Numbers divisible by their individual digits, but not by the product of their digits.: Difference between revisions
(→{{header|Haskell}}: Added a variant obtaining digit lists numerically.) |
|||
| Line 510: | Line 510: | ||
and another approach might be to obtain (unordered) digit lists numerically, rather by string conversion. |
and another approach might be to obtain (unordered) digit lists numerically, rather by string conversion. |
||
<lang haskell>import Data. |
<lang haskell>import Data.Bool (bool) |
||
import Data.List (unfoldr) |
|||
import Data.List.Split (chunksOf) |
import Data.List.Split (chunksOf) |
||
import Data.Tuple (swap) |
import Data.Tuple (swap) |
||
| Line 529: | Line 530: | ||
digits :: Int -> [Int] |
digits :: Int -> [Int] |
||
digits = |
digits = |
||
unfoldr $ |
|||
where |
|||
(bool Nothing . Just . swap . flip quotRem 10) <*> (0 <) |
|||
go x |
|||
| 0 < x = Just $ swap $ quotRem x 10 |
|||
| otherwise = Nothing |
|||
--------------------------- TEST ------------------------- |
--------------------------- TEST ------------------------- |
||
Revision as of 22:34, 10 April 2021
- Task
Find and show positive decimal integers divisible by their individual digits, but not divisible by the product of their digits,
where n < 1000
8086 Assembly
<lang asm> cpu 8086 org 100h section .text mov si,1 ; Current number number: mov bp,1 ; BP holds product mov di,si ; DI holds number digit: mov ax,di ; Get digit xor dx,dx mov cx,10 div cx mov di,ax ; Store remaining digits in DI test dx,dx ; Is the digit zero? jz next ; Then this number is not valid mov cx,dx ; Is the number divisible by the digit? xor dx,dx mov ax,si div cx test dx,dx jnz next ; If not, this number is not valid mov ax,bp ; Otherwise, multiply digit into product mul cx mov bp,ax test di,di ; More digits? jnz digit ; If so, do next digit mov ax,si ; Is the number divisible by the product? xor dx,dx div bp test dx,dx jz next ; If so, this number is not valid mov ax,si ; Otherwise, print the number call prnum next: inc si ; Next number cmp si,1000 ; Are we there yet? jne number ; If not, do the next number ret ; But if so, stop ;;; Print number in AX prnum: mov bx,dbuf ; Start of buffer mov cx,10 ; Divisor .dgt: xor dx,dx ; Divide by 10 div cx add dl,'0' ; Make ASCII digit dec bx mov [bx],dl ; Store digit test ax,ax ; Any more digits remaining? jnz .dgt ; If so, next digits mov dx,bx ; Print string using MS-DOS mov ah,9 int 21h ret section .data db '*****' dbuf: db 13,10,'$'</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
Ada
<lang Ada>with Ada.Text_Io; with Ada.Integer_Text_Io;
procedure Numbers_Divisible is
function Is_Divisible (N : Natural) return Boolean is
function To_Decimal (C : Character) return Natural
is ( Character'Pos (C) - Character'Pos ('0'));
Image : constant String := N'Image;
Digit : Natural;
Prod : Natural := 1;
begin
for A in Image'First + 1 .. Image'Last loop
Digit := To_Decimal (Image (A));
if Digit = 0 then
return False;
end if;
if N mod Digit /= 0 then
return False;
end if;
Prod := Prod * Digit;
end loop;
return N mod Prod /= 0;
end Is_Divisible;
Count : Natural := 0;
begin
for N in 1 .. 999 loop
if Is_Divisible (N) then
Count := Count + 1;
Ada.Integer_Text_Io.Put (N, Width => 5);
if Count mod 15 = 0 then
Ada.Text_Io.New_Line;
end if;
end if;
end loop;
end Numbers_Divisible;</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
ALGOL W
<lang algolw>begin % find numbers divisible by their digits but not the product of their digits %
% returns true if n is divisible by its digits but not the product of its %
% digits, false otherwise %
logical procedure divisibleByDigitsButNotDigitProduct ( integer value n ) ;
begin
integer v, p;
logical matches;
v := n;
p := 1;
matches := v not = 0;
while matches and v > 0 do begin
integer d;
d := v rem 10;
v := v div 10;
if d = 0 then matches := false else matches := n rem d = 0;
p := p * d
end while_matches_and_v_gt_0 ;
if matches then begin
if p = 0 then matches := false else matches := n rem p not = 0
end if_matche ;
matches
end divisibleByDigitsButNotDigitProduct ;
integer count;
% show the members of the seuence up to 1000 %
write( "Numbers below 1000 that are divisible by their digits but not the product of their digits:" );
write();
count := 0;
for i := 0 until 999 do begin
if divisibleByDigitsButNotDigitProduct( i ) then begin
writeon( i_w := 3, s_w := 0, " ", i );
count := count + 1;
if count rem 15 = 0 then write()
end if_divisibleByDigitsButNotDigitProduct__i
end for_i
end.</lang>
- Output:
Numbers below 1000 that are divisible by their digits but not the product of their digits: 22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
APL
<lang APL>(⊢(/⍨)((⍎¨∘⍕)((∧/0=|)∧0≠(×/⊣)|⊢)⊢)¨)⍳999</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555
636 648 666 728 777 784 824 848 864 888 936 999
BASIC
<lang basic>10 DEFINT A-Z 20 FOR I=1 TO 999 30 N=I: P=1 40 D=N MOD 10 50 IF D=0 THEN 110 60 P=P*D 70 IF I MOD D THEN 110 80 N=N\10 90 IF N THEN 40 100 IF I MOD P <> 0 THEN PRINT I, 110 NEXT I</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
C
<lang c>#include <stdio.h>
int divisible(int n) {
int p = 1;
int c, d;
for (c=n; c; c /= 10) {
d = c % 10;
if (!d || n % d) return 0;
p *= d;
}
return n % p;
}
int main() {
int n, c=0;
for (n=1; n<1000; n++) {
if (divisible(n)) {
printf("%5d", n);
if (!(++c % 10)) printf("\n");
}
}
printf("\n");
return 0;
}</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
Cowgol
<lang cowgol>include "cowgol.coh";
sub divisible(n: uint16): (r: uint8) is
var product: uint16 := 1;
var c := n;
r := 1;
while c != 0 loop
var digit := c % 10;
if digit == 0 or n % digit != 0 then
r := 0;
return;
end if;
product := product * digit;
c := c / 10;
end loop;
if n % product == 0 then
r := 0;
end if;
end sub;
var n: uint16 := 1; var c: uint8 := 1; while n < 1000 loop
if divisible(n) != 0 then
print_i16(n);
c := c + 1;
if c % 10 == 1 then
print_nl();
else
print_char('\t');
end if;
end if;
n := n + 1;
end loop; print_nl();</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
F#
<lang fsharp> // Nigel Galloway. April 9th., 2021 let rec fN i g e l=match g%10,g/10 with (0,_)->false |(n,_) when i%n>0->false |(n,0)->i%(l*n)>0 |(n,g)->fN i g (e+n) (l*n) seq{1..999}|>Seq.filter(fun n->fN n n 0 1)|>Seq.iter(printf "%d "); printfn "" </lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
Factor
<lang factor>USING: combinators.short-circuit grouping kernel math math.functions math.ranges math.text.utils prettyprint sequences ;
- needle? ( n -- ? )
dup 1 digit-groups dup product
{
[ 2nip zero? not ]
[ nip divisor? not ]
[ drop [ divisor? ] with all? ]
} 3&& ;
1000 [1..b] [ needle? ] filter 9 group simple-table.</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
FOCAL
<lang FOCAL>01.10 F I=1,999;D 2 01.20 Q
02.10 S N=I 02.15 S P=1 02.20 S Z=FITR(N/10) 02.25 S D=N-Z*10 02.30 S N=Z 02.35 S P=P*D 02.40 I (-D)2.45,2.65 02.45 S Z=I/D 02.60 I (FITR(Z)-Z)2.65,2.7 02.65 R 02.70 I (-N)2.2 02.75 S Z=I/P 02.80 I (FITR(Z)-Z)2.85,2.65 02.85 T %4,I,!</lang>
- Output:
= 22 = 33 = 44 = 48 = 55 = 66 = 77 = 88 = 99 = 122 = 124 = 126 = 155 = 162 = 168 = 184 = 222 = 244 = 248 = 264 = 288 = 324 = 333 = 336 = 366 = 396 = 412 = 424 = 444 = 448 = 488 = 515 = 555 = 636 = 648 = 666 = 728 = 777 = 784 = 824 = 848 = 864 = 888 = 936 = 999
Forth
<lang forth>: divisible? { n -- ? }
1 { p }
n
begin
dup 0 >
while
10 /mod swap
dup 0= if
2drop false exit
then
dup n swap mod 0<> if
2drop false exit
then
p * to p
repeat
drop n p mod 0<> ;
- main
0 { count }
1000 1 do
i divisible? if
i 4 .r
count 1+ to count
count 10 mod 0= if cr else space then
then
loop cr ;
main bye</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
FreeBASIC
This function does a bit more than the task asks for, just to make things interesting. <lang freebasic>function divdignp( n as const integer ) as ubyte
'returns 1 if the number is divisible by its digits
' 2 if it is NOT divisible by the product of its digits
' 3 if both are true
' 0 if neither are true
dim as integer m = n, p = 1, r = 1, d
while m>0
d = m mod 10
m \= 10
p *= d
if d<>0 andalso n mod d <> 0 then r = 0
wend
if p<>0 andalso n mod p <> 0 then r += 2
return r
end function
for i as uinteger = 1 to 999
if divdignp(i) = 3 then print i;" ";
next i : print</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
Haskell
<lang haskell>import Data.List.Split (chunksOf) import Text.Printf
divisible :: Int -> Bool divisible = divdgt <*> dgt
where
dgt = map (read . pure) . show
divdgt x d =
notElem 0 d
&& 0 /= x `mod` product d
&& all ((0 ==) . mod x) d
numbers :: [Int] numbers = filter divisible [1 ..]
main :: IO () main = putStr $ unlines $ map (concatMap $ printf "%5d") split
where n = takeWhile (< 1000) numbers split = chunksOf 10 n</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
and another approach might be to obtain (unordered) digit lists numerically, rather by string conversion.
<lang haskell>import Data.Bool (bool) import Data.List (unfoldr) import Data.List.Split (chunksOf) import Data.Tuple (swap)
-- DIVISIBLE BY ALL DIGITS, BUT NOT BY PRODUCT OF ALL DIGITS
p :: Int -> Bool p n =
( ( (&&)
. all
( (&&) . (0 /=)
<*> (0 ==) . rem n
)
)
<*> (0 /=) . rem n . product
)
$ digits n
digits :: Int -> [Int] digits =
unfoldr $ (bool Nothing . Just . swap . flip quotRem 10) <*> (0 <)
TEST -------------------------
main :: IO () main =
let xs = [1 .. 1000] >>= (\n -> [show n | p n])
w = length $ last xs
in (putStrLn . unlines) $
unwords
<$> chunksOf
10
(fmap (justifyRight w ' ') xs)
justifyRight :: Int -> Char -> String -> String justifyRight n c = (drop . length) <*> (replicate n c <>)</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
J
<lang J>([ #~ ((10 #.^:_1]) ((0:~:*/@[|]) *. *./@(0:=|)) ])"0) >:i.999</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
Julia
<lang julia>isonlydigdivisible(n) = (d = digits(n); !(0 in d) && all(x -> n % x == 0, d) && n % prod(d) != 0)
foreach(p -> print(rpad(p[2], 5), p[1] % 15 == 0 ? "\n" : ""), enumerate(filter(isonlydigdivisible, 1:1000)))
</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
MAD
<lang MAD> NORMAL MODE IS INTEGER
PRINT COMMENT $ $
INTERNAL FUNCTION(N)
ENTRY TO DVDGT.
P=1
C=N
DGT WHENEVER C.NE.0
Z = C/10
D = C-Z*10
WHENEVER D.E.0 .OR. N/D*D.NE.N, FUNCTION RETURN 0B
P = P*D
C = Z
TRANSFER TO DGT
END OF CONDITIONAL
FUNCTION RETURN N/P*P.NE.N
END OF FUNCTION
THROUGH TEST, FOR I=1, 1, I.E.1000
TEST WHENEVER DVDGT.(I), PRINT FORMAT FMT, I
VECTOR VALUES FMT = $I4*$
END OF PROGRAM </lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
Phix
function didbntp(integer n) integer w = n, p = 1 while w do integer d = remainder(w,10) if d=0 or remainder(n,d) then return false end if p *= d w = floor(w/10) end while return remainder(n,p)!=0 end function sequence res = apply(filter(tagset(1000),didbntp),sprint) printf(1,"found %d didbntp thingies less than one thousand: %s\n",{length(res),join(shorten(res,"",5),",")})
- Output:
found 45 didbntp thingies less than one thousand: 22,33,44,48,55,...,848,864,888,936,999
Raku
<lang perl6>say "{+$_} matching numbers:\n{.batch(10)».fmt('%3d').join: "\n"}" given
(^1000).grep: -> $n { $n.contains(0) ?? False !! all |($n.comb).map($n %% *), $n % [*] $n.comb };</lang>
- Output:
45 matching numbers: 22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
REXX
<lang rexx>/*REXX pgm finds numbers divisible by its individual digits, but not by product of digs.*/ parse arg hi cols . /*obtain optional argument from the CL.*/ if hi== | hi=="," then hi= 1000 /*Not specified? Then use the default.*/ if cols== | cols=="," then cols= 10 /* " " " " " " */ w= 10 /*width of a number in any column. */
@ndnp= ' base ten integers < ' commas(hi) " that are divisible" ,
'by its digits, but not by the product of its digits'
if cols>0 then say ' index │'center(@ndnp, 1 + cols*(w+1) ) if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') finds= 0; idx= 1 /*initialize # of found numbers & index*/ $= /*a list of integers found (so far). */
do j=1 for hi-1; L= length(j); != 1 /*search for integers within the range.*/
if pos(0, j)>0 then iterate /*Does J have a zero? Yes, then skip. */
do k=1 for L; x= substr(j, k, 1) /*extract a single decimal digit from J*/
if j//x\==0 then iterate j /*J ÷ by this digit? No, then skip it.*/
!= ! * x /*compute the running product of digits*/
end /*k*/
if j//!==0 then iterate /*J ÷ by its digit product? Yes, skip.*/
finds= finds + 1 /*bump the number of found integers. */
if cols==0 then iterate /*Build the list (to be shown later)? */
$= $ right( commas(j), w) /*add the number found to the $ list.*/
if finds//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\== then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/ if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') say say 'Found ' commas(finds) @ndnp exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?</lang>
- output when using the default inputs:
index │ base ten integers < 1,000 that are divisible by its digits, but not by the product of its digits ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 22 33 44 48 55 66 77 88 99 122 11 │ 124 126 155 162 168 184 222 244 248 264 21 │ 288 324 333 336 366 396 412 424 444 448 31 │ 488 515 555 636 648 666 728 777 784 824 41 │ 848 864 888 936 999 ───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── Found 45 base ten integers < 1,000 that are divisible by its digits, but not by the product of its digits
Ring
<lang ring> load "stdlib.ring"
decimals(0) see "working..." + nl see "Numbers divisible by their individual digits, but not by the product of their digits are:" + nl
row = 0 limit = 1000
for n = 1 to limit
flag = 1
pro = 1
strn = string(n)
for m = 1 to len(strn)
temp = strn[m]
if temp != 0
pro = pro * number(temp)
ok
if n%temp = 0
flag = 1
else
flag = 0
exit
ok
next
bool = ((n%pro) != 0)
if flag = 1 and bool
row = row + 1
see "" + n + " "
if row%10 = 0
see nl
ok
ok
next
see nl + "Found " + row + " numbers" + nl see "done..." + nl </lang>
- Output:
working... Numbers divisible by their individual digits, but not by the product of their digits are: 22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999 Found 45 numbers done...
Snobol
<lang snobol> define('divis(n)i,d,p') :(divis_end) divis p = 1
i = n
digit d = remdr(i,10)
p = ne(d,0) eq(remdr(n,d),0) p * d :f(freturn)
i = gt(i,9) i / 10 :s(digit)
ne(remdr(n,p)) :s(return)f(freturn)
divis_end
n = 1
loop output = divis(n) n
n = lt(n,1000) n + 1 :s(loop)
end</lang>
- Output:
22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999
Wren
<lang ecmascript>import "/math" for Int, Nums import "/seq" for Lst import "/fmt" for Fmt
var res = [] for (n in 1..999) {
var digits = Int.digits(n)
if (digits.all { |d| n % d == 0 }) {
var prod = Nums.prod(digits)
if (prod > 0 && n % prod != 0) res.add(n)
}
} System.print("Numbers < 1000 divisible by their digits, but not by the product thereof:") for (chunk in Lst.chunks(res, 9)) Fmt.print("$4d", chunk) System.print("\n%(res.count) such numbers found")</lang>
- Output:
Numbers < 1000 divisible by their digits, but not by the product thereof: 22 33 44 48 55 66 77 88 99 122 124 126 155 162 168 184 222 244 248 264 288 324 333 336 366 396 412 424 444 448 488 515 555 636 648 666 728 777 784 824 848 864 888 936 999 45 such numbers found