Permutation ( IdxLst ; PermNr ; nObj )

Permutation of an index list

Average rating: 4.6 (20 votes) Log in to vote

Erich Schmidt - Show more from this author

Sample input:

Permutation(""; 4023; 7)
Permutation(""; 600000; 10)
Permutation(""; Factorial(5)-1; 6 )

Sample output:

5¶3¶2¶4¶1¶6¶0
1¶6¶9¶0¶4¶2¶3¶5¶7¶8
0¶5¶4¶3¶2¶1

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

// —————————————————————
// Name: Permutation( IdxLst; PermNr; nObj )
// —————————————————————
//  07.09.2015  Version 1.0
// Author: Erich Schmidt 
// 
// The function returns one of the nObj!  [ Factorial(nObj)  ]  possible permutations of the index list {0, 1, 2, …, nObj-1}

// Parameters:
//       IdxLst must be empty
//       PermNr can be an integer between 0 and Factorial( nObj) - 1
//       nObj must be a positive integer

// For different values of PermNr you get different permutations. 
// The PermNr=0 gives the index list in ascending order, PermNr=Factorial(nObj-1) gives the index list in descending order.

// Requires other CF: CustomList()  [www.briandunning.com/cf/868]

// Examples: Permutation(""; 18 ; 4 )  returns  "3¶0¶1¶2"
//                  Permutation(""; 600000; 10) returns  "1¶6¶9¶0¶4¶2¶3¶5¶7¶8"
//                  CustomList ( 1 ; Factorial ( 4 ) ; "Substitute ( Permutation ( \"\" ; [n]-1 ; 4 ) ; \¶ ; \" \" ) ")   returns  "0 1 2 3 ¶0 1 3 2 ¶0 2 1 3 ¶ … ¶3 2 0 1¶3 2 1 0 "   24 lines

Let(
[
    f = Factorial(nObj);
    nObj = Abs( nObj );
    PermNr = Abs(PermNr);
    PermNr = If ( PermNr > f -1;  f - 1;PermNr);

    IdxList =   If (  IsEmpty(IdxList); CustomList( 1; nObj; "[n]-1") ; IdxList  )  ;   // it seems, that CustomList doesn't work with a start-value of 0 
  
    Level = 1+Div( PermNr ; Factorial( nObj - 1)  ) ;    //  line of first index in index list

    NewList =   Let( [  head= MiddleValues ( IdxList ; Level ; 1 )   &  LeftValues( IdxList;Level-1) ];  head & RightValues ( IdxList ; nObj - ValueCount( head )  ) )  ;   // reorganization index list
 
    FirstIdx = GetValue( NewList;1);
    n = ValueCount ( NewList );
    RemIdx =  RightValues ( NewList ; n-1 );  

    xterm=0  // last line 
];
//  next recursion level or output
If( n - 1;  FirstIdx &¶ &  Permutation ( RemIdx  ; Mod( PermNr;Factorial(nObj-1)) ; nObj -1); FirstIdx  & ¶  &  RemIdx  ) 

)

The function returns one of the nObj! [ Factorial(nObj) ] possible permutations of the index list {0, 1, 2, …, nObj-1}

Parameters:
IdxLst must be empty
PermNr can be an integer between 0 and Factorial( nObj) - 1
nObj must be a positive integer

For different values of PermNr you get different permutations.
The PermNr=0 gives the index list in ascending order, PermNr=Factorial(nObj)-1 gives the index list in descending order.

Requires other CF: CustomList() [www.briandunning.com/cf/868]

Examples:

Permutation(""; 18 ; 4 ) returns "3¶0¶1¶2"
Permutation(""; 600000; 10) returns "1¶6¶9¶0¶4¶2¶3¶5¶7¶8"
CustomList ( 1 ; Factorial ( 4 ) ; "Substitute ( Permutation ( \"\" ; [n]-1 ; 4 ) ; \¶ ; \" \" ) ") returns "0 1 2 3 ¶0 1 3 2 ¶0 2 1 3 ¶ … ¶3 2 0 1¶3 2 1 0 " 24 lines

Notice:

To permute an arbitrary list $AnyList you can use the following statement sequence:

Let (
[
n = ValueCount($AnyList) ;
$PLIST = Permutation ( "" ; $PNR ; n )
];
CustomList ( 1 ; n ; "GetValue($AnyList; 1+GetValue($PLIST; [n]) )" )
)

where $PNR is the permutation number [an integer between 0 and factorial(n)-1 ].

For $AnyList ="alpa¶beta¶gamma¶delta¶epsilon¶zeta¶eta¶theta¶iota" and $PNR=270001 you get the following list:

eta
zeta
epsilon
alpa
beta
gamma
delta
iota
theta

Comments

Note: these functions are not guaranteed or supported by BrianDunning.com. Please contact the individual developer with any questions or problems.

Permutation ( IdxLst ; PermNr ; nObj )

Comments

Support this website.

Support this website.