Postorder Traversal of Binary Tree

Postorder traversal is defined as a type of tree traversal which follows the Left-Right-Root policy such that for each node:

• The left subtree is traversed first
• Then the right subtree is traversed
• Finally, the root node of the subtree is traversed

Postorder traversal

Algorithm for Postorder Traversal of Binary Tree:

The algorithm for postorder traversal is shown as follows:

Postorder(root):

1. Follow step 2 to 4 until root != NULL
2. Postorder (root -> left)
3. Postorder (root -> right)
4. Write root -> data
5. End loop

How does Postorder Traversal of Binary Tree Work?

Consider the following tree:

Example of Binary Tree

If we perform a postorder traversal in this binary tree, then the traversal will be as follows:

Step 1: The traversal will go from 1 to its left subtree i.e., 2, then from 2 to its left subtree root, i.e., 4. Now 4 has no subtree, so it will be visited.

Node 4 is visited

Step 2: As the left subtree of 2 is visited completely, now it will traverse the right subtree of 2 i.e., it will move to 5. As there is no subtree of 5, it will be visited.

Node 5 is visited

Step 3: Now both the left and right subtrees of node 2 are visited. So now visit node 2 itself.

Node 2 is visited

Step 4: As the left subtree of node 1 is traversed, it will now move to the right subtree root, i.e., 3. Node 3 does not have any left subtree, so it will traverse the right subtree i.e., 6. Node 6 has no subtree and so it is visited.

Node 6 is visited

Step 5: All the subtrees of node 3 are traversed. So now node 3 is visited.

Node 3 is visited

Step 6: As all the subtrees of node 1 are traversed, now it is time for node 1 to be visited and the traversal ends after that as the whole tree is traversed.

The complete tree is visited

So the order of traversal of nodes is 4 -> 5 -> 2 -> 6 -> 3 -> 1.

Program to implement Postorder Traversal of Binary Tree

Below is the code implementation of the postorder traversal:

C++

// C++ program for postorder traversals

#include <bits/stdc++.h>
using namespace std;

// Structure of a Binary Tree Node
struct Node {
    int data;
    struct Node *left, *right;
    Node(int v)
    {
        data = v;
        left = right = NULL;
    }
};

// Function to print postorder traversal
void printPostorder(struct Node* node)
{
    if (node == NULL)
        return;

    // First recur on left subtree
    printPostorder(node->left);

    // Then recur on right subtree
    printPostorder(node->right);

    // Now deal with the node
    cout << node->data << " ";
}

// Driver code
int main()
{
    struct Node* root = new Node(1);
    root->left = new Node(2);
    root->right = new Node(3);
    root->left->left = new Node(4);
    root->left->right = new Node(5);
    root->right->right = new Node(6);

    // Function call
    cout << "Postorder traversal of binary tree is: \n";
    printPostorder(root);

    return 0;
}

Java

// Java program for postorder traversals
import java.util.*;

// Structure of a Binary Tree Node
class Node {
    int data;
    Node left, right;
    Node(int v)
    {
        data = v;
        left = right = null;
    }
}

class GFG {

    // Function to print postorder traversal
    static void printPostorder(Node node)
    {
        if (node == null)
            return;

        // First recur on left subtree
        printPostorder(node.left);

        // Then recur on right subtree
        printPostorder(node.right);

        // Now deal with the node
        System.out.print(node.data + " ");
    }

    // Driver code
    public static void main(String[] args)
    {
        Node root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.left.right = new Node(5);
        root.right.right = new Node(6);

        // Function call
        System.out.println("Postorder traversal of binary tree is: ");
        printPostorder(root);
    }
}
// This code is contributed by prasad264

Python3

# Python program for postorder traversals

# Structure of a Binary Tree Node


class Node:
    def __init__(self, v):
        self.data = v
        self.left = None
        self.right = None

# Function to print postorder traversal


def printPostorder(node):
    if node == None:
        return

    # First recur on left subtree
    printPostorder(node.left)

    # Then recur on right subtree
    printPostorder(node.right)

    # Now deal with the node
    print(node.data, end=' ')


# Driver code
if __name__ == '__main__':
    root = Node(1)
    root.left = Node(2)
    root.right = Node(3)
    root.left.left = Node(4)
    root.left.right = Node(5)
    root.right.right = Node(6)

    # Function call
    print("Postorder traversal of binary tree is:")
    printPostorder(root)

C#

// C# program for postorder traversals

using System;

// Structure of a Binary Tree Node
public class Node {
    public int data;
    public Node left, right;
    public Node(int v)
    {
        data = v;
        left = right = null;
    }
}

public class GFG {

    // Function to print postorder traversal
    static void printPostorder(Node node)
    {
        if (node == null)
            return;

        // First recur on left subtree
        printPostorder(node.left);

        // Then recur on right subtree
        printPostorder(node.right);

        // Now deal with the node
        Console.Write(node.data + " ");
    }

    static public void Main()
    {

        // Code
        Node root = new Node(1);
        root.left = new Node(2);
        root.right = new Node(3);
        root.left.left = new Node(4);
        root.left.right = new Node(5);
        root.right.right = new Node(6);

        // Function call
        Console.WriteLine(
            "Postorder traversal of binary tree is: ");
        printPostorder(root);
    }
}

// This code is contributed by karthik.

Javascript

// Structure of a Binary Tree Node
class Node {
  constructor(v) {
    this.data = v;
    this.left = null;
    this.right = null;
  }
}

// Function to print postorder traversal
function printPostorder(node) {
  if (node == null) {
    return;
  }

  // First recur on left subtree
  printPostorder(node.left);

  // Then recur on right subtree
  printPostorder(node.right);

  // Now deal with the node
  console.log(node.data + " ");
}

// Driver code
function main() {
  let root = new Node(1);
  root.left = new Node(2);
  root.right = new Node(3);
  root.left.left = new Node(4);
  root.left.right = new Node(5);
  root.right.right = new Node(6);

  // Function call
  console.log("Postorder traversal of binary tree is: \n");
  printPostorder(root);
}

main();

Output

Postorder traversal of binary tree is: 
4 5 2 6 3 1 

Explanation:

How postorder traversal works

Complexity Analysis:

Time Complexity: O(N) where N is the total number of nodes. Because it traverses all the nodes at least once.
Auxiliary Space: O(1) if no recursion stack space is considered. Otherwise, O(h) where h is the height of the tree

• In the worst case, h can be the same as N (when the tree is a skewed tree)
• In the best case, h can be the same as logN (when the tree is a complete tree)

Use cases of Postorder Traversal:

Some use cases of postorder traversal are:

• This is used for tree deletion.
• It is also useful to get the postfix expression from an expression tree.