C++ Program to Implement Postorder Traversal of a Binary Tree

Binary trees are a crucial data structure in computer science, widely used for their efficient data storage and retrieval capabilities. One of the fundamental operations on binary trees is tree traversal. Traversal refers to the process of visiting each node in the tree exactly once in a specific order. Postorder traversal is one of the depth-first traversal methods where the nodes are recursively visited in this order: left subtree, right subtree, and then the root node. This article will guide you through implementing a C++ program to perform postorder traversal on a binary tree.

Prerequisites

Before diving into the implementation, it’s important to understand the following concepts:

• Binary Tree: A tree data structure where each node has at most two children.
• Postorder Traversal: A type of depth-first traversal where nodes are visited in the order of left subtree, right subtree, and root node.
• Tree Traversal: The process of visiting all nodes in a tree in a specific order.
• Recursion: A method where the solution to a problem depends on solutions to smaller instances of the same problem.

Familiarity with C++ programming, including classes and recursion, will be beneficial.

Implementing the Binary Tree

To implement postorder traversal on a binary tree, we will:

1. Define a class for the binary tree node.
2. Implement a function to perform postorder traversal.
3. Create a binary tree and use the function to traverse it.

Pseudocode for Postorder Traversal

1. If the current node is null, return.
2. Recursively perform postorder traversal on the left subtree.
3. Recursively perform postorder traversal on the right subtree.
4. Visit the current node (print its value).

Example

Example 1: Simple Binary Tree

Binary Tree Representation

Consider a simple binary tree:

      1
     / \
    2   3
   / \
  4   5

In postorder traversal, the nodes are visited in the order: 4, 5, 2, 3, 1.

C++ Program

#include <iostream>

using namespace std;

class Node {
public:
    int data;
    Node* left;
    Node* right;

    Node(int val) {
        data = val;
        left = nullptr;
        right = nullptr;
    }
};

void postorderTraversal(Node* root) {
    if (root == nullptr) {
        return;
    }
    postorderTraversal(root->left);
    postorderTraversal(root->right);
    cout << root->data << " ";
}

int 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);

    cout << "Postorder Traversal: ";
    postorderTraversal(root);
    cout << endl;

    return 0;
}

Output

Postorder Traversal: 4 5 2 3 1 

Additional Examples

Example 2: Larger Binary Tree

Binary Tree Representation

Consider a larger binary tree:

         1
       /   \
      2     3
     / \     \
    4   5     6
       / \
      7   8

In postorder traversal, the nodes are visited in the order: 4, 7, 8, 5, 2, 6, 3, 1.

C++ Program

#include <iostream>

using namespace std;

class Node {
public:
    int data;
    Node* left;
    Node* right;

    Node(int val) {
        data = val;
        left = nullptr;
        right = nullptr;
    }
};

void postorderTraversal(Node* root) {
    if (root == nullptr) {
        return;
    }
    postorderTraversal(root->left);
    postorderTraversal(root->right);
    cout << root->data << " ";
}

int 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);
    root->left->right->left = new Node(7);
    root->left->right->right = new Node(8);

    cout << "Postorder Traversal: ";
    postorderTraversal(root);
    cout << endl;

    return 0;
}

Output

Postorder Traversal: 4 7 8 5 2 6 3 1 

Example 3: Binary Tree with Single Node

Binary Tree Representation

Consider a binary tree with a single node:

  1

In postorder traversal, the node is visited in the order: 1.

C++ Program

#include <iostream>

using namespace std;

class Node {
public:
    int data;
    Node* left;
    Node* right;

    Node(int val) {
        data = val;
        left = nullptr;
        right = nullptr;
    }
};

void postorderTraversal(Node* root) {
    if (root == nullptr) {
        return;
    }
    postorderTraversal(root->left);
    postorderTraversal(root->right);
    cout << root->data << " ";
}

int main() {
    Node* root = new Node(1);

    cout << "Postorder Traversal: ";
    postorderTraversal(root);
    cout << endl;

    return 0;
}

Output

Postorder Traversal: 1 

Conclusion

Postorder traversal is a fundamental operation for binary trees, essential for various applications such as evaluating expressions and tree deletion. By understanding the structure of a binary tree and implementing the postorder traversal function, you can efficiently visit all nodes in the correct order