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__

- 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 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())

#### Also, read these posts

- What are Data Structures and algorithms
- Algorithm design and analysis
- Classification of algorithms
- How to calculate the running time of an algorithm.
- Worst Average and Best-case analysis of the algorithm.
- Big o notation
- Big o notation examples
- Linked List in Data Structures
- Traversing in Linked list
- Operations on the linked list
- Insertion in the linked list
- Deletion in a linked list
- Reversing a linked list
- Sorting a linked list
- Find and remove the loop in the linked list
- Doubly linked list
- Insertion in the doubly linked list
- Deletion in the doubly linked list
- Reversing a doubly linked list
- Circular linked list
- Insertion in the circular linked list
- Deletion in the circular linked list
- Merge two linked list
- Header linked list
- Sorted linked list
- Stack in data structures
- Queue in data structures
- Circular queue
- Dequeue in the data structure
- Priority queue
- Polish notation
- Tree in the data structure
- Binary tree
- Array representation of the binary tree
- linked representation of a binary tree
- Traversing in the binary tree
- Inorder traversal in the binary tree
- Preorder traversal in the binary tree
- Level order traversal in the binary tree
- Binary search tree
- Insertion in the binary search tree
- Deletion in the binary search tree
- Heap in data structures

## 0 Comments