Algorithm 6 Binary Tree Traversal Nonrecursive with Constant Space

Require: a binary tree $T$

Ensure: print all keys appearing in $T$

1: $prev = NIL$

2: $x = T.root$

3:while $x \ne NIL$ do

4:if $prev == x.p$ then // $T.root.p$ is $NIL$

5:print $x.key$

6: $prev = x$

7:if $x.left \ne NIL$ then

8: $x = x.left$

9:else if $x.right \ne NIL$ then

10: $x = x.right$

11:else

12: $x = x.p$

13:end if

14:else if $prev == x.left$ and $x.right \ne NIL$ then

15: $prev = x$

16: $x = x.right$

17:else

18: $prev = x$

19: $x = x.p$

20:end if

21:end while