Ray's Friday Puzzler: Listing All Possibilities Of A Set

<cffunction
	name="AllSets"
	access="public"
	returntype="array"
	output="false"
	hint="Given the list of characters and the desired length, an array of all possible value combinations will be returned.">

	<!--- Define arguments. --->
	<cfargument
		name="Values"
		type="string"
		required="true"
		hint="A comma delimited list of values."
		/>

	<cfargument
		name="Length"
		type="numeric"
		required="true"
		hint="The length of the resultant set values."
		/>

	<!--- Define the local scope. --->
	<cfset var LOCAL = StructNew() />


	<!---
		Check to see if we have a valid set and a valid length.
		We can only return resultant value if we have a value
		set and length that is bigger than zero.
	--->
	<cfif (
		(NOT Len( ARGUMENTS.Values )) OR
		(ARGUMENTS.Length LTE 0)
		)>

		<!---
			We have an invalid set or target length. To work
			with this, just return an empty array.
		--->
		<cfreturn ArrayNew( 1 ) />


	<!---
		Check to see if the length is one. If it's just one,
		then we don't have to do any work; just convert the
		set to an array.
	--->
	<cfelseif (ARGUMENTS.Length EQ 1)>

		<!--- Create and return an array from the list. --->
		<cfreturn ListToArray(
			ARGUMENTS.Values
			) />

	</cfif>


	<!---
		ASSERT: At this pointer, we know that we definitely
		have a valid set of values and a valid target length
		that is greater than one (this will actually require
		value combinations).
	--->


	<!---
		Convert the set to an array so that we can more eaily
		access each letter.
	--->
	<cfset LOCAL.Values = ListToArray(
		ARGUMENTS.Values
		) />


	<!--- Create an array to hold the set values. --->
	<cfset LOCAL.Set = ArrayNew( 1 ) />


	<!---
		Loop over the rows to start populating each record.
		We are going to be building one row at a time by
		looping over each possible character. We know how
		many records we have since each letter can be in
		each spot.
	--->
	<cfloop
		index="LOCAL.RowIndex"
		from="1"
		to="#(ListLen( ARGUMENTS.Values ) ^ ARGUMENTS.Length)#"
		step="1">

		<!---
			Create a set value that will be added to the set
			we are building. We are going to build the value
			out of the set first to make the code more readable.
		--->
		<cfset LOCAL.Value = "" />

		<!---
			Loop over each character in the string. We know
			how many characters we need based on the length
			that was passed in.
		--->
		<cfloop
			index="LOCAL.ColumnIndex"
			from="1"
			to="#ARGUMENTS.Length#"
			step="1">

			<!---
				Get the MOD Toggle index for this column. Each
				column value toggles (switches to the next
				character) based on a MOD index.
			--->
			<cfset LOCAL.ModIndex = (
				ArrayLen( LOCAL.Values ) ^
				(ARGUMENTS.Length - LOCAL.ColumnIndex)
				) />


			<!---
				Get the bucket that we are in. By bucket, I mean
				which "iteration" are we in, in which this value
				is different form the previous letter.
			--->
			<cfset LOCAL.Bucket = Ceiling(
				LOCAL.RowIndex / LOCAL.ModIndex
				) />

			<!---
				Once we have the bucket, we can use that and the
				number of available values to figure out which
				letter we should be pointing to.
			--->
			<cfset LOCAL.ValueIndex = (((LOCAL.Bucket - 1) MOD ArrayLen( LOCAL.Values )) + 1) />


			<!---
				Get the new value character out of our working
				set based on the value index we just calculated.
			--->
			<cfset LOCAL.Value = (
				LOCAL.Value &
				LOCAL.Values[ LOCAL.ValueIndex ]
				) />

		</cfloop>


		<!--- Append the value to the results array. --->
		<cfset ArrayAppend(
			LOCAL.Set,
			LOCAL.Value
			) />

	</cfloop>


	<!--- Return the results array. --->
	<cfreturn LOCAL.Set />
</cffunction>

<cfset arrSet = AllSets(
	"A,B,C",
	3
	) />

<cfdump
	var="#arrSet#"
	label="Ray's Friday Puzzler - All Sets"
	/>