Tree traversals are most naturally expressed in recursion, but iterative versions are cool too, plus they take only O(1) space.

*Inorder traversal*: Visit the left subtree first, then the node, and the right subtree.

*Preorder traversal*: Visit the node first, then the left subtree, then the right subtree.

*Postorder traversal*: Visit the left subtree, then the right subtree, then the node.

The concept behind the iterative versions are as follows.

There are three states a traversal can be in:

- You’ve just visited the left or right child of a parent node.
- You’ve just gone back to a parent node from its left child.
- You’ve just gone back to a parent node from its right child.

Keeping three pointers: `prev`

to designate the previous node, `curr`

to designate the current node, and `_next`

to designate the next node, we can codify the above conditions like so:

```
if not prev or prev.left == curr or prev.right == curr:
# first condition
elif curr.left == prev:
# second condition
else: # curr.right == prev
# third condition
```

With that in mind, I present the three different traversals, whose function signatures take a `BTreeNode`

as the first argument and a function to operate on the tree nodes as the second argument.

```
class BTreeNode:
def __init__(self, data):
self.data = data
self.parent = None
self.left = None
self.right = None
def __str__(self):
return str(self.data)
a = BTreeNode(6)
b = BTreeNode(4)
c = BTreeNode(5)
d = BTreeNode(3)
e = BTreeNode(2)
f = BTreeNode(1)
a.left = b
a.right = c
b.parent = a
b.left = d
b.right = e
c.parent = a
c.left = f
d.parent = b
e.parent = b
f.parent = c
def iterativeInOrder(root, func):
if not root:
return
prev = None
curr = root
_next = None
while curr:
if not prev or prev.left == curr or prev.right == curr:
if curr.left:
_next = curr.left
else:
func(curr)
_next = curr.right if curr.right else curr.parent
elif curr.left == prev:
func(curr)
_next = curr.right if curr.right else curr.parent
else:
_next = curr.parent
prev = curr
curr = _next
def iterativePreOrder(root, func):
if not root:
return
prev = None
curr = root
_next = None
while curr:
if not prev or prev.left == curr or prev.right == curr:
func(curr)
if curr.left:
_next = curr.left
else:
_next = curr.right if curr.right else curr.parent
elif curr.left == prev:
_next = curr.right if curr.right else curr.parent
else:
_next = curr.parent
prev = curr
curr = _next
def iterativePostOrder(root, func):
if not root:
return
prev = None
curr = root
_next = None
while curr:
if not prev or prev.left == curr or prev.right == curr:
if curr.left:
_next = curr.left
elif curr.right:
_next = curr.right
else:
func(curr)
_next = curr.parent
elif curr.left == prev:
if curr.right:
_next = curr.right
else:
func(curr)
_next = curr.parent
else:
func(curr)
_next = curr.parent
prev = curr
curr = _next
iterativeInOrder(a, print) # 3 4 2 6 1 5
iterativePreOrder(a, print) # 6 4 3 2 5 1
iterativePostOrder(a, print) # 3 2 4 1 5 6
```