d, x;
unsigned char cnt[10] = {0}, dig[10] = {0};
 
for (d = 0; xx > ~0U; xx /= 10)
cnt[ dig[d++] = xx % 10 ]++;
 
for (x = xx; x; x /= 10)
cnt[ dig[d++] = x % 10 ]++;
 
while(d-- && dig[x++] == cnt[d]);
 
return d == -1;
}
 
int main()
{
int i;
for (i = 1; i < 100000000; i++) /* don't handle 0 */
if (self_desc(i)) printf("%d\n", i);
 
return 0;
}
output
1210
2020
21200
3211000
42101000

Backtracking version[edit]

Backtracks on each digit from right to left, takes advantage of constraints "sum of digit values = number of digits" and "sum of (digit index * digit value) = number of digits". It is using as argument the list of allowed digits (example 012345789 to run the program in standard base 10).

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
 
#define BASE_MIN 2
#define BASE_MAX 94
 
void selfdesc(unsigned long);
 
const char *ref = "!\"#$%&'()*+,-./0123456789:;<=>[email protected][\\]^_`abcdefghijklmnopqrstuvwxyz{|}~";
char *digs;
unsigned long *nums, *inds, inds_sum, inds_val, base;
 
int main(int argc, char *argv[]) {
int used[BASE_MAX];
unsigned long digs_n, i;
if (argc != 2) {
fprintf(stderr, "Usage is %s <digits>\n", argv[0]);
return EXIT_FAILURE;
}
digs = argv[1];
digs_n = strlen(digs);
if (digs_n < BASE_MIN || digs_n > BASE_MAX) {
fprintf(stderr, "Invalid number of digits\n");
return EXIT_FAILURE;
}
for (i = 0; i < BASE_MAX; i++) {
used[i] = 0;
}
for (i = 0; i < digs_n && strchr(ref, digs[i]) && !used[digs[i]-*ref]; i++) {
used[digs[i]-*ref] = 1;
}
if (i < digs_n) {
fprintf(stderr, "Invalid digits\n");
return EXIT_FAILURE;
}
nums = calloc(digs_n, sizeof(unsigned long));
if (!nums) {
fprintf(stderr, "Could not allocate memory for nums\n");
return EXIT_FAILURE;
}
inds = malloc(sizeof(unsigned long)*digs_n);
if (!inds) {
fprintf(stderr, "Could not allocate memory for inds\n");
free(nums);
return EXIT_FAILURE;
}
inds_sum = 0;
inds_val = 0;
for (base = BASE_MIN; base <= digs_n; base++) {
selfdesc(base);
}
free(inds);
free(nums);
return EXIT_SUCCESS;
}
 
void selfdesc(unsigned long i) {
unsigned long diff_sum, upper_min, j, lower, upper, k;
if (i) {
diff_sum = base-inds_sum;
upper_min = inds_sum ? diff_sum:base-1;
j = i-1;
if (j) {
lower = 0;
upper = (base-inds_val)/j;
}
else {
lower = diff_sum;
upper = diff_sum;
}
if (upper < upper_min) {
upper_min = upper;
}
for (inds[j] = lower; inds[j] <= upper_min; inds[j]++) {
nums[inds[j]]++;
inds_sum += inds[j];
inds_val += inds[j]*j;
for (k = base-1; k > j && nums[k] <= inds[k] && inds[k]-nums[k] <= i; k--);
if (k == j) {
selfdesc(i-1);
}
inds_val -= inds[j]*j;
inds_sum -= inds[j];
nums[inds[j]]--;
}
}
else {
for (j = 0; j < base; j++) {
putchar(digs[inds[j]]);
}
puts("");
}
}

Output for base 36

$ time ./selfdesc.exe 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ
1210
2020
21200
3211000
42101000
521001000
6210001000
72100001000
821000001000
9210000001000
A2100000001000
B21000000001000
C210000000001000
D2100000000001000
E21000000000001000
F210000000000001000
G2100000000000001000
H21000000000000001000
I210000000000000001000
J2100000000000000001000
K21000000000000000001000
L210000000000000000001000
M2100000000000000000001000
N21000000000000000000001000
O210000000000000000000001000
P2100000000000000000000001000
Q21000000000000000000000001000
R210000000000000000000000001000
S2100000000000000000000000001000
T21000000000000000000000000001000
U210000000000000000000000000001000
V2100000000000000000000000000001000
W21000000000000000000000000000001000
 
real 0m0.094s
user 0m0.046s
sys 0m0.030s

C++[edit]

 
#include <iostream>
 
//--------------------------------------------------------------------------------------------------
typedef unsigned long long bigint;
 
//--------------------------------------------------------------------------------------------------
using namespace std;
 
//--------------------------------------------------------------------------------------------------
class sdn
{
public:
bool check( bigint n )
{
int cc = digitsCount( n );
return compare( n, cc );
}
 
void displayAll( bigint s )
{
for( bigint y = 1; y < s; y++ )
if( check( y ) )
cout << y << " is a Self-Describing Number." << endl;
}
 
private:
bool compare( bigint n, int cc )
{
bigint a;
while( cc )
{
cc--; a = n % 10;
if( dig[cc] != a ) return false;
n -= a; n /= 10;
}
return true;
}
 
int digitsCount( bigint n )
{
int cc = 0; bigint a;
memset( dig, 0, sizeof( dig ) );
while( n )
{
a = n % 10; dig[a]++;
cc++ ; n -= a; n /= 10;
}
return cc;
}
 
int dig[10];
};
//--------------------------------------------------------------------------------------------------
int main( int argc, char* argv[] )
{
sdn s;
s. displayAll( 1000000000000 );
cout << endl << endl; system( "pause" );
 
bigint n;
while( true )
{
system( "cls" );
cout << "Enter a positive whole number ( 0 to QUIT ): "; cin >> n;
if( !n ) return 0;
if( s.check( n ) ) cout << n << " is";
else cout << n << " is NOT";
cout << " a Self-Describing Number!" << endl << endl;
system( "pause" );
}
 
return 0;
}
 
Output:
1210 is a Self-Describing Number.
2020 is a Self-Describing Number.
21200 is a Self-Describing Number.
3211000 is a Self-Describing Number.
42101000 is a Self-Describing Number.
521001000 is a Self-Describing Number.
[...]

Alternate version[edit]

Uses C++11. Build with

g++ -std=c++11 sdn.cpp
#include <algorithm>
#include <array>
#include <iostream>
 
bool is_self_describing(unsigned long long int n) noexcept {
if (n == 0) {
return false;
}
 
std::array<char, 10> digits = {0}, counts = {0};
std::size_t i = digits.size();
 
do {
counts[digits[--i] = n % 10]++;
} while ((n /= 10) > 0 && i < digits.size());
 
return n == 0 && std::equal(begin(digits) + i, end(digits), begin(counts));
}
 
int main() {
for (unsigned long long int i = 0; i < 10000000000; ++i) {
if (is_self_describing(i)) {
std::cout << i << "\n";
}
}
}

Output:

1210
2020
21200
3211000
42101000
521001000
6210001000

Common Lisp[edit]

Not terribly speedy brute force. I played around with "counting" the digits directly into a number by adding in appropriate powers of 10 for each digit I see but trailing zeroes kind of gum up the works. I still think it's possible and probably much faster because it wouldn't have to allocate an array and then turn around and "interpret" it back out but I didn't really pursue it.

(defun to-ascii (str) (mapcar #'char-code (coerce str 'list)))
 
(defun to-digits (n)
(mapcar #'(lambda(v) (- v 48)) (to-ascii (princ-to-string n))))
 
(defun count-digits (n)
(do
((counts (make-array '(10) :initial-contents '(0 0 0 0 0 0 0 0 0 0)))
(curlist (to-digits n) (cdr curlist)))
((null curlist) counts)
(setf (aref counts (car curlist)) (+ 1 (aref counts (car curlist)))))))
 
(defun self-described-p (n)
(if (not (numberp n))
nil
(do ((counts (count-digits n))
(ipos 0 (+ 1 ipos))
(digits (to-digits n) (cdr digits)))
((null digits) t)
(if (not (eql (car digits) (aref counts ipos))) (return nil)))))

Output:

(loop for i from 1 to 4000000 do (if (self-described-p i) (print i)))
 
1210
2020
21200
3211000
NIL

D[edit]

Functional Version[edit]

import std.stdio, std.algorithm, std.range, std.conv, std.string;
 
bool isSelfDescribing(in long n) pure nothrow @safe {
auto nu = n.text.representation.map!q{ a - '0' };
return nu.length.iota.map!(a => nu.count(a)).equal(nu);
}
 
void main() {
4_000_000.iota.filter!isSelfDescribing.writeln;
}
Output:
[1210, 2020, 21200, 3211000]

A Faster Version[edit]

bool isSelfDescribing2(ulong n) nothrow @nogc {
if (n <= 0)
return false;
 
__gshared static uint[10] digits, d;
digits[] = 0;
d[] = 0;
int i;
 
if (n < uint.max) {
uint nu = cast(uint)n;
for (i = 0; nu > 0 && i < digits.length; nu /= 10, i++) {
d[i] = nu % 10;
digits[d[i]]++;
}
if (nu > 0)
return false;
} else {
for (i = 0; n > 0 && i < digits.length; n /= 10, i++) {
d[i] = n % 10;
digits[d[i]]++;
}
if (n > 0)
return false;
}
 
foreach (immutable k; 0 .. i)
if (d[k] != digits[i - k - 1])
return false;
return true;
}
 
void main() {
import std.stdio;
 
foreach (immutable x; [1210, 2020, 21200, 3211000,
42101000, 521001000, 6210001000])
assert(x.isSelfDescribing2);
 
foreach (immutable i; 0 .. 4_000_000)
if (i.isSelfDescribing2)
i.writeln;
}
Output:
1210
2020
21200
3211000

(About 0.29 seconds run time for 4 million tests.)

Output with foreach(i;0..600_000_000):

1210
2020
21200
3211000
42101000
521001000

Elixir[edit]

defmodule Self_describing do
def number(n) do
digits = Integer.digits(n)
Enum.map(0..length(digits)-1, fn s ->
length(Enum.filter(digits, fn c -> c==s end))
end) == digits
end
end
 
m = 3300000
Enum.filter(0..m, fn n -> Self_describing.number(n) end)
Output:
[1210, 2020, 21200, 3211000]

Erlang[edit]

 
 
sdn(N) -> lists:map(fun(S)->length(lists:filter(fun(C)->C-$0==S end,N))+$0 end,lists:seq(0,length(N)-1))==N.
gen(M) -> lists:filter(fun(N)->sdn(integer_to_list(N)) end,lists:seq(0,M)).
 
 

Forth[edit]

\ where unavailable.
: third ( A b c -- A b c A ) >r over r> swap ;
: (.) ( u -- c-addr u ) 0 <# #s #> ;
 
\ COUNT is a standard word with a very different meaning, so this
\ would typically be beheaded, or given another name, or otherwise
\ given a short lifespan, so to speak.
: count ( c-addr1 u1 c -- c-addr1 u1 c+1 u )
0 2over bounds do
over i [email protected] = if 1+ then
loop swap 1+ swap ;
 
: self-descriptive? ( u -- f )
(.) [char] 0 third third bounds ?do
count i [email protected] [char] 0 - <> if drop 2drop false unloop exit then
loop drop 2drop true ;

FreeBASIC[edit]

' FB 1.05.0 Win64
 
Function selfDescribing (n As UInteger) As Boolean
If n = 0 Then Return False
Dim ns As String = Str(n)
Dim count(0 To 9) As Integer '' all elements zero by default
While n > 0
count(n Mod 10) += 1
n \= 10
Wend
For i As Integer = 0 To Len(ns) - 1
If ns[i] - 48 <> count(i) Then Return False '' numerals have ascii values from 48 to 57
Next
Return True
End Function
 
Print "The self-describing numbers less than 100 million are:"
For i As Integer = 0 To 99999999
If selfDescribing(i) Then Print i; " ";
Next
Print
Print "Press any key to quit"
Sleep
Output:
The self-describing numbers less than 100 million are:
 1210  2020  21200  3211000  42101000

Go[edit]

package main
 
import (
"fmt"
"strconv"
"strings"
)
 
// task 1 requirement
func sdn(n int64) bool {
if n >= 1e10 {
return false
}
s := strconv.FormatInt(n, 10)
for d, p := range s {
if int(p)-'0' != strings.Count(s, strconv.Itoa(d)) {
return false
}
}
return true
}
 
// task 2 code (takes a while to run)
func main() {
for n := int64(0); n < 1e10; n++ {
if sdn(n) {
fmt.Println(n)
}
}
}

Output produced by above program:

1210
2020
21200
3211000
42101000
521001000
6210001000

Haskell[edit]

import Data.Char
 
count :: Int -> [Int] -> Int
count x = length . filter (x ==)
 
isSelfDescribing :: Integer -> Bool
isSelfDescribing n =
nu == f where
nu = map digitToInt (show n)
f = map (\a -> count a nu) [0 .. ((length nu)-1)]
 
main = do
let tests = [1210, 2020, 21200, 3211000,
42101000, 521001000, 6210001000]
print $ map isSelfDescribing tests
print $ filter isSelfDescribing [0 .. 4000000]

Output:

[True,True,True,True,True,True,True]
[1210,2020,21200,3211000]

Here are functions for generating all the self-describing numbers of a certain length. We capitalize on the fact (from Wikipedia) that a self-describing number of length n is a base-n number (i.e. all digits are 0..n-1).

import Data.Char (intToDigit)
import Control.Monad (replicateM, forM_)
 
count :: Int -> [Int] -> Int
count x = length . filter (x ==)
 
-- all the combinations of n digits of base n
-- a base-n number are represented as a list of ints, one per digit
allBaseNNumsOfLength :: Int -> [[Int]]
allBaseNNumsOfLength n = replicateM n [0..n-1]
 
isSelfDescribing :: [Int] -> Bool
isSelfDescribing num =
all (\(i,x) -> x == count i num) $ zip [0..] num
 
-- translate it back into an integer in base-10
decimalize :: [Int] -> Int
decimalize = read . map intToDigit
 
main = forM_ [1..7] $
print . map decimalize . filter isSelfDescribing . allBaseNNumsOfLength

Icon and Unicon[edit]

The following program contains the procedure is_self_describing to test if a number is a self-describing number, and the procedure self_describing_numbers to generate them.

 
procedure count (test_item, str)
result := 0
every item := !str do
if test_item == item then result +:= 1
return result
end
 
procedure is_self_describing (n)
ns := string (n) # convert to a string
every i := 1 to *ns do {
if count (string(i-1), ns) ~= ns[i] then fail
}
return 1 # success
end
 
# generator for creating self_describing_numbers
procedure self_describing_numbers ()
n := 1
repeat {
if is_self_describing(n) then suspend n
n +:= 1
}
end
 
procedure main ()
# write the first 4 self-describing numbers
every write (self_describing_numbers ()\4)
end
 

A slightly more concise solution can be derived from the above by taking more advantage of Icon's (and Unicon's) automatic goal-directed evaluation:

 
procedure is_self_describing (n)
ns := string (n) # convert to a string
every i := 1 to *ns do {
if count (string(i-1), ns) ~= ns[i] then fail
}
return n # on success, return the self-described number
end
 
procedure self_describing_numbers ()
suspend is_self_describing(seq())
end

J[edit]

Solution:
   digits   =: 10&#.^:_1
counts =: _1 + [: #/.~ [email protected]:# , ]
selfdesc =: = counts&.digits"0 NB. Note use of "under"
Example:
   selfdesc 2020 1210 21200 3211000 43101000 42101000
1 1 1 1 0 1
Extra credit:
   [email protected]:selfdesc i. 1e6
1210 2020 21200

Discussion: The use of &. here is a great example of its surprisingly broad applicability, and the elegance it can produce.

The use of "0 is less satisfying, expressing an essentially scalar solution, and that such an approach runs against the grain of J becomes quite evident when executing the extra credit sentence.

It would not be difficult to rephrase the verb in a way that would take advantage of J's array mastery, but it would cost us of some of the simplicity and elegance of the existing solution. More gratifying would be some kind of closed-form, algebraic formula that could identify the SDNs directly, without test-and-filter.

That said, note that this is an incomplete implementation of the extra-credit problem -- and, hypothetically speaking, numbers longer than 9 digits could be valid results in the extra-credit problem (we just have to be sure that digit positions which are not occupied by digits we can represent have 0 for their count). This might allow us to treat numbers up to just under 19 digits as self describing numbers. This is a slightly larger range of numbers than we get for positive integers from signed 64 bit representation. So a proper solution to this problem on currently available hardware (one that finds the complete result in some useful span of time) probably should use a non-brute-force solution.

Java[edit]

public class SelfDescribingNumbers{
public static boolean isSelfDescribing(int a){
String s = Integer.toString(a);
for(int i = 0; i < s.length(); i++){
String s0 = s.charAt(i) + "";
int b = Integer.parseInt(s0); // number of times i-th digit must occur for it to be a self describing number
int count = 0;
for(int j = 0; j < s.length(); j++){
int temp = Integer.parseInt(s.charAt(j) + "");
if(temp == i){
count++;
}
if (count > b) return false;
}
if(count != b) return false;
}
return true;
}
 
public static void main(String[] args){
for(int i = 0; i < 100000000; i++){
if(isSelfDescribing(i)){
System.out.println(i);
}
}
}
}

JavaScript[edit]

Works with: SpiderMonkey
function is_self_describing(n) {
var digits = Number(n).toString().split("").map(function(elem) {return Number(elem)});
var len = digits.length;
var count = digits.map(function(x){return 0});
 
digits.forEach(function(digit, idx, ary) {
if (digit >= count.length)
return false
count[digit] ++;
});
 
return digits.equals(count);
}
 
Array.prototype.equals = function(other) {
if (this === other)
return true; // same object
if (this.length != other.length)
return false;
for (idx in this)
if (this[idx] !== other[idx])
return false;
return true;
}
 
for (var i=1; i<=3300000; i++)
if (is_self_describing(i))
print(i);

outputs

1210
2020
21200
3211000

jq[edit]

Works with: jq version 1.4
# If your jq includes all/2 then comment out the following definition, 
# which is slightly less efficient:
def all(generator; condition):
reduce generator as $i (true; if . then $i | condition else . end);
def selfie:
def count(value): reduce .[] as $i (0; if $i == value then . + 1 else . end);
def digits: tostring | explode | map(. - 48);
 
digits
| if add != length then false
else . as $digits
| all ( range(0; length); . as $i | $digits | (.[$i] == count($i)) )
end;

The task:

range(0; 100000001) | select(selfie)
Output:
$ jq -n -f Self-describing_numbers.jq
1210
2020
21200
3211000
42101000

Julia[edit]

function selfie(x)
y = reverse(digits(x))
len = length(y)
sum(y) != len && return false
for i = 1:len
y[i] != sum(y .== i-1) && return false
end
return true
end
Output:
julia> selfie(2020)
true

julia> selfie(2021)
false

julia> selfies(x) = for i = 1:x selfie(i) && println(i) end
# methods for generic function selfies
selfies(x) at none:1

julia> @time selfies(4000000)
1210
2020
21200
3211000
elapsed time: 1.901413209 seconds

K[edit]

  sdn: {n~+/'n=/:!#n:0$'$x}'
sdn 1210 2020 2121 21200 3211000 42101000
1 1 0 1 1 1
 
&[email protected]!:1e6
1210 2020 21200

Kotlin[edit]

// version 1.0.6
 
fun selfDescribing(n: Int): Boolean {
if (n <= 0) return false
val ns = n.toString()
val count = IntArray(10)
var nn = n
while (nn > 0) {
count[nn % 10] += 1
nn /= 10
}
for (i in 0 until ns.length)
if( ns[i] - '0' != count[i]) return false
return true
}
 
fun main(args: Array<String>) {
println("The self-describing numbers less than 100 million are:")
for (i in 0..99999999) if (selfDescribing(i)) print("$i ")
println()
}
Output:
The self-describing numbers less than 100 million are:
1210 2020 21200 3211000 42101000

Liberty BASIC[edit]

'adapted from BASIC solution
FOR x = 1 TO 5000000
a$ = TRIM$(STR$(x))
b = LEN(a$)
FOR c = 1 TO b
d$ = MID$(a$, c, 1)
v(VAL(d$)) = v(VAL(d$)) + 1
w(c - 1) = VAL(d$)
NEXT c
r = 0
FOR n = 0 TO 10
IF v(n) = w(n) THEN r = r + 1
v(n) = 0
w(n) = 0
NEXT n
IF r = 11 THEN PRINT x; " is a self-describing number"
NEXT x
PRINT
PRINT "End"

LiveCode[edit]

function selfDescNumber n
local tSelfD, tLen
put len(n) into tLen
repeat with x = 0 to (tLen - 1)
put n into nCopy
replace x with empty in nCopy
put char (x + 1) of n = (tLen - len(nCopy)) into tSelfD
if not tSelfD then exit repeat
end repeat
return tSelfD
end selfDescNumber
To list the self-describing numbers to 10 million
on mouseUp
repeat with n = 0 to 10000000
if selfDescNumber(n) then
put n into selfNum[n]
end if
end repeat
combine selfNum using comma
put selfNum
end mouseUp
Output
1210,2020,21200,3211000

[edit]

TO XX
BT
MAKE "AA (ARRAY 10 0)
MAKE "BB (ARRAY 10 0)
FOR [Z 0 9][SETITEM :Z :AA "0 SETITEM :Z :BB "0 ]
FOR [A 1 50000][
MAKE "B COUNT :A
MAKE "Y 0
MAKE "X 0
MAKE "R 0
MAKE "J 0
MAKE "K 0
 
FOR [C 1 :B][MAKE "D ITEM :C :A
SETITEM :C - 1 :AA :D
MAKE "X ITEM :D :BB
MAKE "Y :X + 1
SETITEM :D :BB :Y
MAKE "R 0]
FOR [Z 0 9][MAKE "J ITEM :Z :AA
MAKE "K ITEM :Z :BB
IF :J = :K [MAKE "R :R + 1]]
IF :R = 10 [PR :A]
FOR [Z 0 9][SETITEM :Z :AA "0 SETITEM :Z :BB "0 ]]
PR [END]
END

Lua[edit]

function Is_self_describing( n )
local s = tostring( n )
 
local t = {}
for i = 0, 9 do t[i] = 0 end
 
for i = 1, s:len() do
local idx = tonumber( s:sub(i,i) )
t[idx] = t[idx] + 1
end
 
for i = 1, s:len() do
if t[i-1] ~= tonumber( s:sub(i,i) ) then return false end
end
 
return true
end
 
for i = 1, 999999999 do
print( Is_self_describing( i ) )
end

Mathematica[edit]

isSelfDescribing[n_Integer] := (RotateRight[DigitCount[n]] == PadRight[IntegerDigits[n], 10])
Select[Range[10^10 - 1], isSelfDescribing]
-> {1210,2020,21200,3211000,42101000,521001000,6210001000}

MATLAB / Octave[edit]

function z = isSelfDescribing(n)
s = int2str(n)-'0'; % convert to vector of digits
y = hist(s,0:9);
z = all(y(1:length(s))==s);
end;

Test function:

for k = 1:1e10, 
if isSelfDescribing(k),
printf('%i\n',k);
end
end;

Output:

  1210
  2020
  21200
  ... 

Nim[edit]

import strutils
 
proc count(s, sub): int =
var i = 0
while true:
i = s.find(sub, i)
if i < 0:
break
inc i
inc result
 
proc isSelfDescribing(n): bool =
let s = $n
for i, ch in s:
if s.count($i) != parseInt("" & ch):
return false
return true
 
for x in 0 .. 4_000_000:
if isSelfDescribing(x): echo x

Output:

1210
2020
21200
321100

ooRexx[edit]

 
-- REXX program to check if a number (base 10) is self-describing.
parse arg x y .
if x=='' then exit
if y=='' then y=x
-- 10 digits is the maximum size number that works here, so cap it
numeric digits 10
y=min(y, 9999999999)
 
loop number = x to y
loop i = 1 to number~length
digit = number~subchar(i)
-- return on first failure
if digit \= number~countstr(i - 1) then iterate number
end
say number "is a self describing number"
end
 

output when using the input of: 0 999999999

1210 is a self-describing number.
2020 is a self-describing number.
21200 is a self-describing number.
3211000 is a self-describing number.
42101000 is a self-describing number.
521001000 is a self-describing number.
6210001000 is a self-describing number.

PARI/GP[edit]

This is a finite set...

S=[1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000];
isself(n)=vecsearch(S,n)

Pascal[edit]

Program SelfDescribingNumber;
 
uses
SysUtils;
 
function check(number: longint): boolean;
var
i, d: integer;
a: string;
count, w : array [0..9] of integer;
 
begin
a := intToStr(number);
for i := 0 to 9 do
begin
count[i] := 0;
w[i] := 0;
end;
for i := 1 to length(a) do
begin
d := ord(a[i]) - ord('0');
inc(count[d]);
w[i - 1] := d;
end;
check := true;
i := 0;
while check and (i <= 9) do
begin
check := count[i] = w[i];
inc(i);
end;
end;
 
var
x: longint;
 
begin
writeln ('Autodescriptive numbers from 1 to 100000000:');
for x := 1 to 100000000 do
if check(x) then
writeln (' ', x);
writeln('Job done.');
end.

Output:

:> ./SelfDescribingNumber
Autodescriptive numbers from 1 to 100000000:
 1210
 2020
 21200
 3211000
 42101000
Job done.

Perl[edit]

The idea is to make two arrays: the first one contains the digits at their positions and the second one contains the digits counts.

The number is self-descriptive If the arrays are equal.

sub is_selfdesc
{
local $_ = shift;
my @b = (0) x length;
$b[$_]++ for my @a = split //;
return "@a" eq "@b";
}
 
# check all numbers from 0 to 100k plus two 'big' ones
for (0 .. 100000, 3211000, 42101000) {
print "$_\n" if is_selfdesc($_);
}

Output:

1210
2020
21200
3211000
42101000

Perl 6[edit]

my @values = <1210 2020 21200 3211000
42101000 521001000 6210001000 27 115508>;
 
for @values -> $test {
say "$test is {sdn($test) ?? '' !! 'NOT ' }a self describing number.";
}
 
sub sdn($n) {
my $s = $n.Str;
my $chars = $s.chars;
my @a = +«$s.comb;
my @b;
for @a -> $i {
return False if $i >= $chars;
++@b[$i];
}
@b[$_] //= 0 for ^$chars;
@a eqv @b;
}
 
.say if .&sdn for ^9999999;

Output:

1210 is a self describing number.
2020 is a self describing number.
21200 is a self describing number.
3211000 is a self describing number.
42101000 is a self describing number.
521001000 is a self describing number.
6210001000 is a self describing number.
27 is NOT a self describing number.
115508 is NOT a self describing number.
1210
2020
21200
3211000

Phix[edit]

Translation of: Ada
function self_desc(integer i)
sequence digits = repeat(0,10), counts = repeat(0,10)
integer n = 0, digit
while 1 do
digit := mod(i,10)
digits[10-n] := digit
counts[digit+1] += 1
i = floor(i/10)
if i=0 then exit end if
n += 1
end while
return digits[10-n..10] = counts[1..n+1]
end function
 
atom t0 = time()
for i=10 to 100_000_000 by 10 do
if self_desc(i) then ?i end if
end for
printf(1,"done (%3.2fs)",time()-t0)
Output:
1210
2020
21200
3211000
42101000
done (21.78s)

PHP[edit]

Works with: PHP 5.

<?php
 
function is_describing($number) {
foreach (str_split((int) $number) as $place => $value) {
if (substr_count($number, $place) != $value) {
return false;
}
}
return true;
}
 
for ($i = 0; $i <= 50000000; $i += 10) {
if (is_describing($i)) {
echo $i . PHP_EOL;
}
}
 
?>

Output:

1210
2020
21200
3211000
42101000

PicoLisp[edit]

(de selfDescribing (N)
(fully '((D I) (= D (cnt = N (circ I))))
(setq N (mapcar format (chop N)))
(range 0 (length N)) ) )

Output:

: (filter selfDescribing (range 1 4000000))
-> (1210 2020 21200 3211000)

PowerShell[edit]

According to the Wiki definition, the sum of the products of the index and the digit contained at the index should equal the number of digits in the number:

 
function Test-SelfDescribing ([int]$Number)
{
[int[]]$digits = $Number.ToString().ToCharArray() | ForEach-Object {[Char]::GetNumericValue($_)}
[int]$sum = 0
 
for ($i = 0; $i -lt $digits.Count; $i++)
{
$sum += $i * $digits[$i]
}
 
$sum -eq $digits.Count
}
 
 
Test-SelfDescribing -Number 2020
 
Output:
True

It takes a very long while to test 100,000,000 numbers, and since they are already known just test a few:

 
11,2020,21200,321100 | ForEach-Object {
[PSCustomObject]@{
Number = $_
IsSelfDescribing = Test-SelfDescribing -Number $_
}
} | Format-Table -AutoSize
 
Output:
Number IsSelfDescribing
------ ----------------
    11            False
  2020             True
 21200             True
321100            False

Prolog[edit]

Works with SWI-Prolog and library clpfd written by Markus Triska.

:- use_module(library(clpfd)).
 
self_describling :-
forall(between(1, 10, I),
(findall(N, self_describling(I,N), L),
format('Len ~w, Numbers ~w~n', [I, L]))).
 
% search of the self_describling numbers of a given len
self_describling(Len, N) :-
length(L, Len),
Len1 is Len - 1,
L = [H|T],
 
% the first figure is greater than 0
H in 1..Len1,
 
% there is a least to figures so the number of these figures
% is at most Len - 2
Len2 is Len - 2,
T ins 0..Len2,
 
% the sum of the figures is equal to the len of the number
sum(L, #=, Len),
 
% There is at least one figure corresponding to the number of zeros
H1 #= H+1,
element(H1, L, V),
V #> 0,
 
% create the list
label(L),
 
% test the list
msort(L, LNS),
packList(LNS,LNP),
numlist(0, Len1, NumList),
verif(LNP,NumList, L),
 
% list is OK, create the number
maplist(atom_number, LA, L),
number_chars(N, LA).
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% testing a number (not use in this program)
self_describling(N) :-
number_chars(N, L),
maplist(atom_number, L, LN),
msort(LN, LNS),
packList(LNS,LNP), !,
length(L, Len),
Len1 is Len - 1,
numlist(0, Len1, NumList),
verif(LNP,NumList, LN).
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% verif(PackList, Order_of_Numeral, Numeral_of_the_nuber_to_test)
% Packlist is of the form [[Number_of_Numeral, Order_of_Numeral]|_]
% Test succeed when
 
% All lists are empty
verif([], [], []).
 
% Packlist is empty and all lasting numerals are 0
verif([], [_N|S], [0|T]) :-
verif([], S, T).
 
% Number of numerals N is V
verif([[V, N]|R], [N|S], [V|T]) :-
verif(R, S, T).
 
% Number of numerals N is 0
verif([[V, N1]|R], [N|S], [0|T]) :-
N #< N1,
verif([[V,N1]|R], S, T).
 
 
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ?- packList([a,a,a,b,c,c,c,d,d,e], L).
% L = [[3,a],[1,b],[3,c],[2,d],[1,e]] .
% ?- packList(R, [[3,a],[1,b],[3,c],[2,d],[1,e]]).
% R = [a,a,a,b,c,c,c,d,d,e] .
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
packList([],[]).
 
packList([X],[[1,X]]) :- !.
 
 
packList([X|Rest],[XRun|Packed]):-
run(X,Rest, XRun,RRest),
packList(RRest,Packed).
 
 
run(Var,[],[1, Var],[]).
 
run(Var,[Var|LRest],[N1, Var],RRest):-
N #> 0,
N1 #= N + 1,
run(Var,LRest,[N, Var],RRest).
 
 
run(Var,[Other|RRest], [1, Var],[Other|RRest]):-
dif(Var,Other).

Output

 ?- self_describling.
Len 1, Numbers []
Len 2, Numbers []
Len 3, Numbers []
Len 4, Numbers [1210,2020]
Len 5, Numbers [21200]
Len 6, Numbers []
Len 7, Numbers [3211000]
Len 8, Numbers [42101000]
Len 9, Numbers [521001000]
Len 10, Numbers [6210001000]
true.

PureBasic[edit]

Procedure isSelfDescribing(x.q)
;returns 1 if number is self-describing, otherwise it returns 0
Protected digitCount, digit, i, digitSum
Dim digitTally(10)
Dim digitprediction(10)
 
If x <= 0
ProcedureReturn 0 ;number must be positive and non-zero
EndIf
 
While x > 0 And i < 10
digit = x % 10
digitSum + digit
If digitSum > 10
ProcedureReturn 0 ;sum of digits' values exceeds maximum possible
EndIf
digitprediction(i) = digit
digitTally(digit) + 1
x / 10
i + 1
Wend
digitCount = i - 1
 
If digitSum < digitCount Or x > 0
ProcedureReturn 0 ;sum of digits' values is too small or number has more than 10 digits
EndIf
 
For i = 0 To digitCount
If digitTally(i) <> digitprediction(digitCount - i)
ProcedureReturn 0 ;number is not self-describing
EndIf
Next
ProcedureReturn 1 ;number is self-describing
EndProcedure
 
Procedure displayAll()
Protected i, j, t
PrintN("Starting search for all self-describing numbers..." + #CRLF$)
For j = 0 To 9
PrintN(#CRLF$ + "Searching possibilites " + Str(j * 1000000000) + " -> " + Str((j + 1) * 1000000000 - 1)+ "...")
t = ElapsedMilliseconds()
For i = 0 To 999999999
If isSelfDescribing(j * 1000000000 + i)
PrintN(Str(j * 1000000000 + i))
EndIf
Next
PrintN("Time to search this range of possibilities: " + Str((ElapsedMilliseconds() - t) / 1000) + "s.")
Next
PrintN(#CRLF$ + "Search complete.")
EndProcedure
 
If OpenConsole()
 
DataSection
Data.q 1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000, 3214314
EndDataSection
 
Define i, x.q
For i = 1 To 8
Read.q x
Print(Str(x) + " is ")
If Not isSelfDescribing(x)
Print("not ")
EndIf
PrintN("selfdescribing.")
Next
PrintN(#CRLF$)
 
displayAll()
 
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf

Sample output:

1210 is selfdescribing.
2020 is selfdescribing.
21200 is selfdescribing.
3211000 is selfdescribing.
42101000 is selfdescribing.
521001000 is selfdescribing.
6210001000 is selfdescribing.
3214314 is not selfdescribing.


Starting search for all self-describing numbers...


Searching possibilites 0 -> 999999999...
1210
2020
21200
3211000
42101000
521001000
Time to search this range of possibilities: 615s.

Searching possibilites 1000000000 -> 1999999999...
Time to search this range of possibilities: 614s.

Searching possibilites 2000000000 -> 2999999999...
Time to search this range of possibilities: 628s.

Searching possibilites 3000000000 -> 3999999999...
Time to search this range of possibilities: 631s.

Searching possibilites 4000000000 -> 4999999999...
Time to search this range of possibilities: 630s.

Searching possibilites 5000000000 -> 5999999999...
Time to search this range of possibilities: 628s.

Searching possibilites 6000000000 -> 6999999999...
6210001000
Time to search this range of possibilities: 629s.

Searching possibilites 7000000000 -> 7999999999...
Time to search this range of possibilities: 631s.

Searching possibilites 8000000000 -> 8999999999...
Time to search this range of possibilities: 629s.

Searching possibilites 9000000000 -> 9999999999...
Time to search this range of possibilities: 629s.

Search complete.

Python[edit]

>>> def isSelfDescribing(n):
s = str(n)
return all(s.count(str(i)) == int(ch) for i, ch in enumerate(s))
 
>>> [x for x in range(4000000) if isSelfDescribing(x)]
[1210, 2020, 21200, 3211000]
>>> [(x, isSelfDescribing(x)) for x in (1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000)]
[(1210, True), (2020, True), (21200, True), (3211000, True), (42101000, True), (521001000, True), (6210001000, True)]

Generator[edit]

From here.

def impl(d, c, m):
if m < 0: return
if d == c[:len(d)]: print d
for i in range(c[len(d)],m+1):
dd = d+[i]
if i<len(dd) and c[i]==dd[i]: continue
impl(dd,c[:i]+[c[i]+1]+c[i+1:],m-i)
 
def self(n): impl([], [0]*(n+1), n)
 
self(10)

Output:

[]
[1, 2, 1, 0]
[2, 0, 2, 0]
[2, 1, 2, 0, 0]
[3, 2, 1, 1, 0, 0, 0]
[4, 2, 1, 0, 1, 0, 0, 0]
[5, 2, 1, 0, 0, 1, 0, 0, 0]
[6, 2, 1, 0, 0, 0, 1, 0, 0, 0] 

Racket[edit]

#lang racket
(define (get-digits number (lst null))
(if (zero? number)
lst
(get-digits (quotient number 10) (cons (remainder number 10) lst))))
 
(define (self-describing? number)
(if (= number 0) #f
(let ((digits (get-digits number)))
(for/fold ((bool #t))
((i (in-range (length digits))))
(and bool
(= (count (lambda (x) (= x i)) digits)
(list-ref digits i)))))))

Sadly, the implementation is too slow for the optional task, taking somewhere around 3 minutes to check all numbers below 100.000.000

REXX[edit]

Also see:   OEIS A46043   and   OEIS A138480.

digit by digit test[edit]

/*REXX program determines if a number (in base 10)  is a  self─describing,              */
/*────────────────────────────────────────────────────── self─descriptive, */
/*────────────────────────────────────────────────────── autobiographical, or a */
/*────────────────────────────────────────────────────── curious number. */
parse arg x y . /*obtain optional arguments from the CL*/
if x=='' | x=="," then exit /*Not specified? Then get out of Dodge*/
if y=='' | y=="," then y=x /* " " Then use the X value.*/
w=length(y) /*use Y's width for aligned output. */
numeric digits max(9, w) /*ensure we can handle larger numbers. */
if x==y then do /*handle the case of a single number. */
noYes=test_SDN(y) /*is it or ain't it? */
say y word("is isn't", noYes+1) 'a self-describing number.'
exit
end
 
do n=x to y
if test_SDN(n) then iterate /*if not self─describing, try again. */
say right(n,w) 'is a self-describing number.' /*is it? */
end /*n*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
test_SDN: procedure; parse arg ?; L=length(?) /*obtain the argument and its length.*/
do j=L to 1 by -1 /*parsing backwards is slightly faster.*/
if substr(?,j,1)\==L-length(space(translate(?,,j-1),0)) then return 1
end /*j*/
return 0 /*faster if used inverted truth table. */
        ╔══════════════════════════════════════════════════════════════════╗
        ║ The method used above is to TRANSLATE the digit being queried to ║
        ║ blanks,  then use the  SPACE  BIF function to remove all blanks, ║
        ║ and then compare the new number's length to the original length. ║
        ║                                                                  ║
        ║ The difference in  length  is the  number of digits  translated. ║
        ╚══════════════════════════════════════════════════════════════════╝

output   when using the input of:   0   9999999999

      1210 is a self-describing number.
      2020 is a self-describing number.
     21200 is a self-describing number.
   3211000 is a self-describing number.
  42101000 is a self-describing number.
 521001000 is a self-describing number.
6210001000 is a self-describing number.

faster method[edit]

(Uses table lookup.)

/*REXX program  determines  if a  number  (in base 10)   is  a  self-describing  number.*/
parse arg x y . /*obtain optional arguments from the CL*/
if x=='' | x=="," then exit /*Not specified? Then get out of Dodge*/
if y=='' | y=="," then y=x /*Not specified? Then use the X value.*/
w=length(y) /*use Y's width for aligned output. */
numeric digits max(9, w) /*handle the possibility of larger #'s.*/
$= '1210 2020 21200 3211000 42101000 521001000 6210001000' /*the list of numbers.*/
/*test for a single integer. */
if x==y then do /*handle the case of a single number. */
say word("isn't is", wordpos(x, $) + 1) 'a self-describing number.'
exit
end
/* [↓] test for a range of integers.*/
do n=x to y; parse var n '' -1 _ /*obtain the last decimal digit of N. */
if _\==0 then iterate
if wordpos(n, $)==0 then iterate
say right(n,w) 'is a self-describing number.'
end /*n*/
/*stick a fork in it, we're all done. */

output   is the same as the 1st REXX example.

fastest method[edit]

(Uses a table look-up.)

(Results are instantaneous.)

/*REXX program  determines  if a  number  (in base 10)   is  a  self-describing  number.*/
parse arg x y . /*obtain optional arguments from the CL*/
if x=='' | x=="," then exit /*Not specified? Then get out of Dodge*/
if y=='' | y=="," then y=x /*Not specified? Then use the X value.*/
w=length(y) /*use Y's width for aligned output. */
numeric digits max(9, w) /*handle the possibility of larger #'s.*/
$= '1210 2020 21200 3211000 42101000 521001000 6210001000' /*the list of numbers.*/
/*test for a single integer. */
if x==y then do /*handle the case of a single number. */
say word("isn't is", wordpos(x, $) + 1) 'a self-describing number.'
exit
end
/* [↓] test for a range of integers.*/
do n=1 for words($); _=word($, n) /*look for integers that are in range. */
if _<x | _>y then iterate /*if not self-describing, try again. */
say right(_, w) 'is a self-describing number.'
end /*n*/ /*stick a fork in it, we're all done. */

output   is the same as the 1st REXX example.

Ruby[edit]

def self_describing?(n)
digits = n.digits.reverse
digits.each_with_index.all?{|digit, idx| digits.count(idx) == digit}
end
 
3_300_000.times {|n| puts n if self_describing?(n)}

outputs

1210
2020
21200
3211000

Run BASIC[edit]

for i = 0 to 50000000 step 10
a$ = str$(i)
for c = 1 TO len(a$)
d = val(mid$(a$, c, 1))
j(d) = j(d) + 1
k(c-1) = d
next c
r = 0
for n = 0 to 10
r = r + (j(n) = k(n))
j(n) = 0
k(n) = 0
next n
if r = 11 then print i
next i
print "== End =="
end

Seed7[edit]

$ include "seed7_05.s7i";
 
const func boolean: selfDescr (in string: stri) is func
result
var boolean: check is TRUE;
local
var integer: idx is 0;
var array integer: count is [0 .. 9] times 0;
begin
for idx range 1 to length(stri) do
incr(count[ord(stri[idx]) - ord('0')]);
end for;
idx := 1;
while check and idx <= length(stri) do
check := count[pred(idx)] = ord(stri[idx]) - ord('0');
incr(idx);
end while;
end func;
 
const proc: gen (in integer: n) is func
local
var array integer : digits is 0 times 0;
var string: stri is "";
var integer: numberOfOneDigits is 0;
var integer: idx is 0;
begin
while numberOfOneDigits <= 2 and numberOfOneDigits < n - 2 do
digits := n times 0;
digits[1] := n - 2 - numberOfOneDigits;
if digits[1] <> 2 then
digits[digits[1] + 1] := 1;
digits[2] := 2;
digits[3] := 1;
else
digits[2] := ord(numberOfOneDigits <> 0);
digits[3] := 2;
end if;
stri := "";
for idx range 1 to n do
stri &:= chr(ord(digits[idx]) + ord('0'));
end for;
if selfDescr(stri) then
writeln(stri);
end if;
incr(numberOfOneDigits);
end while;
end func;
 
const proc: main is func
local
const array integer: nums is [] (1210, 1337, 2020, 21200, 3211000, 42101000);
var integer: number is 0;
begin
for number range nums do
write(number <& " is ");
if not selfDescr(str(number)) then
write("not ");
end if;
writeln("self describing");
end for;
writeln;
writeln("All autobiograph numbers:");
for number range 1 to 10 do
gen(number);
end for;
end func;

Output:

1210 is self describing
1337 is not self describing
2020 is self describing
21200 is self describing
3211000 is self describing
42101000 is self describing

All autobiograph numbers:
2020
1210
21200
3211000
42101000
521001000
6210001000

Sidef[edit]

Translation of: Perl 6
func sdn(Number n) {
var b = [0]*n.len
var a = n.digits
a.each { |i| b[i] := 0 ++ }
a == b
}
 
var values = [1210, 2020, 21200, 3211000,
42101000, 521001000, 6210001000, 27, 115508]
 
values.each { |test|
say "#{test} is #{sdn(test) ? '' : 'NOT ' }a self describing number."
}
 
say "\nSelf-descriptive numbers less than 1e5 (in base 10):"
^1e5 -> each { |i| say i if sdn(i) }
Output:
1210 is a self describing number.
2020 is a self describing number.
21200 is a self describing number.
3211000 is a self describing number.
42101000 is a self describing number.
521001000 is a self describing number.
6210001000 is a self describing number.
27 is NOT a self describing number.
115508 is NOT a self describing number.

Self-descriptive numbers less than 1e5 (in base 10):
1210
2020
21200

Extra credit: this will generate all the self-describing numbers in bases 7 to 36:

for b in (7 .. 36) {
var n = ((b-4) * b**(b-1) + 2*(b**(b-2)) + b**(b-3) + b**3 -> base(b))
say "base #{'%2d' % b}: #{n}"
}
Output:
base  7: 3211000
base  8: 42101000
base  9: 521001000
base 10: 6210001000
base 11: 72100001000
base 12: 821000001000
base 13: 9210000001000
base 14: a2100000001000
base 15: b21000000001000
base 16: c210000000001000
base 17: d2100000000001000
base 18: e21000000000001000
base 19: f210000000000001000
base 20: g2100000000000001000
base 21: h21000000000000001000
base 22: i210000000000000001000
base 23: j2100000000000000001000
base 24: k21000000000000000001000
base 25: l210000000000000000001000
base 26: m2100000000000000000001000
base 27: n21000000000000000000001000
base 28: o210000000000000000000001000
base 29: p2100000000000000000000001000
base 30: q21000000000000000000000001000
base 31: r210000000000000000000000001000
base 32: s2100000000000000000000000001000
base 33: t21000000000000000000000000001000
base 34: u210000000000000000000000000001000
base 35: v2100000000000000000000000000001000
base 36: w21000000000000000000000000000001000

Tcl[edit]

package require Tcl 8.5
proc isSelfDescribing num {
set digits [split $num ""]
set len [llength $digits]
set count [lrepeat $len 0]
foreach d $digits {
if {$d >= $len} {return false}
lset count $d [expr {[lindex $count $d] + 1}]
}
foreach d $digits c $count {if {$c != $d} {return false}}
return true
}
 
for {set i 0} {$i < 100000000} {incr i} {
if {[isSelfDescribing $i]} {puts $i}
}

UNIX Shell[edit]

Works with: bash

Seeking self-describing numbers up to 100,000,000 is very time consuming, so we'll just verify a few numbers.

selfdescribing() {
local n=$1
local count=()
local i
for ((i=0; i<${#n}; i++)); do
((count[${n:i:1}]++))
done
for ((i=0; i<${#n}; i++)); do
(( ${n:i:1} == ${count[i]:-0} )) || return 1
done
return 0
}
 
for n in 0 1 10 11 1210 2020 21200 3211000 42101000; do
if selfdescribing $n; then
printf "%d\t%s\n" $n yes
else
printf "%d\t%s\n" $n no
fi
done
Output:
0	no
1	no
10	no
11	no
1210	yes
2020	yes
21200	yes
3211000	yes
42101000	yes

VBScript[edit]

Takes a very, very long time to check 100M numbers that I have to terminate the script. But the function works.

 
Function IsSelfDescribing(n)
IsSelfDescribing = False
Set digit = CreateObject("Scripting.Dictionary")
For i = 1 To Len(n)
k = Mid(n,i,1)
If digit.Exists(k) Then
digit.Item(k) = digit.Item(k) + 1
Else
digit.Add k,1
End If
Next
c = 0
For j = 0 To Len(n)-1
l = Mid(n,j+1,1)
If digit.Exists(CStr(j)) Then
If digit.Item(CStr(j)) = CInt(l) Then
c = c + 1
End If
ElseIf l = 0 Then
c = c + 1
Else
Exit For
End If
Next
If c = Len(n) Then
IsSelfDescribing = True
End If
End Function
 
'testing
start_time = Now
s = ""
For m = 1 To 100000000
If IsSelfDescribing(m) Then
WScript.StdOut.WriteLine m
End If
Next
end_time = Now
WScript.StdOut.WriteLine "Elapse Time: " & DateDiff("s",start_time,end_time) & " seconds"
 

XPL0[edit]

code ChOut=8, IntOut=11;
 
func SelfDesc(N); \Returns 'true' if N is self-describing
int N;
int Len, \length = number of digits in N
I, D;
char Digit(10), Count(10);
 
proc Num2Str(N); \Convert integer N to string in Digit
int N;
int R;
[N:= N/10;
R:= rem(0);
if N then Num2Str(N);
Digit(Len):= R;
Len:= Len+1;
];
 
[Len:= 0;
Num2Str(N);
for I:= 0 to Len-1 do Count(I):= 0;
for I:= 0 to Len-1 do
[D:= Digit(I);
if D >= Len then return false;
Count(D):= Count(D)+1;
];
for I:= 0 to Len-1 do
if Count(I) # Digit(I) then return false;
return true;
]; \SelfDesc
 
 
int N;
for N:= 0 to 100_000_000-1 do
if SelfDesc(N) then [IntOut(0, N); ChOut(0, ^ )]

Output:

1210 2020 21200 3211000 42101000 

zkl[edit]

fcn isSelfDescribing(n){
if (n.bitAnd(1)) return(False); // Wikipedia: last digit must be zero
nu:= n.toString();
ns:=["0".."9"].pump(String,nu.inCommon,"len"); //"12233".inCommon("2")-->"22"
(nu+"0000000000")[0,10] == ns; //"2020","2020000000"
}

Since testing a humongous number of numbers is slow, chunk the task into a bunch of threads. Even so, it pegged my 8 way Ivy Bridge Linux box for quite some time (eg the Python & AWK solutions crush this one).

//[1..0x4_000_000].filter(isSelfDescribing).println();
const N=0d500_000;
[1..0d100_000_000, N] // chunk and thread, 200 in this case
.apply(fcn(n){ n.filter(N,isSelfDescribing) }.future)
.filter().apply("noop").println();

A future is a thread returning a [delayed] result, future.filter/future.noop will block until the future coughs up the result. Since the results are really sparse for the bigger numbers, filter out the empty results.

Output:
L(L(1210,2020,21200),L(3211000),L(42101000))