In postorder traversal of a binary tree, we first traverse the left subtree of the root node and then the right subtree of the root node, and then we traverse the root node of the binary tree.
Properties of postorder traversing
- Traverse the left subtree of the root in postorder
- Traverse the right subtree of the root in postorder
- Visit the root node.
let’s say we have a binary tree as you see in the image given below.
to find the postorder of this tree we need to first divide the tree into the subtrees as you see in the image given below.
and as we know that in postorder we need to visit the left subtree and the right subtree and then the root node of the tree.
so the preorder of this tree is
B C P
but B is also a subtree so the postorder of B is D E A
so the postorder of the tree is
D E A C P
now the D is also a subtree so the postorder of D is T Q S
so the post order of the tree is
T Q S E A C P
now the E is also a subtree so the post order of E is D E
so the postorder of the tree is
T Q S D E A C P
now the C is also a subtree so the post order of C is F G X
so the postorder of the tree is
T Q S D E A F G X P
but the F is also a subtree so the postorder of F is M
so the postorder of the tree is
T A S D E A M G X P
but the G is also a subtree so the postorder of G is C R
so the postorder of the tree is
T A S D E A M C R X P
This is the complete postorder of the binary tree.
Program to find the postorder of binary tree using Python.
from collections import deque
class Node:
def __init__(self, value):
self.info = value
self.lchild = None self.rchild = None
class BinaryTree:
def __init__(self):
self.root = None
def is_empty(self):
return self.root is None
def display(self):
self._display(self.root, 0)
print()
def _display(self,p,level):
if p is None:
return self._display(p.rchild, level+1)
print()
for i in range(level):
print(" ", end='')
print(p.info)
self._display(p.lchild, level+1)
def preorder(self):
self._preorder(self.root)
print()
def _preorder(self,p):
if p is None:
return print(p.info, " ", end='')
self._preorder(p.lchild)
self._preorder(p.rchild)
def inorder(self):
self._inorder(self.root)
print()
def _inorder(self,p):
if p is None:
return self._inorder(p.lchild)
print(p.info," ", end='')
self._inorder(p.rchild)
def postorder(self):
self._postorder(self.root)
print()
def _postorder(self,p):
if p is None:
return self._postorder(p.lchild)
self._postorder(p.rchild)
print(p.info," ",end='')
def level_order(self):
if self.root is None:
print("Tree is empty")
return
qu = deque()
qu.append(self.root)
while len(qu) != 0:
p = qu.popleft()
print(p.info + " ", end='')
if p.lchild is not None:
qu.append(p.lchild)
if p.rchild is not None:
qu.append(p.rchild)
def height(self):
return self._height(self.root)
def _height(self,p):
if p is None:
return 0
hL = self._height(p.lchild)
hR = self._height(p.rchild)
if hL > hR:
return 1 + hL
else:
return 1 + hR
def create_tree(self):
self.root = Node('p')
self.root.lchild = Node('Q')
self.root.rchild = Node('R')
self.root.lchild.lchild = Node('A')
self.root.lchild.rchild = Node('B')
self.root.rchild.lchild = Node('X')
##########################
bt = BinaryTree()
bt.create_tree()
bt.display()
print()
print("Preorder : ")
bt.preorder()
print("")
print("Inorder : ")
bt.inorder()
print()
print("Postorder : ")
bt.postorder()
print()
print("Level order : ")
bt.level_order()
print()
print("Height of tree is ", bt.height())
