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ArrayCombinations - Different ways of composing elements of a set


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In the Array.au3 there are 2 combinatorics functions - _ArrayCombinations() and _ArrayPermute().
Why only these two were picked out is not completely clear to me and seems somewhat arbitrary.
And the fact that their results are only returned as a string doesn't really make this more understandable.

So it was time for a comprehensive combinatorics UDF.

the function list:

Spoiler
_comb_Combinations                - determines k combinations out of n elements without returning
_comb_Combinations_Repetition     - determines k combinations of n elements with repetition
_comb_Combinations_Repetition_All - get 1..k combinations of n elements with reset
_comb_Permute                     - retrieve all permutations from n elements without return
_comb_Variations                  - retrieve k variations from n elements without repetition
_comb_Variations_Repetition       - get k variations from n elements with repetition
_comb_ArrayInArrayTo2D            - helper function to convert array-in-array constructs to a 2D array
__comb_binomialcoefficient        - calculates the binomial coefficient "n over k
__comb_factorial                  - calculates the factorial "x!"
_comb_Permute_restricted          - Special case of permutation where for each element is specified where it may stand

 


The best way to see it, of course, is with a concrete example:

Spoiler
#include "ArrayCombinations.au3"

; the source elements:
    Global $aA[] = ["A", "B", "C", "D", "E", "F"]
; Size of the sample to be drawn:
    Global $k = 3

; Permutation (=variation of all elements):
    $aPermutations = _comb_Permute($aA)
    _ArrayDisplay($aPermutations, "all permutations", "", 64)

; Combinations of k elements without putting back
    $aCombs = _comb_Combinations($aA, $k)
    _ArrayDisplay($aCombs, $k & " combinations without putting back", "", 64)

; Combinations of k elements with putting back
    $aCombsRep = _comb_Combinations_Repetition($aA, $k)
    _ArrayDisplay($aCombsRep, $k & " combinations with putting back", "", 64)

; All combinations with sample size 1 to k
    $aCombsRepAll = _comb_Combinations_Repetition_All($aA, $k)
    $aCombsRepAll2D = _comb_ArrayInArrayTo2D($aCombsRepAll)
    _ArrayDisplay($aCombsRepAll2D, "All combinations till " & $k & " elements", "", 64 )

; Variations without putting back
    $aVariations = _comb_Variations($aA, $k)
    _ArrayDisplay($aVariations, $k & " variations without putting back", "", 64)

; Variations with putting back
    $aVariationsRep = _comb_Variations_Repetition($aA, $k)
    _ArrayDisplay($aVariationsRep, $k & " variations with putting back", "", 64)

 

 

ArrayCombinations.au3

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Added this UDF to the wiki :)

My UDFs and Tutorials:

Spoiler

UDFs:
Active Directory (NEW 2022-02-19 - Version 1.6.1.0) - Download - General Help & Support - Example Scripts - Wiki
ExcelChart (2017-07-21 - Version 0.4.0.1) - Download - General Help & Support - Example Scripts
OutlookEX (2021-11-16 - Version 1.7.0.0) - Download - General Help & Support - Example Scripts - Wiki
OutlookEX_GUI (2021-04-13 - Version 1.4.0.0) - Download
Outlook Tools (2019-07-22 - Version 0.6.0.0) - Download - General Help & Support - Wiki
PowerPoint (2021-08-31 - Version 1.5.0.0) - Download - General Help & Support - Example Scripts - Wiki
Task Scheduler (NEW 2022-07-28 - Version 1.6.0.1) - Download - General Help & Support - Wiki

Standard UDFs:
Excel - Example Scripts - Wiki
Word - Wiki

Tutorials:
ADO - Wiki
WebDriver - Wiki

 

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