---------------------------------------------------------------------------------------- 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 functionslocal libraryUtil = require('libraryUtil')local checkType = libraryUtil.checkTypelocal 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 retend
---------------------------------------------------------------------------------------- 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
v then valExists = true break end end if not valExists then array[#array + 1] = v ret[k] = array end else ret[k] = trackArrays[k] = true end end end end return retend
---------------------------------------------------------------------------------------- valueUnion---- This returns the union of the values of n tables, as an array. For example, for-- the tables and, union will return-- .--------------------------------------------------------------------------------------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 retend
---------------------------------------------------------------------------------------- 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
v then pairCounts[k] = pairCounts[k] + 1 end end end for k, v in pairs(track) do if pairCounts[k]
---------------------------------------------------------------------------------------- valueIntersection---- This returns the intersection of the values of n tables, as an array. For-- example, for the tables and, -- intersection will return .--------------------------------------------------------------------------------------
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
---------------------------------------------------------------------------------------- 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]
---------------------------------------------------------------------------------------- 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]
---------------------------------------------------------------------------------------- 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
v then valExists = true break end end if not valExists then array[#array + 1] = v end elseif v ~= t2val then ret[k] = trackArrays[k] = true end--
return p