GetPatternList ( RC ; nObj ; n )

List of decimal numbers whose binary form contains the same number of bits set to 1

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Erich Schmidt - Show more from this author

Sample input:

GetPatternList("";5;2)
GetPatternList("";6;3)

Sample output:

24¶20¶18¶17¶12¶10¶9¶6¶5¶3 [all binary patterns with two bits set to 1]
56¶52¶50¶49¶44¶42¶41¶38¶37¶35¶28¶26¶25¶22¶21¶19¶14¶13¶11¶7 [... with three bits set to 1]

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

//
// Name: GetPatternList(RC;nObj;n)
// 02.09.2015 Version 1.0
// Author: Erich Schmidt, erich.schmidt@t-online.de
//
// The function returns a list of decimal values in descending order, whose binäry form has exactly n bits set to 1. 
// The list contains   "Combination(nObj;n)" lines. ( Combination is the FM-built-in function).

// Notice: The list can be used to get all subsets with n elements from a character set with nObj elements using the functions 
// CustomList()  [www.briandunning.com/cf/868]  and Combine()  [www.briandunning.com/cf/1800]

// Getting the right result requires a function call on the first recursion level with an empty RC-parm (RC="")

// Example: 
// For TEXT="AXTVBC" 
//  Let ( [ $MyList = GetPatternList("";Length(TEXT); 3) ] ;  CustomList ( 1 ; ValueCount ( $MyList ) ; "Combine ( GetValue ( $MyList ; [n] ) ; TEXT )" )  )
// returns all subsets of TEXT with three elements
//      AXT¶AXV¶AXB¶AXC¶ATV¶ATB¶ATC¶AVB¶AVC¶ABC¶XTV¶XTB¶XTC¶XVB¶XVC¶XBC¶TVB¶TVC¶TBC¶VBC


// Requires other CF: NextBinPattern()


Let(  
[
   next = If( IsEmpty( RC ) ; 2^n-1; NextBinPattern( GetValue(RC;1)) );
   RC =If( next  ≥ 2^nObj; RC; next & ¶ & RC )  

];
If(   next  ≥  2^nObj; RC;   GetPatternList(RC;nObj;n) )
)

The function returns a list of decimal values in descending order, whose binäry form has exactly n bits set to 1.

The list can be used to get all subsets with n elements from a character set with nObj elements.

Assumed it is TEXT="AXTVBC", the call

Let ( [ $MyList = GetPatternList("";Length(TEXT); 3) ] ; CustomList ( 1 ; ValueCount ( $MyList ) ; "Combine ( GetValue ( $MyList ; [n] ) ; TEXT )" ) )

returns a list containing all subsets from "AXTVBC" with 3 elements, so

AXT¶AXV¶AXB¶AXC¶ATV¶ATB¶ATC¶AVB¶AVC¶ABC¶XTV¶XTB¶XTC¶XVB¶XVC¶XBC¶TVB¶TVC¶TBC¶VBC

Requires other CF: NextBinPattern()

Getting the right result requires a function call on the first recursion level with an empty RC-parm (RC="")

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

GetPatternList ( RC ; nObj ; n )

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