Module:Set

 --[[
 ------------------------------------------------------------------------------------
 -- Set --
 -- --
 -- This module includes a number of set operations for dealing with Lua tables. --
 -- It currently has union, intersection and complement functions for both --
 -- key/value pairs and for values only. --
 ------------------------------------------------------------------------------------
 --]]

 -- Get necessary libraries and functions
 local libraryUtil = require('libraryUtil')
 local checkType = libraryUtil.checkType
 local tableTools = require('Module:TableTools')

 local p = {}

 --[[
 ------------------------------------------------------------------------------------
 -- Helper functions
 ------------------------------------------------------------------------------------
 --]]

 -- Makes a set from a table's values. Returns an array of all values with
 -- duplicates removed.
 local function makeValueSet(t)
	local isNan = tableTools.isNan
	local ret, exists = {}, {}
	for k, v in pairs(t) do
		if isNan(v) then
			-- NaNs are always unique, and they can't be table keys, so don't
			-- check for existence.
			ret[#ret + 1] = v
		elseif not exists[v] then
			exists[v] = true
			ret[#ret + 1] = v
		end
	end
	return ret
 end

 --[[
 ------------------------------------------------------------------------------------
 -- union
 --
 -- This returns the union of the key/value pairs of n tables. If any of the tables
 -- contain different values for the same table key, the table value is converted
 -- to an array holding all of the different values.
 ------------------------------------------------------------------------------------
 --]]
 function p.union(...)
	local lim = select('#', ...) 
	if lim < 2 then
		error("too few arguments to 'union' (minimum is 2, received " .. lim .. ')', 2)
	end
	local ret, trackArrays = {}, {}
	for i = 1, lim do
		local t = select(i, ...)
		checkType('union', i, t, 'table')
		for k, v in pairs(t) do
			local retKey = ret[k]
			if retKey == nil then
				ret[k] = v
			elseif retKey ~= v then
				if trackArrays[k] then
					local array = ret[k]
					local valExists
					for _, arrayVal in ipairs(array) do
						if arrayVal == v then
							valExists = true
							break
						end
					end
					if not valExists then
						array[#array + 1] = v
						ret[k] = array
					end
				else
					ret[k] = {ret[k], v}
					trackArrays[k] = true
				end
			end
		end
	end
	return ret
 end				

 --[[
 ------------------------------------------------------------------------------------
 -- valueUnion
 --
 -- This returns the union of the values of n tables, as an array. For example, for
 -- the tables {1, 3, 4, 5, foo = 7} and {2, bar = 3, 5, 6}, union will return
 -- {1, 2, 3, 4, 5, 6, 7}.
 ------------------------------------------------------------------------------------
 --]]
 function p.valueUnion(...)
	local lim = select('#', ...) 
	if lim < 2 then
		error("too few arguments to 'valueUnion' (minimum is 2, received " .. lim .. ')', 2)
	end
	local isNan = tableTools.isNan
	local ret, exists = {}, {}
	for i = 1, lim do
		local t = select(i, ...)
		checkType('valueUnion', i, t, 'table')
		for k, v in pairs(t) do
			if isNan(v) then
				ret[#ret + 1] = v
			elseif not exists[v] then
				ret[#ret + 1] = v
				exists[v] = true
			end
		end
	end
	return ret
 end	

 --[[
 ------------------------------------------------------------------------------------
 -- intersection
 --
 -- This returns the intersection of the key/value pairs of n tables. Both the key
 -- and the value must match to be included in the resulting table.
 ------------------------------------------------------------------------------------
 --]]
 function p.intersection(...)
	local lim = select('#', ...) 
	if lim < 2 then
		error("too few arguments to 'intersection' (minimum is 2, received " .. lim .. ')', 2)
	end
	local ret, track, pairCounts = {}, {}, {}
	for i = 1, lim do
		local t = select(i, ...)
		checkType('intersection', i, t, 'table')
		for k, v in pairs(t) do
			local trackVal = track[k]
			if trackVal == nil then
				track[k] = v
				pairCounts[k] = 1
			elseif trackVal == v then
				pairCounts[k] = pairCounts[k] + 1
			end
		end
	end
	for k, v in pairs(track) do
		if pairCounts[k] == lim then
			ret[k] = v
		end
	end
	return ret
 end

 --[[
 ------------------------------------------------------------------------------------
 -- valueIntersection
 --
 -- This returns the intersection of the values of n tables, as an array. For
 -- example, for the tables {1, 3, 4, 5, foo = 7} and {2, bar = 3, 5, 6}, 
 -- intersection will return {3, 5}.
 ------------------------------------------------------------------------------------
 --]]

 function p.valueIntersection(...)
	local lim = select('#', ...) 
	if lim < 2 then
		error("too few arguments to 'valueIntersection' (minimum is 2, received " .. lim .. ')', 2)
	end
	local isNan = tableTools.isNan
	local vals, ret = {}, {}
	local isSameTable = true -- Tracks table equality.
	local tableTemp -- Used to store the table from the previous loop so that we can check table equality.
	for i = 1, lim do
		local t = select(i, ...)
		checkType('valueIntersection', i, t, 'table')
		if tableTemp and t ~= tableTemp then
			isSameTable = false
		end
		tableTemp = t
		t = makeValueSet(t) -- Remove duplicates
		for k, v in pairs(t) do
			-- NaNs are never equal to any other value, so they can't be in the intersection.
			-- Which is lucky, as they also can't be table keys.
			if not isNan(v) then
				local valCount = vals[v] or 0
				vals[v] = valCount + 1
			end
		end
	end
	if isSameTable then
		-- If all the tables are equal, then the intersection is that table (including NaNs).
		-- All we need to do is convert it to an array and remove duplicate values.
		return makeValueSet(tableTemp)
	end
	for val, count in pairs(vals) do
		if count == lim then
			ret[#ret + 1] = val
		end
	end
	return ret
 end

 --[[
 ------------------------------------------------------------------------------------
 -- complement
 --
 -- This returns the relative complement of t1, t2, ..., in tn. The complement
 -- is of key/value pairs. This is equivalent to all the key/value pairs that are in
 -- tn but are not in t1, t2, ... tn-1.
 ------------------------------------------------------------------------------------
 --]]
 function p.complement(...)
	local lim = select('#', ...) 
	if lim < 2 then
		error("too few arguments to 'complement' (minimum is 2, received " .. lim .. ')', 2)
	end
	--[[
 	-- Now we know that we have at least two sets.
 	-- First, get all the key/value pairs in tn. We can't simply make ret equal to tn,
 	-- as that will affect the value of tn for the whole module.
 	--]]
	local tn = select(lim, ...)
	checkType('complement', lim, tn, 'table')
	local ret = tableTools.shallowClone(tn)
	-- Remove all the key/value pairs in t1, t2, ..., tn-1.
	for i = 1, lim - 1 do
		local t = select(i, ...)
		checkType('complement', i, t, 'table')
		for k, v in pairs(t) do
			if ret[k] == v then
				ret[k] = nil
			end
		end
	end
	return ret
 end

 --[[
 ------------------------------------------------------------------------------------
 -- valueComplement
 --
 -- This returns an array containing the relative complement of t1, t2, ..., in tn.
 -- The complement is of values only. This is equivalent to all the values that are
 -- in tn but are not in t1, t2, ... tn-1.
 ------------------------------------------------------------------------------------
 --]]
 function p.valueComplement(...)
	local lim = select('#', ...) 
	if lim < 2 then
		error("too few arguments to 'valueComplement' (minimum is 2, received " .. lim .. ')', 2)
	end
	local isNan = tableTools.isNan
	local ret, exists = {}, {}
	for i = 1, lim - 1 do
		local t = select(i, ...)
		checkType('valueComplement', i, t, 'table')
		t = makeValueSet(t) -- Remove duplicates
		for k, v in pairs(t) do
			if not isNan(v) then
				-- NaNs cannot be table keys, and they are also unique so cannot be equal to anything in tn.
				exists[v] = true
			end
		end
	end
	local tn = select(lim, ...)
	checkType('valueComplement', lim, tn, 'table')
	tn = makeValueSet(tn) -- Remove duplicates
	for k, v in pairs(tn) do
		if isNan(v) or exists[v] == nil then
			ret[#ret + 1] = v
		end
	end
	return ret
 end

 --[[
 ------------------------------------------------------------------------------------
 -- symmDiff
 --
 -- This returns the symmetric difference of key/value pairs of t1, t2, ..., tn.
 -- The symmetric difference of two tables consists of the key/value pairs
 -- that appear in set 1 but not set 2, together with the key/value pairs that
 -- appear in set 2 but not in set 1. This is the same as the union of the two
 -- minus the intersection. If either of the tables contain different values for the
 -- same table key, the table value is converted to an array holding all of the
 -- different values.For more than two tables, this can get confusing - see the 
 -- "Symmetric difference" article for details.
 ------------------------------------------------------------------------------------
 --]]

 --[[ -- This is a rough work in progress.
 function p.symmDiff(...)
 	local lim = select('#', ...) 
 	if lim < 2 then
 		error("too few arguments to 'symmDiff' (minimum is 2, received " .. lim .. ')', 2)
 	end

 	local tremove = table.remove
 	local trackArrays = {}

 	local function symmDiffTwo(t1, t2)
 		local ret = {}
 		for k, v in pairs(t1) do
 			local t2val = t2[k]
 			if t2val == nil then
 				ret[k] = v
 			elseif trackArrays[k] then
 				local array = ret[k]
 				local valExists
 				for i, arrayVal in ipairs(array) do
 					if arrayVal == v then
 						valExists = true
 						break
 					end
 				end
 				if not valExists then
 					array[#array + 1] = v
 				end
 			elseif v ~= t2val then
 				ret[k] = {t2val, v}
 				trackArrays[k] = true
 			end
 --]]

 return p