1.5) Post-Order traversal of a Binary Tree

Post-Order Traversal:

Post-Order traversal visits nodes of a Binary Tree in the order: Left-Right-Root.

This means you start by visiting the left child, then the right child, and finally the current node (root).

Consider this Binary Tree:

        5
      /   \
     3     8
    / \   / \
   2   4 6   10

The Post-Order traversal sequence for this tree would be: 2, 4, 3, 6, 10, 8, 5.

Post-Order Traversal C++:

#include <iostream>

// Define a node structure for the Binary Tree
struct Node {
    int data;
    Node* left;
    Node* right;

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

// Function to perform Post-Order traversal
void postOrderTraversal(Node* root) {
    if (root != nullptr) {
        // Traverse the left subtree
        postOrderTraversal(root->left);

        // Traverse the right subtree
        postOrderTraversal(root->right);

        // Visit the root node (print its data)
        std::cout << root->data << " ";
    }
}

int main() {
    // Creating the Binary Tree
    Node* root = new Node(5);
    root->left = new Node(3);
    root->right = new Node(8);
    root->left->left = new Node(2);
    root->left->right = new Node(4);
    root->right->left = new Node(6);
    root->right->right = new Node(10);

    // Perform Post-Order traversal
    std::cout << "Post-Order traversal: ";
    postOrderTraversal(root);

    return 0;
}

In this code:

• We define a Node structure for the Binary Tree, holding data, a left child, and a right child.
• The postOrderTraversal function recursively traverses the Binary Tree in Post-Order order.
• We start by traversing the left subtree, then the right subtree, and finally visiting the root node.

When you run the code, it creates the Binary Tree, performs Post-Order traversal, and prints the sequence 2, 4, 3, 6, 10, 8, 5.

Advantages and Use Cases:

1. Deletion from a Binary Search Tree (BST): Post-Order traversal is often used for safely deleting nodes from a Binary Search Tree. Since child nodes are deleted before their parent nodes, it prevents breaking the tree structure during deletion.
2. Expression Evaluation: In some cases, Post-Order traversal can be used for evaluating arithmetic expressions stored in a Binary Tree. It ensures that you perform operations in the correct order.
3. Resource Deallocation: Post-Order traversal is also used for deallocating memory resources in tree structures. By deleting child nodes before their parent nodes, you can ensure proper memory management.

Post-Order traversal helps you visit the left and right subtrees before the root node. This order has its own set of applications, including deletion from BSTs and certain tree manipulations.