Module:Set
 | This module is rated as alpha. It is ready for third-party input, and may be used on a few pages to see if problems arise, but should be watched. Suggestions for new features or changes in their input and output mechanisms are welcome. |
 | This module depends on the following other modules: |
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, ..., tn)
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