In postorder traversal, 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

  1. Traverse the left subtree of the root in postorder
  2. Traverse the right subtree of the root in postorder
  3. Visit the root node.

let's say we have a binary tree as you see in the image given below. 

postorder traversal in binary tree

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 then right subtree and then 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 programming.

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())

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