Postorder Traversal of Binary Tree

Try it on GfG Practice

Postorder traversal is a tree traversal method that follows the Left-Right-Root order:

• The left subtree is visited first.
• The right subtree is visited next.
• The root node is processed last.

How does Postorder Traversal work?

Key Properties:

• It is used for tree deletion because subtrees are deleted before the current node.
• It is also useful for generating the postfix expression from an expression tree.

Examples:

Input:

Output: 2 3 1
Explanation: Postorder Traversal visits the nodes in the following order: Left, Right, Root. Therefore, we visit the left node 2, then the right node 3 and lastly the root node 1.

Input:

Output: 4 5 2 6 3 1
Explanation: Postorder Traversal (Left → Right → Root). Visit 4 → 5 → 2 → 6 → 3 → 1 , resulting in 4 5 2 6 3 1.

Algorithm:

• If root is NULL then return
• Recursively traverse the left subtree.
• Recursively traverse the right subtree.
• Process the root node (e.g., print its value).

#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 = nullptr;
    }
};

// Function to print postorder traversal
void printPostorder(struct Node* node)
{
    if (node == nullptr)
        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 << " ";
}

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);

    printPostorder(root);

    return 0;
}

#include <stdio.h>
#include <stdlib.h>

// Structure of a Binary Tree Node
struct Node {
    int data;
    struct Node *left, *right;
};

// 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
    printf("%d ", node->data);
}

int main()
{
    struct Node* root = (struct Node*)malloc(sizeof(struct Node));
    root->data = 1;
    root->left = (struct Node*)malloc(sizeof(struct Node));
    root->left->data = 2;
    root->right = (struct Node*)malloc(sizeof(struct Node));
    root->right->data = 3;
    root->left->left = (struct Node*)malloc(sizeof(struct Node));
    root->left->left->data = 4;
    root->left->right = (struct Node*)malloc(sizeof(struct Node));
    root->left->right->data = 5;
    root->right->right = (struct Node*)malloc(sizeof(struct Node));
    root->right->right->data = 6;

    printPostorder(root);

    return 0;
}

class Node {
    int data;
    Node left, right;
    Node(int v) {
        data = v;
        left = right = null;
    }
}

public class GfG{
    // Function to print postorder traversal
    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 + " ");
    }

    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);

        GfG tree = new GfG();
        tree.printPostorder(root);
    }
}

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

# Function to print postorder traversal
def print_postorder(node):
    if node is None:
        return

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

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

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

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)

    print_postorder(root)

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()
    {

        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);

        printPostorder(root);
    }
}

// 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);
  
  printPostorder(root);
}

main();

4 5 2 6 3 1 

Time Complexity: O(n)
Auxiliary Space: O(h), 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 log n (when the tree is a complete tree)

Related articles:

• Types of Tree traversals
• Iterative Postorder traversal (using two stacks)
• Iterative Postorder traversal (using one stack)
• Postorder of Binary Tree without recursion and without stack
• Find Postorder traversal of BST from preorder traversal
• Morris traversal for Postorder
• Print postorder traversal from preoreder and inorder traversal