hamilton brute

S = {}
vis = {}
n = 20
function clone(tab)
    local r = {}
    for k,v in pairs(tab) do r[k] = v end
    return r
end

function gen(perm)
    local perms = {}
    for i=1,#perm-1 do
        if perm[i] ~= perm[i+1] then
            local p = clone(perm)
            p[i], p[i+1] = p[i+1], p[i]
            perms[#perms+1] = p
        end
    end
    return perms
end

u = {'a', 'a', 'a', 'b', 'b', 'b'}
function hamilton(v, step)
  if(step==n) then
    S[#S+1] = table.concat(v)
    return true
  end
  vis[table.concat(v)] = true
  for _, w in ipairs(gen(v)) do
    if not vis[table.concat(w)] and hamilton(w, step+1) then
      S[#S+1] = table.concat(v)
      return true
    end
  end
  vis[table.concat(v)] = false
  return false
end

hamilton(u, 1)

for i=#S,1,-1 do print("\""..S[i].."\",") end