⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
{{task|Discrete math}}
;Task: Write a program that generates all [[wp:Permutation|permutations]] of '''n''' different objects. (Practically numerals!)
;Related tasks:
- [[Find the missing permutation]]
- [[Permutations/Derangements]]
{{Template:Combinations and permutations}}
360 Assembly
{{trans|Liberty BASIC}}
* Permutations 26/10/2015
PERMUTE CSECT
USING PERMUTE,R15 set base register
LA R9,TMP-A n=hbound(a)
SR R10,R10 nn=0
LOOP LA R10,1(R10) nn=nn+1
LA R11,PG pgi=@pg
LA R6,1 i=1
LOOPI1 CR R6,R9 do i=1 to n
BH ELOOPI1
LA R2,A-1(R6) @a(i)
MVC 0(1,R11),0(R2) output a(i)
LA R11,1(R11) pgi=pgi+1
LA R6,1(R6) i=i+1
B LOOPI1
ELOOPI1 XPRNT PG,80
LR R6,R9 i=n
LOOPUIM BCTR R6,0 i=i-1
LTR R6,R6 until i=0
BE ELOOPUIM
LA R2,A-1(R6) @a(i)
LA R3,A(R6) @a(i+1)
CLC 0(1,R2),0(R3) or until a(i)<a(i+1)
BNL LOOPUIM
ELOOPUIM LR R7,R6 j=i
LA R7,1(R7) j=i+1
LR R8,R9 k=n
LOOPWJ CR R7,R8 do while j<k
BNL ELOOPWJ
LA R2,A-1(R7) r2=@a(j)
LA R3,A-1(R8) r3=@a(k)
MVC TMP,0(R2) tmp=a(j)
MVC 0(1,R2),0(R3) a(j)=a(k)
MVC 0(1,R3),TMP a(k)=tmp
LA R7,1(R7) j=j+1
BCTR R8,0 k=k-1
B LOOPWJ
ELOOPWJ LTR R6,R6 if i>0
BNP ILE0
LR R7,R6 j=i
LA R7,1(R7) j=i+1
LOOPWA LA R2,A-1(R7) @a(j)
LA R3,A-1(R6) @a(i)
CLC 0(1,R2),0(R3) do while a(j)<a(i)
BNL AJGEAI
LA R7,1(R7) j=j+1
B LOOPWA
AJGEAI LA R2,A-1(R7) r2=@a(j)
LA R3,A-1(R6) r3=@a(i)
MVC TMP,0(R2) tmp=a(j)
MVC 0(1,R2),0(R3) a(j)=a(i)
MVC 0(1,R3),TMP a(i)=tmp
ILE0 LTR R6,R6 until i<>0
BNE LOOP
XR R15,R15 set return code
BR R14 return to caller
A DC C'ABCD' <== input
TMP DS C temp for swap
PG DC CL80' ' buffer
YREGS
END PERMUTE
{{out}}
ABCD
ABDC
ACBD
ACDB
ADBC
ADCB
BACD
BADC
BCAD
BCDA
BDAC
BDCA
CABD
CADB
CBAD
CBDA
CDAB
CDBA
DABC
DACB
DBAC
DBCA
DCAB
DCBA
```
## ABAP
```ABAP
data: lv_flag type c,
lv_number type i,
lt_numbers type table of i.
append 1 to lt_numbers.
append 2 to lt_numbers.
append 3 to lt_numbers.
do.
perform permute using lt_numbers changing lv_flag.
if lv_flag = 'X'.
exit.
endif.
loop at lt_numbers into lv_number.
write (1) lv_number no-gap left-justified.
if sy-tabix <> '3'.
write ', '.
endif.
endloop.
skip.
enddo.
" Permutation function - this is used to permute:
" Can be used for an unbounded size set.
form permute using iv_set like lt_numbers
changing ev_last type c.
data: lv_len type i,
lv_first type i,
lv_third type i,
lv_count type i,
lv_temp type i,
lv_temp_2 type i,
lv_second type i,
lv_changed type c,
lv_perm type i.
describe table iv_set lines lv_len.
lv_perm = lv_len - 1.
lv_changed = ' '.
" Loop backwards through the table, attempting to find elements which
" can be permuted. If we find one, break out of the table and set the
" flag indicating a switch.
do.
if lv_perm <= 0.
exit.
endif.
" Read the elements.
read table iv_set index lv_perm into lv_first.
add 1 to lv_perm.
read table iv_set index lv_perm into lv_second.
subtract 1 from lv_perm.
if lv_first < lv_second.
lv_changed = 'X'.
exit.
endif.
subtract 1 from lv_perm.
enddo.
" Last permutation.
if lv_changed <> 'X'.
ev_last = 'X'.
exit.
endif.
" Swap tail decresing to get a tail increasing.
lv_count = lv_perm + 1.
do.
lv_first = lv_len + lv_perm - lv_count + 1.
if lv_count >= lv_first.
exit.
endif.
read table iv_set index lv_count into lv_temp.
read table iv_set index lv_first into lv_temp_2.
modify iv_set index lv_count from lv_temp_2.
modify iv_set index lv_first from lv_temp.
add 1 to lv_count.
enddo.
lv_count = lv_len - 1.
do.
if lv_count <= lv_perm.
exit.
endif.
read table iv_set index lv_count into lv_first.
read table iv_set index lv_perm into lv_second.
read table iv_set index lv_len into lv_third.
if ( lv_first < lv_third ) and ( lv_first > lv_second ).
lv_len = lv_count.
endif.
subtract 1 from lv_count.
enddo.
read table iv_set index lv_perm into lv_temp.
read table iv_set index lv_len into lv_temp_2.
modify iv_set index lv_perm from lv_temp_2.
modify iv_set index lv_len from lv_temp.
endform.
```
{{out}}
```txt
1, 3, 2
2, 1, 3
2, 3, 1
3, 1, 2
3, 2, 1
```
## Ada
We split the task into two parts: The first part is to represent permutations, to initialize them and to go from one permutation to another one, until the last one has been reached. This can be used elsewhere, e.g., for the Topswaps [[http://rosettacode.org/wiki/Topswops]] task. The second part is to read the N from the command line, and to actually print all permutations over 1 .. N.
===The generic package Generic_Perm===
When given N, this package defines the Element and Permutation types and exports procedures to set a permutation P to the first one, and to change P into the next one:
```ada
generic
N: positive;
package Generic_Perm is
subtype Element is Positive range 1 .. N;
type Permutation is array(Element) of Element;
procedure Set_To_First(P: out Permutation; Is_Last: out Boolean);
procedure Go_To_Next(P: in out Permutation; Is_Last: out Boolean);
end Generic_Perm;
```
Here is the implementation of the package:
```ada
package body Generic_Perm is
procedure Set_To_First(P: out Permutation; Is_Last: out Boolean) is
begin
for I in P'Range loop
P (I) := I;
end loop;
Is_Last := P'Length = 1;
-- if P has a single element, the fist permutation is the last one
end Set_To_First;
procedure Go_To_Next(P: in out Permutation; Is_Last: out Boolean) is
procedure Swap (A, B : in out Integer) is
C : Integer := A;
begin
A := B;
B := C;
end Swap;
I, J, K : Element;
begin
-- find longest tail decreasing sequence
-- after the loop, this sequence is I+1 .. n,
-- and the ith element will be exchanged later
-- with some element of the tail
Is_Last := True;
I := N - 1;
loop
if P (I) < P (I+1)
then
Is_Last := False;
exit;
end if;
-- next instruction will raise an exception if I = 1, so
-- exit now (this is the last permutation)
exit when I = 1;
I := I - 1;
end loop;
-- if all the elements of the permutation are in
-- decreasing order, this is the last one
if Is_Last then
return;
end if;
-- sort the tail, i.e. reverse it, since it is in decreasing order
J := I + 1;
K := N;
while J < K loop
Swap (P (J), P (K));
J := J + 1;
K := K - 1;
end loop;
-- find lowest element in the tail greater than the ith element
J := N;
while P (J) > P (I) loop
J := J - 1;
end loop;
J := J + 1;
-- exchange them
-- this will give the next permutation in lexicographic order,
-- since every element from ith to the last is minimum
Swap (P (I), P (J));
end Go_To_Next;
end Generic_Perm;
```
===The procedure Print_Perms===
```ada
with Ada.Text_IO, Ada.Command_Line, Generic_Perm;
procedure Print_Perms is
package CML renames Ada.Command_Line;
package TIO renames Ada.Text_IO;
begin
declare
package Perms is new Generic_Perm(Positive'Value(CML.Argument(1)));
P : Perms.Permutation;
Done : Boolean := False;
procedure Print(P: Perms.Permutation) is
begin
for I in P'Range loop
TIO.Put (Perms.Element'Image (P (I)));
end loop;
TIO.New_Line;
end Print;
begin
Perms.Set_To_First(P, Done);
loop
Print(P);
exit when Done;
Perms.Go_To_Next(P, Done);
end loop;
end;
exception
when Constraint_Error
=> TIO.Put_Line ("*** Error: enter one numerical argument n with n >= 1");
end Print_Perms;
```
{{out}}
```txt
>./print_perms 3
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
3 2 1
```
## Aime
```aime
void
f1(record r, ...)
{
if (~r) {
for (text s in r) {
r.delete(s);
rcall(f1, -2, 0, -1, s);
r[s] = 0;
}
} else {
ocall(o_, -2, 1, -1, " ", ",");
o_newline();
}
}
main(...)
{
record r;
ocall(r_put, -2, 1, -1, r, 0);
f1(r);
0;
}
```
{{Out}}
```txt
aime permutations -a Aaa Bb C
Aaa, Bb, C,
Aaa, C, Bb,
Bb, Aaa, C,
Bb, C, Aaa,
C, Aaa, Bb,
C, Bb, Aaa,
```
## ALGOL 68
{{works with|ALGOL 68|Revision 1 - one minor extension to language used - PRAGMA READ, similar to C's #include directive.}}
{{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-2.6 algol68g-2.6].}}
{{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of '''format'''[ted] ''transput''.}}
'''File: prelude_permutations.a68'''
```algol68
# -*- coding: utf-8 -*- #
COMMENT REQUIRED BY "prelude_permutations.a68"
MODE PERMDATA = ~;
PROVIDES:
# PERMDATA*=~* #
# perm*=~ list* #
END COMMENT
MODE PERMDATALIST = REF[]PERMDATA;
MODE PERMDATALISTYIELD = PROC(PERMDATALIST)VOID;
# Generate permutations of the input data list of data list #
PROC perm gen permutations = (PERMDATALIST data list, PERMDATALISTYIELD yield)VOID: (
# Warning: this routine does not correctly handle duplicate elements #
IF LWB data list = UPB data list THEN
yield(data list)
ELSE
FOR elem FROM LWB data list TO UPB data list DO
PERMDATA first = data list[elem];
data list[LWB data list+1:elem] := data list[:elem-1];
data list[LWB data list] := first;
# FOR PERMDATALIST next data list IN # perm gen permutations(data list[LWB data list+1:] # ) DO #,
## (PERMDATALIST next)VOID:(
yield(data list)
# OD #));
data list[:elem-1] := data list[LWB data list+1:elem];
data list[elem] := first
OD
FI
);
SKIP
```
'''File: test_permutations.a68'''
```algol68
#!/usr/bin/a68g --script #
# -*- coding: utf-8 -*- #
CO REQUIRED BY "prelude_permutations.a68" CO
MODE PERMDATA = INT;
#PROVIDES:#
# PERM*=INT* #
# perm *=int list *#
PR READ "prelude_permutations.a68" PR;
main:(
FLEX[0]PERMDATA test case := (1, 22, 333, 44444);
INT upb data list = UPB test case;
FORMAT
data fmt := $g(0)$,
data list fmt := $"("n(upb data list-1)(f(data fmt)", ")f(data fmt)")"$;
# FOR DATALIST permutation IN # perm gen permutations(test case#) DO (#,
## (PERMDATALIST permutation)VOID:(
printf((data list fmt, permutation, $l$))
# OD #))
)
```
'''Output:'''
```txt
(1, 22, 333, 44444)
(1, 22, 44444, 333)
(1, 333, 22, 44444)
(1, 333, 44444, 22)
(1, 44444, 22, 333)
(1, 44444, 333, 22)
(22, 1, 333, 44444)
(22, 1, 44444, 333)
(22, 333, 1, 44444)
(22, 333, 44444, 1)
(22, 44444, 1, 333)
(22, 44444, 333, 1)
(333, 1, 22, 44444)
(333, 1, 44444, 22)
(333, 22, 1, 44444)
(333, 22, 44444, 1)
(333, 44444, 1, 22)
(333, 44444, 22, 1)
(44444, 1, 22, 333)
(44444, 1, 333, 22)
(44444, 22, 1, 333)
(44444, 22, 333, 1)
(44444, 333, 1, 22)
(44444, 333, 22, 1)
```
## AppleScript
### Recursive
{{trans|JavaScript}}
(Functional ES6 version)
Recursively, in terms of concatMap and delete:
```AppleScript
-- PERMUTATIONS --------------------------------------------------------------
-- permutations :: [a] -> [[a]]
on permutations(xs)
script go
on |λ|(xs)
script h
on |λ|(x)
script ts
on |λ|(ys)
{{x} & ys}
end |λ|
end script
concatMap(ts, go's |λ|(|delete|(x, xs)))
end |λ|
end script
if {} ≠ xs then
concatMap(h, xs)
else
{{}}
end if
end |λ|
end script
go's |λ|(xs)
end permutations
-- TEST ----------------------------------------------------------------------
on run
permutations({"aardvarks", "eat", "ants"})
end run
-- GENERIC FUNCTIONS ---------------------------------------------------------
-- concatMap :: (a -> [b]) -> [a] -> [b]
on concatMap(f, xs)
set lst to {}
set lng to length of xs
tell mReturn(f)
repeat with i from 1 to lng
set lst to (lst & |λ|(contents of item i of xs, i, xs))
end repeat
end tell
return lst
end concatMap
-- delete :: a -> [a] -> [a]
on |delete|(x, xs)
if length of xs > 0 then
set {h, t} to uncons(xs)
if x = h then
t
else
{h} & |delete|(x, t)
end if
else
{}
end if
end |delete|
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: Handler -> Script
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- uncons :: [a] -> Maybe (a, [a])
on uncons(xs)
if length of xs > 0 then
{item 1 of xs, rest of xs}
else
missing value
end if
end uncons
```
{{Out}}
```txt
{{"aardvarks", "eat", "ants"}, {"aardvarks", "ants", "eat"},
{"eat", "aardvarks", "ants"}, {"eat", "ants", "aardvarks"},
{"ants", "aardvarks", "eat"}, {"ants", "eat", "aardvarks"}}
```
{{trans|Pseudocode}}
(Fast recursive Heap's algorithm)
```AppleScript
to DoPermutations(aList, n)
--> Heaps's algorithm (Permutation by interchanging pairs) AppleScript by Jean.O.matiC
if n = 1 then
tell (a reference to Permlist) to copy aList to its end
-- or: copy aList as text (for concatenated results)
else
repeat with i from 1 to n
DoPermutations(aList, n - 1)
if n mod 2 = 0 then -- n is even
tell aList to set [item i, item n] to [item n, item i] -- swaps items i and n of aList
else
tell aList to set [item 1, item n] to [item n, item 1] -- swaps items 1 and n of aList
end if
set i to i + 1
end repeat
end if
return (a reference to Permlist) as list
end DoPermutations
--> Example 1 (list of words)
set [SourceList, Permlist] to [{"Good", "Johnny", "Be"}, {}]
DoPermutations(SourceList, SourceList's length)
--> result (value of Permlist)
{{"Good", "Johnny", "Be"}, {"Johnny", "Good", "Be"}, {"Be", "Good", "Johnny"}, ¬
{"Good", "Be", "Johnny"}, {"Johnny", "Be", "Good"}, {"Be", "Johnny", "Good"}}
--> Example 2 (characters with concatenated results)
set [SourceList, Permlist] to [{"X", "Y", "Z"}, {}]
DoPermutations(SourceList, SourceList's length)
--> result (value of Permlist)
{"XYZ", "YXZ", "ZXY", "XZY", "YZX", "ZYX"}
--> Example 3 (Integers)
set [SourceList, Permlist] to [{1, 2, 3}, {}]
DoPermutations(SourceList, SourceList's length)
--> result (value of Permlist)
{{1, 2, 3}, {2, 1, 3}, {3, 1, 2}, {1, 3, 2}, {2, 3, 1}, {3, 2, 1}}
--> Example 4 (Integers with concatenated results)
set [SourceList, Permlist] to [{1, 2, 3}, {}]
DoPermutations(SourceList, SourceList's length)
--> result (value of Permlist)
{"123", "213", "312", "132", "231", "321"}
```
===Non-recursive===
As a right fold (which turns out to be significantly faster than recurse + delete):
```applescript
-- permutations :: [a] -> [[a]]
on permutations(xs)
script go
on |λ|(x, a)
script
on |λ|(ys)
script infix
on |λ|(n)
if ys ≠ {} then
take(n, ys) & {x} & drop(n, ys)
else
{x}
end if
end |λ|
end script
map(infix, enumFromTo(0, (length of ys)))
end |λ|
end script
concatMap(result, a)
end |λ|
end script
foldr(go, {{}}, xs)
end permutations
-- TEST ---------------------------------------------------
on run
permutations({1, 2, 3})
--> {{1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}}
end run
-- GENERIC ------------------------------------------------
-- concatMap :: (a -> [b]) -> [a] -> [b]
on concatMap(f, xs)
set lng to length of xs
set acc to {}
tell mReturn(f)
repeat with i from 1 to lng
set acc to acc & |λ|(item i of xs, i, xs)
end repeat
end tell
return acc
end concatMap
-- drop :: Int -> [a] -> [a]
on drop(n, xs)
if n < length of xs then
items (1 + n) thru -1 of xs
else
{}
end if
end drop
-- enumFromTo :: Int -> Int -> [Int]
on enumFromTo(m, n)
if m ≤ n then
set lst to {}
repeat with i from m to n
set end of lst to i
end repeat
return lst
else
return {}
end if
end enumFromTo
-- foldr :: (a -> b -> b) -> b -> [a] -> b
on foldr(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from lng to 1 by -1
set v to |λ|(item i of xs, v, i, xs)
end repeat
return v
end tell
end foldr
-- Lift 2nd class handler function into 1st class script wrapper
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map
-- min :: Ord a => a -> a -> a
on min(x, y)
if y < x then
y
else
x
end if
end min
-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
end take
```
{{Out}}
```txt
{{1, 2, 3}, {2, 1, 3}, {2, 3, 1}, {1, 3, 2}, {3, 1, 2}, {3, 2, 1}}
```
## AutoHotkey
from the forum topic http://www.autohotkey.com/forum/viewtopic.php?t=77959
```AutoHotkey
#NoEnv
StringCaseSense On
o := str := "Hello"
Loop
{
str := perm_next(str)
If !str
{
MsgBox % clipboard := o
break
}
o.= "`n" . str
}
perm_Next(str){
p := 0, sLen := StrLen(str)
Loop % sLen
{
If A_Index=1
continue
t := SubStr(str, sLen+1-A_Index, 1)
n := SubStr(str, sLen+2-A_Index, 1)
If ( t < n )
{
p := sLen+1-A_Index, pC := SubStr(str, p, 1)
break
}
}
If !p
return false
Loop
{
t := SubStr(str, sLen+1-A_Index, 1)
If ( t > pC )
{
n := sLen+1-A_Index, nC := SubStr(str, n, 1)
break
}
}
return SubStr(str, 1, p-1) . nC . Reverse(SubStr(str, p+1, n-p-1) . pC . SubStr(str, n+1))
}
Reverse(s){
Loop Parse, s
o := A_LoopField o
return o
}
```
{{out}}
Hello
Helol
Heoll
Hlelo
Hleol
Hlleo
Hlloe
Hloel
Hlole
Hoell
Holel
Holle
eHllo
eHlol
eHoll
elHlo
elHol
ellHo
elloH
eloHl
elolH
eoHll
eolHl
eollH
lHelo
lHeol
lHleo
lHloe
lHoel
lHole
leHlo
leHol
lelHo
leloH
leoHl
leolH
llHeo
llHoe
lleHo
lleoH
lloHe
lloeH
loHel
loHle
loeHl
loelH
lolHe
loleH
oHell
oHlel
oHlle
oeHll
oelHl
oellH
olHel
olHle
oleHl
olelH
ollHe
olleH
```
### Alternate Version
Alternate version to produce numerical permutations of combinations.
```ahk
P(n,k="",opt=0,delim="",str="") { ; generate all n choose k permutations lexicographically
;1..n = range, or delimited list, or string to parse
; to process with a different min index, pass a delimited list, e.g. "0`n1`n2"
;k = length of result
;opt 0 = no repetitions
;opt 1 = with repetitions
;opt 2 = run for 1..k
;opt 3 = run for 1..k with repetitions
;str = string to prepend (used internally)
;returns delimited string, error message, or (if k > n) a blank string
i:=0
If !InStr(n,"`n")
If n in 2,3,4,5,6,7,8,9
Loop, %n%
n := A_Index = 1 ? A_Index : n "`n" A_Index
Else
Loop, Parse, n, %delim%
n := A_Index = 1 ? A_LoopField : n "`n" A_LoopField
If (k = "")
RegExReplace(n,"`n","",k), k++
If k is not Digit
Return "k must be a digit."
If opt not in 0,1,2,3
Return "opt invalid."
If k = 0
Return str
Else
Loop, Parse, n, `n
If (!InStr(str,A_LoopField) || opt & 1)
s .= (!i++ ? (opt & 2 ? str "`n" : "") : "`n" )
. P(n,k-1,opt,delim,str . A_LoopField . delim)
Return s
}
```
{{out}}
```ahk
MsgBox % P(3)
```
---------------------------
permute.ahk
---------------------------
123
132
213
231
312
321
---------------------------
OK
---------------------------
```
```ahk
MsgBox % P("Hello",3)
```
---------------------------
permute.ahk
---------------------------
Hel
Hel
Heo
Hle
Hlo
Hle
Hlo
Hoe
Hol
Hol
eHl
eHl
eHo
elH
elo
elH
elo
eoH
eol
eol
lHe
lHo
leH
leo
loH
loe
lHe
lHo
leH
leo
loH
loe
oHe
oHl
oHl
oeH
oel
oel
olH
ole
olH
ole
---------------------------
OK
---------------------------
```
```ahk
MsgBox % P("2`n3`n4`n5",2,3)
```
---------------------------
permute.ahk
---------------------------
2
22
23
24
25
3
32
33
34
35
4
42
43
44
45
5
52
53
54
55
---------------------------
OK
---------------------------
```
```ahk
MsgBox % P("11 a text ] u+z",3,0," ")
```
---------------------------
permute.ahk
---------------------------
11 a text
11 a ]
11 a u+z
11 text a
11 text ]
11 text u+z
11 ] a
11 ] text
11 ] u+z
11 u+z a
11 u+z text
11 u+z ]
a 11 text
a 11 ]
a 11 u+z
a text 11
a text ]
a text u+z
a ] 11
a ] text
a ] u+z
a u+z 11
a u+z text
a u+z ]
text 11 a
text 11 ]
text 11 u+z
text a 11
text a ]
text a u+z
text ] 11
text ] a
text ] u+z
text u+z 11
text u+z a
text u+z ]
] 11 a
] 11 text
] 11 u+z
] a 11
] a text
] a u+z
] text 11
] text a
] text u+z
] u+z 11
] u+z a
] u+z text
u+z 11 a
u+z 11 text
u+z 11 ]
u+z a 11
u+z a text
u+z a ]
u+z text 11
u+z text a
u+z text ]
u+z ] 11
u+z ] a
u+z ] text
---------------------------
OK
---------------------------
```
## Arturo
```arturo
print $(permutations #(1 2 3))
```
{{out}}
```txt
#(#(1 2 3) #(1 3 2) #(2 1 3) #(2 3 1) #(3 1 2) #(3 2 1))
```
## Batch File
Recursive permutation generator.
```Batch File
@echo off
setlocal enabledelayedexpansion
set arr=ABCD
set /a n=4
:: echo !arr!
call :permu %n% arr
goto:eof
:permu num &arr
setlocal
if %1 equ 1 call echo(!%2! & exit /b
set /a "num=%1-1,n2=num-1"
set arr=!%2!
for /L %%c in (0,1,!n2!) do (
call:permu !num! arr
set /a n1="num&1"
if !n1! equ 0 (call:swapit !num! 0 arr) else (call:swapit !num! %%c arr)
)
call:permu !num! arr
endlocal & set %2=%arr%
exit /b
:swapit from to &arr
setlocal
set arr=!%3!
set temp1=!arr:~%~1,1!
set temp2=!arr:~%~2,1!
set arr=!arr:%temp1%=@!
set arr=!arr:%temp2%=%temp1%!
set arr=!arr:@=%temp2%!
:: echo %1 %2 !%~3! !arr!
endlocal & set %3=%arr%
exit /b
```
{{out}}
```txt
ABCD
BACD
CABD
ACBD
BCAD
CBAD
DBAC
BDAC
ADBC
DABC
BADC
ABDC
ACDB
CADB
DACB
ADCB
CDAB
DCAB
DCBA
CDBA
BDCA
DBCA
CBDA
BCDA
```
## BBC BASIC
The procedure PROC_NextPermutation() will give the next lexicographic permutation of an integer array.
```bbcbasic
DIM List%(3)
List%() = 1, 2, 3, 4
FOR perm% = 1 TO 24
FOR i% = 0 TO DIM(List%(),1)
PRINT List%(i%);
NEXT
PRINT
PROC_NextPermutation(List%())
NEXT
END
DEF PROC_NextPermutation(A%())
LOCAL first, last, elementcount, pos
elementcount = DIM(A%(),1)
IF elementcount < 1 THEN ENDPROC
pos = elementcount-1
WHILE A%(pos) >= A%(pos+1)
pos -= 1
IF pos < 0 THEN
PROC_Permutation_Reverse(A%(), 0, elementcount)
ENDPROC
ENDIF
ENDWHILE
last = elementcount
WHILE A%(last) <= A%(pos)
last -= 1
ENDWHILE
SWAP A%(pos), A%(last)
PROC_Permutation_Reverse(A%(), pos+1, elementcount)
ENDPROC
DEF PROC_Permutation_Reverse(A%(), first, last)
WHILE first < last
SWAP A%(first), A%(last)
first += 1
last -= 1
ENDWHILE
ENDPROC
```
'''Output:'''
```txt
1 2 3 4
1 2 4 3
1 3 2 4
1 3 4 2
1 4 2 3
1 4 3 2
2 1 3 4
2 1 4 3
2 3 1 4
2 3 4 1
2 4 1 3
2 4 3 1
3 1 2 4
3 1 4 2
3 2 1 4
3 2 4 1
3 4 1 2
3 4 2 1
4 1 2 3
4 1 3 2
4 2 1 3
4 2 3 1
4 3 1 2
4 3 2 1
```
## Bracmat
```bracmat
( perm
= prefix List result original A Z
. !arg:(?.)
| !arg:(?prefix.?List:?original)
& :?result
& whl
' ( !List:%?A ?Z
& !result perm$(!prefix !A.!Z):?result
& !Z !A:~!original:?List
)
& !result
)
& out$(perm$(.a 2 "]" u+z);
```
Output:
```txt
(a 2 ] u+z.)
(a 2 u+z ].)
(a ] u+z 2.)
(a ] 2 u+z.)
(a u+z 2 ].)
(a u+z ] 2.)
(2 ] u+z a.)
(2 ] a u+z.)
(2 u+z a ].)
(2 u+z ] a.)
(2 a ] u+z.)
(2 a u+z ].)
(] u+z a 2.)
(] u+z 2 a.)
(] a 2 u+z.)
(] a u+z 2.)
(] 2 u+z a.)
(] 2 a u+z.)
(u+z a 2 ].)
(u+z a ] 2.)
(u+z 2 ] a.)
(u+z 2 a ].)
(u+z ] a 2.)
(u+z ] 2 a.)
```
## C
### version 1
Non-recursive algorithm to generate all permutations. It prints objects in lexicographical order.
```c
#include
int main (int argc, char *argv[]) {
//here we check arguments
if (argc < 2) {
printf("Enter an argument. Example 1234 or dcba:\n");
return 0;
}
//it calculates an array's length
int x;
for (x = 0; argv[1][x] != '\0'; x++);
//buble sort the array
int f, v, m;
for(f=0; f < x; f++) {
for(v = x-1; v > f; v-- ) {
if (argv[1][v-1] > argv[1][v]) {
m=argv[1][v-1];
argv[1][v-1]=argv[1][v];
argv[1][v]=m;
}
}
}
//it calculates a factorial to stop the algorithm
char a[x];
int k=0;
int fact=k+1;
while (k!=x) {
a[k]=argv[1][k];
k++;
fact = k*fact;
}
a[k]='\0';
//Main part: here we permutate
int i, j;
int y=0;
char c;
while (y != fact) {
printf("%s\n", a);
i=x-2;
while(a[i] > a[i+1] ) i--;
j=x-1;
while(a[j] < a[i] ) j--;
c=a[j];
a[j]=a[i];
a[i]=c;
i++;
for (j = x-1; j > i; i++, j--) {
c = a[i];
a[i] = a[j];
a[j] = c;
}
y++;
}
}
```
### version 2
Non-recursive algorithm to generate all permutations. It prints them from right to left.
```c
#include
int main() {
char a[] = "4321"; //array
int i, j;
int f=24; //factorial
char c; //buffer
while (f--) {
printf("%s\n", a);
i=1;
while(a[i] > a[i-1]) i++;
j=0;
while(a[j] < a[i])j++;
c=a[j];
a[j]=a[i];
a[i]=c;
i--;
for (j = 0; j < i; i--, j++) {
c = a[i];
a[i] = a[j];
a[j] = c;
}
}
}
```
### version 3
See [[wp:Permutation#Systematic_generation_of_all_permutations|lexicographic generation]] of permutations.
```c
#include
#include
/* print a list of ints */
int show(int *x, int len)
{
int i;
for (i = 0; i < len; i++)
printf("%d%c", x[i], i == len - 1 ? '\n' : ' ');
return 1;
}
/* next lexicographical permutation */
int next_lex_perm(int *a, int n) {
# define swap(i, j) {t = a[i]; a[i] = a[j]; a[j] = t;}
int k, l, t;
/* 1. Find the largest index k such that a[k] < a[k + 1]. If no such
index exists, the permutation is the last permutation. */
for (k = n - 1; k && a[k - 1] >= a[k]; k--);
if (!k--) return 0;
/* 2. Find the largest index l such that a[k] < a[l]. Since k + 1 is
such an index, l is well defined */
for (l = n - 1; a[l] <= a[k]; l--);
/* 3. Swap a[k] with a[l] */
swap(k, l);
/* 4. Reverse the sequence from a[k + 1] to the end */
for (k++, l = n - 1; l > k; l--, k++)
swap(k, l);
return 1;
# undef swap
}
void perm1(int *x, int n, int callback(int *, int))
{
do {
if (callback) callback(x, n);
} while (next_lex_perm(x, n));
}
/* Boothroyd method; exactly N! swaps, about as fast as it gets */
void boothroyd(int *x, int n, int nn, int callback(int *, int))
{
int c = 0, i, t;
while (1) {
if (n > 2) boothroyd(x, n - 1, nn, callback);
if (c >= n - 1) return;
i = (n & 1) ? 0 : c;
c++;
t = x[n - 1], x[n - 1] = x[i], x[i] = t;
if (callback) callback(x, nn);
}
}
/* entry for Boothroyd method */
void perm2(int *x, int n, int callback(int*, int))
{
if (callback) callback(x, n);
boothroyd(x, n, n, callback);
}
/* same as perm2, but flattened recursions into iterations */
void perm3(int *x, int n, int callback(int*, int))
{
/* calloc isn't strictly necessary, int c[32] would suffice
for most practical purposes */
int d, i, t, *c = calloc(n, sizeof(int));
/* curiously, with GCC 4.6.1 -O3, removing next line makes
it ~25% slower */
if (callback) callback(x, n);
for (d = 1; ; c[d]++) {
while (d > 1) c[--d] = 0;
while (c[d] >= d)
if (++d >= n) goto done;
t = x[ i = (d & 1) ? c[d] : 0 ], x[i] = x[d], x[d] = t;
if (callback) callback(x, n);
}
done: free(c);
}
#define N 4
int main()
{
int i, x[N];
for (i = 0; i < N; i++) x[i] = i + 1;
/* three different methods */
perm1(x, N, show);
perm2(x, N, show);
perm3(x, N, show);
return 0;
}
```
### version 4
See [[wp:Permutation#Systematic_generation_of_all_permutations|lexicographic generation]] of permutations.
```c
#include
#include
/* print a list of ints */
int show(int *x, int len)
{
int i;
for (i = 0; i < len; i++)
printf("%d%c", x[i], i == len - 1 ? '\n' : ' ');
return 1;
}
/* next lexicographical permutation */
int next_lex_perm(int *a, int n) {
# define swap(i, j) {t = a[i]; a[i] = a[j]; a[j] = t;}
int k, l, t;
/* 1. Find the largest index k such that a[k] < a[k + 1]. If no such
index exists, the permutation is the last permutation. */
for (k = n - 1; k && a[k - 1] >= a[k]; k--);
if (!k--) return 0;
/* 2. Find the largest index l such that a[k] < a[l]. Since k + 1 is
such an index, l is well defined */
for (l = n - 1; a[l] <= a[k]; l--);
/* 3. Swap a[k] with a[l] */
swap(k, l);
/* 4. Reverse the sequence from a[k + 1] to the end */
for (k++, l = n - 1; l > k; l--, k++)
swap(k, l);
return 1;
# undef swap
}
void perm1(int *x, int n, int callback(int *, int))
{
do {
if (callback) callback(x, n);
} while (next_lex_perm(x, n));
}
/* Boothroyd method; exactly N! swaps, about as fast as it gets */
void boothroyd(int *x, int n, int nn, int callback(int *, int))
{
int c = 0, i, t;
while (1) {
if (n > 2) boothroyd(x, n - 1, nn, callback);
if (c >= n - 1) return;
i = (n & 1) ? 0 : c;
c++;
t = x[n - 1], x[n - 1] = x[i], x[i] = t;
if (callback) callback(x, nn);
}
}
/* entry for Boothroyd method */
void perm2(int *x, int n, int callback(int*, int))
{
if (callback) callback(x, n);
boothroyd(x, n, n, callback);
}
/* same as perm2, but flattened recursions into iterations */
void perm3(int *x, int n, int callback(int*, int))
{
/* calloc isn't strictly necessary, int c[32] would suffice
for most practical purposes */
int d, i, t, *c = calloc(n, sizeof(int));
/* curiously, with GCC 4.6.1 -O3, removing next line makes
it ~25% slower */
if (callback) callback(x, n);
for (d = 1; ; c[d]++) {
while (d > 1) c[--d] = 0;
while (c[d] >= d)
if (++d >= n) goto done;
t = x[ i = (d & 1) ? c[d] : 0 ], x[i] = x[d], x[d] = t;
if (callback) callback(x, n);
}
done: free(c);
}
#define N 4
int main()
{
int i, x[N];
for (i = 0; i < N; i++) x[i] = i + 1;
/* three different methods */
perm1(x, N, show);
perm2(x, N, show);
perm3(x, N, show);
return 0;
}
```
## C++
The C++ standard library provides for this in the form of std::next_permutation and std::prev_permutation.
```cpp
#include
#include
#include
#include
template
void print(const std::vector &vec)
{
for (typename std::vector::const_iterator i = vec.begin(); i != vec.end(); ++i)
{
std::cout << *i;
if ((i + 1) != vec.end())
std::cout << ",";
}
std::cout << std::endl;
}
int main()
{
//Permutations for strings
std::string example("Hello");
std::sort(example.begin(), example.end());
do {
std::cout << example << '\n';
} while (std::next_permutation(example.begin(), example.end()));
// And for vectors
std::vector another;
another.push_back(1234);
another.push_back(4321);
another.push_back(1234);
another.push_back(9999);
std::sort(another.begin(), another.end());
do {
print(another);
} while (std::next_permutation(another.begin(), another.end()));
return 0;
}
```
{{out}}
```txt
Hello
Helol
Heoll
Hlelo
Hleol
Hlleo
Hlloe
Hloel
Hlole
Hoell
Holel
Holle
eHllo
eHlol
eHoll
elHlo
elHol
ellHo
elloH
eloHl
elolH
eoHll
eolHl
eollH
lHelo
lHeol
lHleo
lHloe
lHoel
lHole
leHlo
leHol
lelHo
leloH
leoHl
leolH
llHeo
llHoe
lleHo
lleoH
lloHe
lloeH
loHel
loHle
loeHl
loelH
lolHe
loleH
oHell
oHlel
oHlle
oeHll
oelHl
oellH
olHel
olHle
oleHl
olelH
ollHe
olleH
1234,1234,4321,9999
1234,1234,9999,4321
1234,4321,1234,9999
1234,4321,9999,1234
1234,9999,1234,4321
1234,9999,4321,1234
4321,1234,1234,9999
4321,1234,9999,1234
4321,9999,1234,1234
9999,1234,1234,4321
9999,1234,4321,1234
9999,4321,1234,1234
```
## C#
Recursive Linq
{{works with|C sharp|C#|7}}
```csharp>public static IEnumerable> Permutations values)
{
if (values.Count() == 1)
return new [] {values};
return values.SelectMany(v => Permutations(values.Where(x=> x != v)),(v, p) => p.Prepend(v));
}
```
Usage
```sharp
Enumerable.Range(0,5).Permutations()
```
A recursive Iterator. Runs under C#2 (VS2005), i.e. no `var`, no lambdas,...
```csharp>public class Permutations AllFor(T[] array)
{
if (array == null || array.Length == 0)
{
yield return new T[0];
}
else
{
for (int pick = 0; pick < array.Length; ++pick)
{
T item = array[pick];
int i = -1;
T[] rest = System.Array.FindAll(
array, delegate(T p) { return ++i != pick; }
);
foreach (T[] restPermuted in AllFor(rest))
{
i = -1;
yield return System.Array.ConvertAll(
array,
delegate(T p) {
return ++i == 0 ? item : restPermuted[i - 1];
}
);
}
}
}
}
}
```
Usage:
```c#
namespace Permutations_On_RosettaCode
{
class Program
{
static void Main(string[] args)
{
string[] list = "a b c d".Split();
foreach (string[] permutation in Permutations.AllFor(list))
{
System.Console.WriteLine(string.Join(" ", permutation));
}
}
}
}
```
Recursive version
```c#
using System;
class Permutations
{
static int n = 4;
static int [] buf = new int [n];
static bool [] used = new bool [n];
static void Main()
{
for (int i = 0; i < n; i++) used [i] = false;
rec(0);
}
static void rec(int ind)
{
for (int i = 0; i < n; i++)
{
if (!used [i])
{
used [i] = true;
buf [ind] = i;
if (ind + 1 < n) rec(ind + 1);
else Console.WriteLine(string.Join(",", buf));
used [i] = false;
}
}
}
}
```
Alternate recursive version
```c#
using System;
class Permutations
{
static int n = 4;
static int [] buf = new int [n];
static int [] next = new int [n+1];
static void Main()
{
for (int i = 0; i < n; i++) next [i] = i + 1;
next[n] = 0;
rec(0);
}
static void rec(int ind)
{
for (int i = n; next[i] != n; i = next[i])
{
buf [ind] = next[i];
next[i]=next[next[i]];
if (ind < n - 1) rec(ind + 1);
else Console.WriteLine(string.Join(",", buf));
next[i] = buf [ind];
}
}
}
```
## Clojure
### Library function
In an REPL:
```clojure
user=> (require 'clojure.contrib.combinatorics)
nil
user=> (clojure.contrib.combinatorics/permutations [1 2 3])
((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1))
```
### Explicit
Replacing the call to the combinatorics library function by its real implementation.
```clojure
(defn- iter-perm [v]
(let [len (count v),
j (loop [i (- len 2)]
(cond (= i -1) nil
(< (v i) (v (inc i))) i
:else (recur (dec i))))]
(when j
(let [vj (v j),
l (loop [i (dec len)]
(if (< vj (v i)) i (recur (dec i))))]
(loop [v (assoc v j (v l) l vj), k (inc j), l (dec len)]
(if (< k l)
(recur (assoc v k (v l) l (v k)) (inc k) (dec l))
v))))))
(defn- vec-lex-permutations [v]
(when v (cons v (lazy-seq (vec-lex-permutations (iter-perm v))))))
(defn lex-permutations
"Fast lexicographic permutation generator for a sequence of numbers"
[c]
(lazy-seq
(let [vec-sorted (vec (sort c))]
(if (zero? (count vec-sorted))
(list [])
(vec-lex-permutations vec-sorted)))))
(defn permutations
"All the permutations of items, lexicographic by index"
[items]
(let [v (vec items)]
(map #(map v %) (lex-permutations (range (count v))))))
(println (permutations [1 2 3]))
```
## CoffeeScript
```coffeescript
# Returns a copy of an array with the element at a specific position
# removed from it.
arrayExcept = (arr, idx) ->
res = arr[0..]
res.splice idx, 1
res
# The actual function which returns the permutations of an array-like
# object (or a proper array).
permute = (arr) ->
arr = Array::slice.call arr, 0
return [[]] if arr.length == 0
permutations = (for value,idx in arr
[value].concat perm for perm in permute arrayExcept arr, idx)
# Flatten the array before returning it.
[].concat permutations...
```
This implementation utilises the fact that the permutations of an array could be defined recursively, with the fixed point being the permutations of an empty array.
{{out|Usage}}
```coffeescript>coffee
console.log (permute "123").join "\n"
1,2,3
1,3,2
2,1,3
2,3,1
3,1,2
3,2,1
```
## Common Lisp
```lisp
(defun permute (list)
(if list
(mapcan #'(lambda (x)
(mapcar #'(lambda (y) (cons x y))
(permute (remove x list))))
list)
'(()))) ; else
(print (permute '(A B Z)))
```
{{out}}
```txt
((A B Z) (A Z B) (B A Z) (B Z A) (Z A B) (Z B A))
```
Lexicographic next permutation:
```lisp
(defun next-perm (vec cmp) ; modify vector
(declare (type (simple-array * (*)) vec))
(macrolet ((el (i) `(aref vec ,i))
(cmp (i j) `(funcall cmp (el ,i) (el ,j))))
(loop with len = (1- (length vec))
for i from (1- len) downto 0
when (cmp i (1+ i)) do
(loop for k from len downto i
when (cmp i k) do
(rotatef (el i) (el k))
(setf k (1+ len))
(loop while (< (incf i) (decf k)) do
(rotatef (el i) (el k)))
(return-from next-perm vec)))))
;;; test code
(loop for a = "1234" then (next-perm a #'char<) while a do
(write-line a))
```
## Crystal
```Ruby
puts [1, 2, 3].permutations
```
{{out}}
```txt
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
```
## Curry
```curry
insert :: a -> [a] -> [a]
insert x xs = x : xs
insert x (y:ys) = y : insert x ys
permutation :: [a] -> [a]
permutation [] = []
permutation (x:xs) = insert x $ permutation xs
```
## D
### Simple Eager version
Compile with -version=permutations1_main to see the output.
```d
T[][] permutations(T)(T[] items) pure nothrow {
T[][] result;
void perms(T[] s, T[] prefix=[]) nothrow {
if (s.length)
foreach (immutable i, immutable c; s)
perms(s[0 .. i] ~ s[i+1 .. $], prefix ~ c);
else
result ~= prefix;
}
perms(items);
return result;
}
version (permutations1_main) {
void main() {
import std.stdio;
writefln("%(%s\n%)", [1, 2, 3].permutations);
}
}
```
{{out}}
```txt
[1, 2, 3]
[1, 3, 2]
[2, 1, 3]
[2, 3, 1]
[3, 1, 2]
[3, 2, 1]
```
### Fast Lazy Version
Compiled with -version=permutations2_main produces its output.
```d
import std.algorithm, std.conv, std.traits;
struct Permutations(bool doCopy=true, T) if (isMutable!T) {
private immutable size_t num;
private T[] items;
private uint[31] indexes;
private ulong tot;
this (T[] items) pure nothrow @safe @nogc
in {
static enum string L = indexes.length.text;
assert(items.length >= 0 && items.length <= indexes.length,
"Permutations: items.length must be >= 0 && < " ~ L);
} body {
static ulong factorial(in size_t n) pure nothrow @safe @nogc {
ulong result = 1;
foreach (immutable i; 2 .. n + 1)
result *= i;
return result;
}
this.num = items.length;
this.items = items;
foreach (immutable i; 0 .. cast(typeof(indexes[0]))this.num)
this.indexes[i] = i;
this.tot = factorial(this.num);
}
@property T[] front() pure nothrow @safe {
static if (doCopy) {
return items.dup;
} else
return items;
}
@property bool empty() const pure nothrow @safe @nogc {
return tot == 0;
}
@property size_t length() const pure nothrow @safe @nogc {
// Not cached to keep the function pure.
typeof(return) result = 1;
foreach (immutable x; 1 .. items.length + 1)
result *= x;
return result;
}
void popFront() pure nothrow @safe @nogc {
tot--;
if (tot > 0) {
size_t j = num - 2;
while (indexes[j] > indexes[j + 1])
j--;
size_t k = num - 1;
while (indexes[j] > indexes[k])
k--;
swap(indexes[k], indexes[j]);
swap(items[k], items[j]);
size_t r = num - 1;
size_t s = j + 1;
while (r > s) {
swap(indexes[s], indexes[r]);
swap(items[s], items[r]);
r--;
s++;
}
}
}
}
Permutations!(doCopy,T) permutations(bool doCopy=true, T)
(T[] items)
pure nothrow if (isMutable!T) {
return Permutations!(doCopy, T)(items);
}
version (permutations2_main) {
void main() {
import std.stdio, std.bigint;
alias B = BigInt;
foreach (p; [B(1), B(2), B(3)].permutations)
assert((p[0] + 1) > 0);
[1, 2, 3].permutations!false.writeln;
[B(1), B(2), B(3)].permutations!false.writeln;
}
}
```
### Standard Version
```d
void main() {
import std.stdio, std.algorithm;
auto items = [1, 2, 3];
do
items.writeln;
while (items.nextPermutation);
}
```
## Delphi
```Delphi
program TestPermutations;
{$APPTYPE CONSOLE}
type
TItem = Integer; // declare ordinal type for array item
TArray = array[0..3] of TItem;
const
Source: TArray = (1, 2, 3, 4);
procedure Permutation(K: Integer; var A: TArray);
var
I, J: Integer;
Tmp: TItem;
begin
for I:= Low(A) + 1 to High(A) + 1 do begin
J:= K mod I;
Tmp:= A[J];
A[J]:= A[I - 1];
A[I - 1]:= Tmp;
K:= K div I;
end;
end;
var
A: TArray;
I, K, Count: Integer;
S, S1, S2: ShortString;
begin
Count:= 1;
I:= Length(A);
while I > 1 do begin
Count:= Count * I;
Dec(I);
end;
S:= '';
for K:= 0 to Count - 1 do begin
A:= Source;
Permutation(K, A);
S1:= '';
for I:= Low(A) to High(A) do begin
Str(A[I]:1, S2);
S1:= S1 + S2;
end;
S:= S + ' ' + S1;
if Length(S) > 40 then begin
Writeln(S);
S:= '';
end;
end;
if Length(S) > 0 then Writeln(S);
Readln;
end.
```
{{out}}
```txt
4123 4213 4312 4321 4132 4231 3421
3412 2413 1423 2431 1432 3142 3241
2341 1342 2143 1243 3124 3214 2314
1324 2134 1234
```
## Eiffel
```Eiffel
class
APPLICATION
create
make
feature {NONE}
make
do
test := <<2, 5, 1>>
permute (test, 1)
end
test: ARRAY [INTEGER]
permute (a: ARRAY [INTEGER]; k: INTEGER)
-- All permutations of 'a'.
require
count_positive: a.count > 0
k_valid_index: k > 0
local
t: INTEGER
do
if k = a.count then
across
a as ar
loop
io.put_integer (ar.item)
end
io.new_line
else
across
k |..| a.count as c
loop
t := a [k]
a [k] := a [c.item]
a [c.item] := t
permute (a, k + 1)
t := a [k]
a [k] := a [c.item]
a [c.item] := t
end
end
end
end
```
{{out}}
```txt
251
215
521
512
152
125
```
## Elixir
{{trans|Erlang}}
```elixir
defmodule RC do
def permute([]), do: [[]]
def permute(list) do
for x <- list, y <- permute(list -- [x]), do: [x|y]
end
end
IO.inspect RC.permute([1, 2, 3])
```
{{out}}
```txt
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
```
## Erlang
Shortest form:
```Erlang
-module(permute).
-export([permute/1]).
permute([]) -> [[]];
permute(L) -> [[X|Y] || X<-L, Y<-permute(L--[X])].
```
Y-combinator (for shell):
```Erlang
F = fun(L) -> G = fun(_, []) -> [[]]; (F, L) -> [[X|Y] || X<-L, Y<-F(F, L--[X])] end, G(G, L) end.
```
More efficient zipper implementation:
```Erlang
-module(permute).
-export([permute/1]).
permute([]) -> [[]];
permute(L) -> zipper(L, [], []).
% Use zipper to pick up first element of permutation
zipper([], _, Acc) -> lists:reverse(Acc);
zipper([H|T], R, Acc) ->
% place current member in front of all permutations
% of rest of set - both sides of zipper
prepend(H, permute(lists:reverse(R, T)),
% pass zipper state for continuation
T, [H|R], Acc).
prepend(_, [], T, R, Acc) -> zipper(T, R, Acc); % continue in zipper
prepend(X, [H|T], ZT, ZR, Acc) -> prepend(X, T, ZT, ZR, [[X|H]|Acc]).
```
Demonstration (escript):
```Erlang
main(_) -> io:fwrite("~p~n", [permute:permute([1,2,3])]).
```
{{out}}
```txt
[[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]]
```
## Euphoria
{{trans|PureBasic}}
```euphoria
function reverse(sequence s, integer first, integer last)
object x
while first < last do
x = s[first]
s[first] = s[last]
s[last] = x
first += 1
last -= 1
end while
return s
end function
function nextPermutation(sequence s)
integer pos, last
object x
if length(s) < 1 then
return 0
end if
pos = length(s)-1
while compare(s[pos], s[pos+1]) >= 0 do
pos -= 1
if pos < 1 then
return -1
end if
end while
last = length(s)
while compare(s[last], s[pos]) <= 0 do
last -= 1
end while
x = s[pos]
s[pos] = s[last]
s[last] = x
return reverse(s, pos+1, length(s))
end function
object s
s = "abcd"
puts(1, s & '\t')
while 1 do
s = nextPermutation(s)
if atom(s) then
exit
end if
puts(1, s & '\t')
end while
```
{{out}}
```txt
abcd abdc acbd acdb adbc adcb bacd badc bcad bcda
bdac bdca cabd cadb cbad cbda cdab cdba dabc dacb
dbac dbca dcab dcba
```
=={{header|F Sharp|F#}}==
```fsharp
let rec insert left x right = seq {
match right with
| [] -> yield left @ [x]
| head :: tail ->
yield left @ [x] @ right
yield! insert (left @ [head]) x tail
}
let rec perms permute =
seq {
match permute with
| [] -> yield []
| head :: tail -> yield! Seq.collect (insert [] head) (perms tail)
}
[]
let main argv =
perms (Seq.toList argv)
|> Seq.iter (fun x -> printf "%A\n" x)
0
```
```txt
>RosettaPermutations 1 2 3
["1"; "2"; "3"]
["2"; "1"; "3"]
["2"; "3"; "1"]
["1"; "3"; "2"]
["3"; "1"; "2"]
["3"; "2"; "1"]
```
Translation of Haskell "insertion-based approach" (last version)
```fsharp
let permutations xs =
let rec insert x = function
| [] -> [[x]]
| head :: tail -> (x :: (head :: tail)) :: (List.map (fun l -> head :: l) (insert x tail))
List.fold (fun s e -> List.collect (insert e) s) [[]] xs
```
## Factor
The all-permutations word is part of factor's standard library. See http://docs.factorcode.org/content/word-all-permutations,math.combinatorics.html
## Fortran
```fortran
program permutations
implicit none
integer, parameter :: value_min = 1
integer, parameter :: value_max = 3
integer, parameter :: position_min = value_min
integer, parameter :: position_max = value_max
integer, dimension (position_min : position_max) :: permutation
call generate (position_min)
contains
recursive subroutine generate (position)
implicit none
integer, intent (in) :: position
integer :: value
if (position > position_max) then
write (*, *) permutation
else
do value = value_min, value_max
if (.not. any (permutation (: position - 1) == value)) then
permutation (position) = value
call generate (position + 1)
end if
end do
end if
end subroutine generate
end program permutations
```
{{out}}
```txt
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
```
### Alternate solution
Instead of looking up unused values, this program starts from [1, ..., n] and does only swaps, hence the array always represents a valid permutation.
The values need to be "swapped back" after the recursive call.
```fortran
program allperm
implicit none
integer :: n, i
integer, allocatable :: a(:)
read *, n
allocate(a(n))
a = [ (i, i = 1, n) ]
call perm(1)
deallocate(a)
contains
recursive subroutine perm(i)
integer :: i, j, t
if (i == n) then
print *, a
else
do j = i, n
t = a(i)
a(i) = a(j)
a(j) = t
call perm(i + 1)
t = a(i)
a(i) = a(j)
a(j) = t
end do
end if
end subroutine
end program
```
### Fortran Speed Test
So ... what is the fastest algorithm?
Here below is the speed test for a couple of algorithms of permutation. We can add more algorithms into this frame-work. When they work in the same circumstance, we can see which is the fastest one.
```fortran
program testing_permutation_algorithms
implicit none
integer :: nmax
integer, dimension(:),allocatable :: ida
logical :: mtc
logical :: even
integer :: i
integer(8) :: ic
integer :: clock_rate, clock_max, t1, t2
real(8) :: dt
integer :: pos_min, pos_max
!
!
! Beginning:
!
write(*,*) 'INPUT N:'
read *, nmax
write(*,*) 'N =', nmax
allocate ( ida(1:nmax) )
!
!
! (1) Starting:
!
do i = 1, nmax
ida(i) = i
enddo
!
ic = 0
call system_clock ( t1, clock_rate, clock_max )
!
mtc = .false.
!
do
call subnexper ( nmax, ida, mtc, even )
!
! 1) counting the number of permutatations
!
ic = ic + 1
!
! 2) writing out the result:
!
! do i = 1, nmax
! write (100,"(i3,',')",advance = "no") ida(i)
! enddo
! write(100,*)
!
! repeat if not being finished yet, otherwise exit.
!
if (mtc) then
cycle
else
exit
endif
!
enddo
!
call system_clock ( t2, clock_rate, clock_max )
dt = ( dble(t2) - dble(t1) )/ dble(clock_rate)
!
! Finishing (1)
!
write(*,*) "1) subnexper:"
write(*,*) 'Total permutations :', ic
write(*,*) 'Total time elapsed :', dt
!
!
! (2) Starting:
!
do i = 1, nmax
ida(i) = i
enddo
!
pos_min = 1
pos_max = nmax
!
ic = 0
call system_clock ( t1, clock_rate, clock_max )
!
call generate ( pos_min )
!
call system_clock ( t2, clock_rate, clock_max )
dt = ( dble(t2) - dble(t1) )/ dble(clock_rate)
!
! Finishing (2)
!
write(*,*) "2) generate:"
write(*,*) 'Total permutations :', ic
write(*,*) 'Total time elapsed :', dt
!
!
! (3) Starting:
!
do i = 1, nmax
ida(i) = i
enddo
!
ic = 0
call system_clock ( t1, clock_rate, clock_max )
!
i = 1
call perm ( i )
!
call system_clock ( t2, clock_rate, clock_max )
dt = ( dble(t2) - dble(t1) )/ dble(clock_rate)
!
! Finishing (3)
!
write(*,*) "3) perm:"
write(*,*) 'Total permutations :', ic
write(*,*) 'Total time elapsed :', dt
!
!
! (4) Starting:
!
do i = 1, nmax
ida(i) = i
enddo
!
ic = 0
call system_clock ( t1, clock_rate, clock_max )
!
do
!
! 1) counting the number of permutatations
!
ic = ic + 1
!
! 2) writing out the result:
!
! do i = 1, nmax
! write (100,"(i3,',')",advance = "no") ida(i)
! enddo
! write(100,*)
!
! repeat if not being finished yet, otherwise exit.
!
if ( nextp(nmax,ida) ) then
cycle
else
exit
endif
!
enddo
!
call system_clock ( t2, clock_rate, clock_max )
dt = ( dble(t2) - dble(t1) )/ dble(clock_rate)
!
! Finishing (4)
!
write(*,*) "4) nextp:"
write(*,*) 'Total permutations :', ic
write(*,*) 'Total time elapsed :', dt
!
!
! What's else?
! ...
!
!==
deallocate(ida)
!
stop
!==
contains
!==
! Modified version of SUBROUTINE NEXPER from the book of
! Albert Nijenhuis and Herbert S. Wilf, "Combinatorial
! Algorithms For Computers and Calculators", 2nd Ed, p.59.
!
subroutine subnexper ( n, a, mtc, even )
implicit none
integer,intent(in) :: n
integer,dimension(n),intent(inout) :: a
logical,intent(inout) :: mtc, even
!
! local varialbes:
!
integer,save :: nm3
integer :: ia, i, s, d, i1, l, j, m
!
if (mtc) goto 10
nm3 = n-3
do i = 1,n
a(i) = i
enddo
mtc = .true.
5 even = .true.
if ( n .eq. 1 ) goto 8
6 if ( a(n) .ne. 1 .or. a(1) .ne. 2+mod(n,2) ) return
if ( n .le. 3 ) goto 8
do i = 1,nm3
if( a(i+1) .ne. a(i)+1 ) return
enddo
8 mtc = .false.
return
10 if ( n .eq. 1 ) goto 27
if( .not. even ) goto 20
ia = a(1)
a(1) = a(2)
a(2) = ia
even = .false.
goto 6
20 s = 0
do i1 = 2,n
ia = a(i1)
i = i1-1
d = 0
do j = 1,i
if ( a(j) .gt. ia ) d = d+1
enddo
s = d+s
if ( d .ne. i*mod(s,2) ) goto 35
enddo
27 a(1) = 0
goto 8
35 m = mod(s+1,2)*(n+1)
do j = 1,i
if(isign(1,a(j)-ia) .eq. isign(1,a(j)-m)) cycle
m = a(j)
l = j
enddo
a(l) = ia
a(i1) = m
even = .true.
return
end subroutine
!=====
!
! http://rosettacode.org/wiki/Permutations#Fortran
!
recursive subroutine generate (pos)
implicit none
integer,intent(in) :: pos
integer :: val
if (pos > pos_max) then
!
! 1) counting the number of permutatations
!
ic = ic + 1
!
! 2) writing out the result:
!
! write (*,*) permutation
!
else
do val = 1, nmax
if (.not. any (ida( : pos-1) == val)) then
ida(pos) = val
call generate (pos + 1)
endif
enddo
endif
end subroutine
!=====
!
! http://rosettacode.org/wiki/Permutations#Fortran
!
recursive subroutine perm (i)
implicit none
integer,intent(inout) :: i
!
integer :: j, t, ip1
!
if (i == nmax) then
!
! 1) couting the number of permutatations
!
ic = ic + 1
!
! 2) writing out the result:
!
! write (*,*) a
!
else
ip1 = i+1
do j = i, nmax
t = ida(i)
ida(i) = ida(j)
ida(j) = t
call perm ( ip1 )
t = ida(i)
ida(i) = ida(j)
ida(j) = t
enddo
endif
return
end subroutine
!=====
!
! http://rosettacode.org/wiki/Permutations#Fortran
!
function nextp ( n, a )
logical :: nextp
integer,intent(in) :: n
integer,dimension(n),intent(inout) :: a
!
! local variables:
!
integer i,j,k,t
!
i = n-1
10 if ( a(i) .lt. a(i+1) ) goto 20
i = i-1
if ( i .eq. 0 ) goto 20
goto 10
20 j = i+1
k = n
30 t = a(j)
a(j) = a(k)
a(k) = t
j = j+1
k = k-1
if ( j .lt. k ) goto 30
j = i
if (j .ne. 0 ) goto 40
!
nextp = .false.
!
return
!
40 j = j+1
if ( a(j) .lt. a(i) ) goto 40
t = a(i)
a(i) = a(j)
a(j) = t
!
nextp = .true.
!
return
end function
!=====
!
! What's else ?
! ...
!=====
end program
```
An example of performance:
1) Compiled with GNU fortran compiler:
gfortran -O3 testing_permutation_algorithms.f90 ; ./a.out
INPUT N:
10
N = 10
1) subnexper:
Total permutations : 3628800
Total time elapsed : 4.9000000000000002E-002
2) generate:
Total permutations : 3628800
Total time elapsed : 0.84299999999999997
3) perm:
Total permutations : 3628800
Total time elapsed : 5.6000000000000001E-002
4) nextp:
Total permutations : 3628800
Total time elapsed : 2.9999999999999999E-002
b) Compiled with Intel compiler:
ifort -O3 testing_permutation_algorithms.f90 ; ./a.out
INPUT N:
10
N = 10
1) subnexper:
Total permutations : 3628800
Total time elapsed : 8.240000000000000E-002
2) generate:
Total permutations : 3628800
Total time elapsed : 0.616200000000000
3) perm:
Total permutations : 3628800
Total time elapsed : 5.760000000000000E-002
4) nextp:
Total permutations : 3628800
Total time elapsed : 3.600000000000000E-002
So far, we have conclusion from the above performance:
1) subnexper is the 3rd fast with ifort and the 2nd with gfortran.
2) generate is the slowest one with not only ifort but gfortran.
3) perm is the 2nd fast one with ifort and the 3rd one with gfortran.
4) nextp is the fastest one with both ifort and gfortran (the winner in this test).
Note: It is worth mentioning that the performance of this test is dependent not only on algorithm, but also on computer where the test runs. Therefore we should run the test on our own computer and make conclusion by ourselves.
### Fortran 77
Here is an alternate, iterative version in Fortran 77.
{{trans|Ada}}
```fortran
program nptest
integer n,i,a
logical nextp
external nextp
parameter(n=4)
dimension a(n)
do i=1,n
a(i)=i
enddo
10 print *,(a(i),i=1,n)
if(nextp(n,a)) go to 10
end
function nextp(n,a)
integer n,a,i,j,k,t
logical nextp
dimension a(n)
i=n-1
10 if(a(i).lt.a(i+1)) go to 20
i=i-1
if(i.eq.0) go to 20
go to 10
20 j=i+1
k=n
30 t=a(j)
a(j)=a(k)
a(k)=t
j=j+1
k=k-1
if(j.lt.k) go to 30
j=i
if(j.ne.0) go to 40
nextp=.false.
return
40 j=j+1
if(a(j).lt.a(i)) go to 40
t=a(i)
a(i)=a(j)
a(j)=t
nextp=.true.
end
```
## FreeBASIC
```freebasic
' version 07-04-2017
' compile with: fbc -s console
' Heap's algorithm non-recursive
Sub perms(n As Long)
Dim As ULong i, j, count = 1
Dim As ULong a(0 To n -1), c(0 To n -1)
For j = 0 To n -1
a(j) = j +1
Print a(j);
Next
Print " ";
i = 0
While i < n
If c(i) < i Then
If (i And 1) = 0 Then
Swap a(0), a(i)
Else
Swap a(c(i)), a(i)
End If
For j = 0 To n -1
Print a(j);
Next
count += 1
If count = 12 Then
Print
count = 0
Else
Print " ";
End If
c(i) += 1
i = 0
Else
c(i) = 0
i += 1
End If
Wend
End Sub
' ------=< MAIN >=------
perms(4)
' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
```
{{out}}
```txt
1234 2134 3124 1324 2314 3214 4213 2413 1423 4123 2143 1243
1342 3142 4132 1432 3412 4312 4321 3421 2431 4231 3241 2341
```
## GAP
GAP can handle permutations and groups. Here is a straightforward implementation : for each permutation p in S(n) (symmetric group),
compute the images of 1 .. n by p. As an alternative, List(SymmetricGroup(n)) would yield the permutations as GAP ''Permutation'' objects,
which would probably be more manageable in later computations.
```gap>gap
List(SymmetricGroup(4), p -> Permuted([1 .. 4], p));
perms(4);
[ [ 1, 2, 3, 4 ], [ 4, 2, 3, 1 ], [ 2, 4, 3, 1 ], [ 3, 2, 4, 1 ], [ 1, 4, 3, 2 ], [ 4, 1, 3, 2 ], [ 2, 1, 3, 4 ],
[ 3, 1, 4, 2 ], [ 1, 3, 4, 2 ], [ 4, 3, 1, 2 ], [ 2, 3, 1, 4 ], [ 3, 4, 1, 2 ], [ 1, 2, 4, 3 ], [ 4, 2, 1, 3 ],
[ 2, 4, 1, 3 ], [ 3, 2, 1, 4 ], [ 1, 4, 2, 3 ], [ 4, 1, 2, 3 ], [ 2, 1, 4, 3 ], [ 3, 1, 2, 4 ], [ 1, 3, 2, 4 ],
[ 4, 3, 2, 1 ], [ 2, 3, 4, 1 ], [ 3, 4, 2, 1 ] ]
```
GAP has also built-in functions to get permutations
```gap
# All arrangements of 4 elements in 1 .. 4
Arrangements([1 .. 4], 4);
# All permutations of 1 .. 4
PermutationsList([1 .. 4]);
```
Here is an implementation using a function to compute next permutation in lexicographic order:
```gap
NextPermutation := function(a)
local i, j, k, n, t;
n := Length(a);
i := n - 1;
while i > 0 and a[i] > a[i + 1] do
i := i - 1;
od;
j := i + 1;
k := n;
while j < k do
t := a[j];
a[j] := a[k];
a[k] := t;
j := j + 1;
k := k - 1;
od;
if i = 0 then
return false;
else
j := i + 1;
while a[j] < a[i] do
j := j + 1;
od;
t := a[i];
a[i] := a[j];
a[j] := t;
return true;
fi;
end;
Permutations := function(n)
local a, L;
a := List([1 .. n], x -> x);
L := [ ];
repeat
Add(L, ShallowCopy(a));
until not NextPermutation(a);
return L;
end;
Permutations(3);
[ [ 1, 2, 3 ], [ 1, 3, 2 ],
[ 2, 1, 3 ], [ 2, 3, 1 ],
[ 3, 1, 2 ], [ 3, 2, 1 ] ]
```
## Glee
```glee
$$ n !! k dyadic: Permutations for k out of n elements (in this case k = n)
$$ #s monadic: number of elements in s
$$ ,, monadic: expose with space-lf separators
$$ s[n] index n of s
'Hello' 123 7.9 '•'=>s;
s[s# !! (s#)],,
```
Result:
```glee
Hello 123 7.9 •
Hello 123 • 7.9
Hello 7.9 123 •
Hello 7.9 • 123
Hello • 123 7.9
Hello • 7.9 123
123 Hello 7.9 •
123 Hello • 7.9
123 7.9 Hello •
123 7.9 • Hello
123 • Hello 7.9
123 • 7.9 Hello
7.9 Hello 123 •
7.9 Hello • 123
7.9 123 Hello •
7.9 123 • Hello
7.9 • Hello 123
7.9 • 123 Hello
• Hello 123 7.9
• Hello 7.9 123
• 123 Hello 7.9
• 123 7.9 Hello
• 7.9 Hello 123
• 7.9 123 Hello
```
## Go
### recursive
```go
package main
import "fmt"
func main() {
demoPerm(3)
}
func demoPerm(n int) {
// create a set to permute. for demo, use the integers 1..n.
s := make([]int, n)
for i := range s {
s[i] = i + 1
}
// permute them, calling a function for each permutation.
// for demo, function just prints the permutation.
permute(s, func(p []int) { fmt.Println(p) })
}
// permute function. takes a set to permute and a function
// to call for each generated permutation.
func permute(s []int, emit func([]int)) {
if len(s) == 0 {
emit(s)
return
}
// Steinhaus, implemented with a recursive closure.
// arg is number of positions left to permute.
// pass in len(s) to start generation.
// on each call, weave element at pp through the elements 0..np-2,
// then restore array to the way it was.
var rc func(int)
rc = func(np int) {
if np == 1 {
emit(s)
return
}
np1 := np - 1
pp := len(s) - np1
// weave
rc(np1)
for i := pp; i > 0; i-- {
s[i], s[i-1] = s[i-1], s[i]
rc(np1)
}
// restore
w := s[0]
copy(s, s[1:pp+1])
s[pp] = w
}
rc(len(s))
}
```
{{out}}
```txt
[1 2 3]
[1 3 2]
[3 1 2]
[2 1 3]
[2 3 1]
[3 2 1]
```
=== non-recursive, lexicographical order ===
```go
package main
import "fmt"
func main() {
var a = []int{1, 2, 3}
fmt.Println(a)
var n = len(a) - 1
var i, j int
for c := 1; c < 6; c++ { // 3! = 6:
i = n - 1
j = n
for a[i] > a[i+1] {
i--
}
for a[j] < a[i] {
j--
}
a[i], a[j] = a[j], a[i]
j = n
i += 1
for i < j {
a[i], a[j] = a[j], a[i]
i++
j--
}
fmt.Println(a)
}
}
```
{{out}}
```txt
[1 2 3]
[1 3 2]
[2 1 3]
[2 3 1]
[3 1 2]
[3 2 1]
```
## Groovy
Solution:
```groovy
def makePermutations = { l -> l.permutations() }
```
Test:
```groovy
def list = ['Crosby', 'Stills', 'Nash', 'Young']
def permutations = makePermutations(list)
assert permutations.size() == (1..<(list.size()+1)).inject(1) { prod, i -> prod*i }
permutations.each { println it }
```
{{out}}
[Young, Crosby, Stills, Nash]
[Crosby, Stills, Young, Nash]
[Nash, Crosby, Young, Stills]
[Stills, Nash, Crosby, Young]
[Young, Stills, Crosby, Nash]
[Stills, Crosby, Nash, Young]
[Stills, Crosby, Young, Nash]
[Stills, Young, Nash, Crosby]
[Nash, Stills, Young, Crosby]
[Crosby, Young, Nash, Stills]
[Crosby, Nash, Young, Stills]
[Crosby, Nash, Stills, Young]
[Nash, Young, Stills, Crosby]
[Young, Nash, Stills, Crosby]
[Nash, Young, Crosby, Stills]
[Young, Stills, Nash, Crosby]
[Crosby, Stills, Nash, Young]
[Stills, Young, Crosby, Nash]
[Young, Nash, Crosby, Stills]
[Nash, Stills, Crosby, Young]
[Young, Crosby, Nash, Stills]
[Nash, Crosby, Stills, Young]
[Crosby, Young, Stills, Nash]
[Stills, Nash, Young, Crosby]
```
## Haskell
```haskell
import Data.List (permutations)
main = mapM_ print (permutations [1,2,3])
```
A simple implementation, that assumes elements are unique and support equality:
```haskell
import Data.List (delete)
permutations :: Eq a => [a] -> [[a]]
permutations [] = [[]]
permutations xs = [ x:ys | x <- xs, ys <- permutations (delete x xs)]
```
A slightly more efficient implementation that doesn't have the above restrictions:
```haskell
permutations :: [a] -> [[a]]
permutations [] = [[]]
permutations xs = [ y:zs | (y,ys) <- select xs, zs <- permutations ys]
where select [] = []
select (x:xs) = (x,xs) : [ (y,x:ys) | (y,ys) <- select xs ]
```
The above are all selection-based approaches. The following is an insertion-based approach:
```haskell
permutations :: [a] -> [[a]]
permutations = foldr (concatMap . insertEverywhere) [[]]
where insertEverywhere :: a -> [a] -> [[a]]
insertEverywhere x [] = [[x]]
insertEverywhere x l@(y:ys) = (x:l) : map (y:) (insertEverywhere x ys)
```
A serialized version:
{{Trans|Mathematica}}
```haskell
permutations :: [a] -> [[a]]
permutations =
foldr (\x ac -> ac >>= (fmap . ins x) <*> (enumFromTo 0 . length)) [[]]
where
ins x xs n =
let (a, b) = splitAt n xs
in a ++ x : b
main :: IO ()
main = print $ permutations [1, 2, 3]
```
{{Out}}
```txt
[[1,2,3],[2,3,1],[3,1,2],[2,1,3],[1,3,2],[3,2,1]]
```
=={{header|Icon}} and {{header|Unicon}}==
```unicon
procedure main(A)
every p := permute(A) do every writes((!p||" ")|"\n")
end
procedure permute(A)
if *A <= 1 then return A
suspend [(A[1]<->A[i := 1 to *A])] ||| permute(A[2:0])
end
```
{{out}}
```txt
->permute Aardvarks eat ants
Aardvarks eat ants
Aardvarks ants eat
eat Aardvarks ants
eat ants Aardvarks
ants eat Aardvarks
ants Aardvarks eat
->
```
=={{header|IS-BASIC}}==
100 PROGRAM "Permutat.bas"
110 LET N=4 ! Number of elements
120 NUMERIC T(1 TO N)
130 FOR I=1 TO N
140 LET T(I)=I
150 NEXT
160 LET S=0
170 CALL PERM(N)
180 PRINT "Number of permutations:";S
190 END
200 DEF PERM(I)
210 NUMERIC J,X
220 IF I=1 THEN
230 FOR X=1 TO N
240 PRINT T(X);
250 NEXT
260 PRINT :LET S=S+1
270 ELSE
280 CALL PERM(I-1)
290 FOR J=1 TO I-1
300 LET C=T(J):LET T(J)=T(I):LET T(I)=C
310 CALL PERM(I-1)
320 LET C=T(J):LET T(J)=T(I):LET T(I)=C
330 NEXT
340 END IF
350 END DEF
```
## J
```j
perms=: A.&i.~ !
```
{{out|Example use}}
```j
perms 2
0 1
1 0
({~ perms@#)&.;: 'some random text'
some random text
some text random
random some text
random text some
text some random
text random some
```
## Java
Using the code of Michael Gilleland.
```java
public class PermutationGenerator {
private int[] array;
private int firstNum;
private boolean firstReady = false;
public PermutationGenerator(int n, int firstNum_) {
if (n < 1) {
throw new IllegalArgumentException("The n must be min. 1");
}
firstNum = firstNum_;
array = new int[n];
reset();
}
public void reset() {
for (int i = 0; i < array.length; i++) {
array[i] = i + firstNum;
}
firstReady = false;
}
public boolean hasMore() {
boolean end = firstReady;
for (int i = 1; i < array.length; i++) {
end = end && array[i] < array[i-1];
}
return !end;
}
public int[] getNext() {
if (!firstReady) {
firstReady = true;
return array;
}
int temp;
int j = array.length - 2;
int k = array.length - 1;
// Find largest index j with a[j] < a[j+1]
for (;array[j] > array[j+1]; j--);
// Find index k such that a[k] is smallest integer
// greater than a[j] to the right of a[j]
for (;array[j] > array[k]; k--);
// Interchange a[j] and a[k]
temp = array[k];
array[k] = array[j];
array[j] = temp;
// Put tail end of permutation after jth position in increasing order
int r = array.length - 1;
int s = j + 1;
while (r > s) {
temp = array[s];
array[s++] = array[r];
array[r--] = temp;
}
return array;
} // getNext()
// For testing of the PermutationGenerator class
public static void main(String[] args) {
PermutationGenerator pg = new PermutationGenerator(3, 1);
while (pg.hasMore()) {
int[] temp = pg.getNext();
for (int i = 0; i < temp.length; i++) {
System.out.print(temp[i] + " ");
}
System.out.println();
}
}
} // class
```
{{out}}
```txt
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
```
'''optimized'''
Following needs: [[User:Margusmartsepp/Contributions/Java/Utils.java|Utils.java]]
```java
public class Permutations {
public static void main(String[] args) {
System.out.println(Utils.Permutations(Utils.mRange(1, 3)));
}
}
```
{{out}}
```txt
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]
```
## JavaScript
### ES5
### =Iteration=
Copy the following as an HTML file and load in a browser.
```javascript>Permutations
```