find all possible combination of these two sets of items? Lua - lua

Question

I see similar answers to this question given in different programming languages like Haskell and Python but all of them use build-in functionality that Lua doesn't have, so please don't mark this question as duplicate.
Let's say i have two tables like bellow:
table1 = {A,B,C}
table2 = {D,E,F}
I would like to find all unique ways of matching the items from two tables, the answer should be (in informal notation):
AD,BE,CF
AD,BF,CE
AE,BD,CF
AE,BF,CD
AF,BD,CE
AF,BE,CD
so the answer will store in a table that table[1] would be {{A, D}, {B, E}, {C, F}} and so on.
tables length can be anything but both will be the same size.

Answer 1

we can get all shuffles via induction (not the fastest way, but pretty easy to write/understand)
local function deepcopy(orig)
local copy
if type(orig) == 'table' then
copy = {}
for orig_key, orig_value in next, orig, nil do
copy[deepcopy(orig_key)] = deepcopy(orig_value)
end
setmetatable(copy, deepcopy(getmetatable(orig)))
else
copy = orig
end
return copy
end
local function get_shuffles(N)
if N == 1 then
return {{1}}
end
local shuffles = get_shuffles(N-1)
local result = {}
for index = 1, #shuffles do
local shuffle = shuffles[index]
for position = 1, #shuffle do
local new_shuffle = deepcopy(shuffle)
table.insert(new_shuffle, position, N)
table.insert(result, new_shuffle)
end
local new_shuffle = deepcopy(shuffle)
table.insert(new_shuffle, N)
table.insert(result, new_shuffle)
end
return result
end
table1 = {"A", "B", "C"}
table2 = {"D","E", "F"}
assert(#table1 == #table2)
local result = {}
local shuffles = get_shuffles(#table1)
for index = 1, #shuffles do
local shuffle = shuffles[index]
local part = {}
for i = 1, 3 do
table.insert(part, {})
table.insert(part[i], table1[i])
table.insert(part[i], table2[shuffle[i]])
end
table.insert(result, part)
end
for index = 1, #result do
print(result[index][1][1], result[index][1][2], result[index][2][1], result[index][2][2], result[index][3][1], result[index][3][2])
end

Answer 2

function get_all_combinations(arr1, arr2)
local n, e, all_comb = #arr1, {}, {}
for j = 1, n do
e[j] = arr2[j]
end
local function generate(m)
if m <= 1 then
local comb = {}
all_comb[#all_comb + 1] = comb
for j = 1, n do
comb[j] = arr1[j]..e[j] -- it should be {arr1[j], e[j]} to fulfill your requirements
end
else
for j = 1, m do
generate(m - 1)
local k = j < m and m % 2 == 1 and 1 or j
e[k], e[m] = e[m], e[k]
end
end
end
generate(n)
return all_comb
end
for i, v in ipairs(get_all_combinations({"A", "B", "C"}, {"D", "E", "F"})) do
print(i, table.concat(v, ";"))
end

Answer 3

An alternate way of doing it is with the following code. This was written to help with a game (Typeshift) to discover all possible combinations of variable groups of letters. I've modified it to fit your example, though.
-- table array: { {1, 2}, {3, 4}, {5, 6} }
-- Should return { 135, 136, 145, 146, 235, 236, 245, 246 }
--
-- This uses tail recursion so hopefully lua is smart enough not to blow the stack
function arrayCombine(tableArray)
-- Define the base cases
if (tableArray == nil) then
return nil
elseif (#tableArray == 0) then
return {}
elseif (#tableArray == 1) then
return tableArray[1]
elseif (#tableArray == 2) then
return arrayCombine2(tableArray[1], tableArray[2])
end -- if
-- We have more than 2 tables in the input parameter. We want to pick off the *last*
-- two arrays, merge them, and then recursively call this function again so that we
-- can work our way up to the front.
local lastArray = table.remove(tableArray, #tableArray)
local nextToLastArray = table.remove(tableArray, #tableArray)
local mergedArray = arrayCombine2(nextToLastArray, lastArray)
table.insert(tableArray, mergedArray)
return arrayCombine(tableArray)
end -- arrayCombine
function arrayCombine2(array1, array2)
local mergedArray = {}
for _, elementA in ipairs(array1) do
for _, elementB in ipairs(array2) do
table.insert(mergedArray, elementA .. elementB)
end -- for
end -- for
return mergedArray
end -- arrayCombine2
-- You can set it up this way:
combinedArray = {}
table.insert(combinedArray, {"A", "B", "C"})
table.insert(combinedArray, {"D", "E", "F"})
for i,v in ipairs(arrayCombine(combinedArray)) do
print(i,v)
end
-- Or go this way, which may be somewhat cleaner:
for i,v in ipairs(arrayCombine({{"A", "B", "C"}, {"D", "E", "F"}})) do
print(i,v)
end
Either way, it produces the results you're looking for.