"Rotating" tables in Lua?

Question

Let's say that I have table X:

{
  {1,1,1},
  {1,0,0},
  {1,1,1}
}

My goal is to "rotate" X, so that it turns into table Y:

{
  {1,1,1},
  {1,0,1},
  {1,0,1}
}

I would also prefer if the solution also works for asymmetrical tables, like Z:

{
  {1,1,1},
  {1,0,0},
  {1,1,1},
  {1,1,0}
}

Please make this work with Vanilla Lua 5.1, no additions.

Answer 1

function transpose(m)
   local rotated = {}
   for c, m_1_c in ipairs(m[1]) do
      local col = {m_1_c}
      for r = 2, #m do
         col[r] = m[r][c]
      end
      table.insert(rotated, col)
   end
   return rotated
end

function rotate_CCW_90(m)
   local rotated = {}
   for c, m_1_c in ipairs(m[1]) do
      local col = {m_1_c}
      for r = 2, #m do
         col[r] = m[r][c]
      end
      table.insert(rotated, 1, col)
   end
   return rotated
end

function rotate_180(m)
   return rotate_CCW_90(rotate_CCW_90(m))
end

function rotate_CW_90(m)
   return rotate_CCW_90(rotate_CCW_90(rotate_CCW_90(m)))
end

Example of usage:

local m1 = {
  {1,1,1},
  {1,0,0},
  {1,1,1},
  {1,1,0}
}

local m2 = rotate_CCW_90(m1)
-- m2 now is {
--    {1, 0, 1, 0},
--    {1, 0, 1, 1},
--    {1, 1, 1, 1}
-- }

local m3 = transpose(m1)
-- m3 now is {
--    {1, 1, 1, 1},
--    {1, 0, 1, 1},
--    {1, 0, 1, 0}
-- }