 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)

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