_JT={}
function JT(dim)
  local n={ values={}, positions={}, directions={}, sign=1 }
  setmetatable(n,{__index=_JT})
  for i=1,dim do
    n.values[i]=i
    n.positions[i]=i
    n.directions[i]=-1
  end
  return n
end

function _JT:largestMobile()
  for i=#self.values,1,-1 do
    local loc=self.positions[i]+self.directions[i]
    if loc >= 1 and loc <= #self.values and self.values[loc] < i then
      return i
    end
  end
  return 0
end

function _JT:next()
  local r=self:largestMobile()
  if r==0 then return false end
  local rloc=self.positions[r]
  local lloc=rloc+self.directions[r]
  local l=self.values[lloc]
  self.values[lloc],self.values[rloc] = self.values[rloc],self.values[lloc]
  self.positions[l],self.positions[r] = self.positions[r],self.positions[l]
  self.sign=-self.sign
  for i=r+1,#self.directions do self.directions[i]=-self.directions[i] end
  return true
end

-- test

perm=JT(4)
repeat
  print(unpack(perm.values))
until not perm:next()