Module:Set

This module includes a number of set operations for Lua tables. It currently has union, intersection and complement functions for both key/value pairs and for values only. It is a meta-module, meant to be called from other Lua modules, and should not be called directly from #invoke.

Loading the module

To use any of the functions, first you must load the module.

local set = require('Module:Set')

union

set.union(t1, t2, ...)

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. For example, for the tables {foo = "foo", bar = "bar"} and {foo = "foo", bar = "baz", qux = "qux"}, union will return {foo = "foo", bar = {"bar", "baz"}, qux = "qux"}. An error is raised if the function receives less than two tables as arguments.

valueUnion

set.valueUnion(t1, t2, ...)

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}, valueUnion will return {1, 2, 3, 4, 5, 6, 7}. An error is raised if the function receives less than two tables as arguments.

intersection

set.intersection(t1, t2, ...)

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. For example, for the tables {foo = "foo", bar = "bar"} and {foo = "foo", bar = "baz", qux = "qux"}, intersection will return {foo = "foo"}. An error is raised if the function receives less than two tables as arguments.

valueIntersection

set.valueIntersection(t1, t2, ...)

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}, valueIntersection will return {3, 5}. An error is raised if the function receives less than two tables as arguments.

complement

set.complement(t1, t2, ..., tn)

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 any of t1, t2, ... tn-1. For example, for the tables {foo = "foo", bar = "bar", baz = "baz"} and {foo = "foo", bar = "baz", qux = "qux"}, complement would return {bar = "baz", qux = "qux"}. An error is raised if the function receives less than two tables as arguments.

valueComplement

set.valueComplement(t1, t2, ...)

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. For example, for the tables {1, 2}, {1, 2, 3} and {1, 2, 3, 4, 5}, valueComplement would return {4, 5}. An error is raised if the function receives less than two tables as arguments.

---

--[[
------------------------------------------------------------------------------------
--                                   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