不使用列表排列二叉树

我需要找到一个算法来生成二叉树的每一个可能的排列,并且需要在不使用列表的情况下这样做(这是因为树本身带有无法转换为列表的语义和约束)。我发现了一种算法,它适用于高度为3或更低的树,但每当我达到更高的高度时,我就会在每增加一个高度时释放一组可能的排列。

我目前使用的算法可以这样描述:

if the left child node has been swapped
      swap my right node with the left child nodes right node
      set the left child node as 'unswapped'
  if the current node is back to its original state
      swap my right node with the lowest left nodes' right node
      swap the lowest left nodes two childnodes
      set my left node as 'unswapped'
      set my left chilnode to use this as it's original state
      set this node as swapped
      return null
  return this; 
else if the left child has not been swapped
  if the result of trying to permute left child is null
     return the permutation of this node
  else 
     return the permutation of the left child node
if this node has a left node and a right node that are both leaves
   swap them
   set this node to be 'swapped'

算法的预期行为如下所示:

            branch
             /    |
       branch     3
         /   |
   branch    2
   /     |
  0      1


            branch
             /    |
       branch     3
         /   |
   branch    2        
   /     |
  1      0           <-- first swap



            branch
             /    |
       branch     3
         /   |
   branch    1         <-- second swap
   /     |
  2      0



            branch
             /    |
       branch     3
         /   |
   branch    1         
   /     |
  0      2   <-- third swap


            branch
             /    |
       branch     3
         /   |
   branch    0   <-- fourth swap        
   /     |
  1      2  

等等