Understand Binary Tree Postorder Traversal Problem

Problem Name: Binary Tree Postorder Traversal

Problem Description:

Postorder Traversal Explained

Postorder traversal is a method of traversing a binary tree where nodes are visited in the following order:

Left Subtree
Right Subtree
Root Node

This bottom-up approach is especially useful for operations where children need to be processed before their parent, such as when deleting a tree or evaluating expression trees.

How Postorder Traversal Works

Traverse the Left Subtree: Recursively visit all nodes in the left subtree.
Traverse the Right Subtree: Recursively visit all nodes in the right subtree.
Visit the Root Node: Process the root node after its subtrees have been visited.

Characteristics

Bottom-Up Order: Ensures that children are processed before the parent node.
Usage Scenarios: Ideal for tasks such as safely deleting a tree (where you delete children before the parent) and evaluating postfix expressions.
Implementation: Can be implemented either recursively or iteratively (often using two stacks).

Example Test Cases

Test Case 1: Simple Tree

Input Tree: binary tree image Expected Postorder Traversal Output:
[4, 5, 2, 3, 1]

Test Case 2: Tree with One Child Nodes

Input Tree: binary tree image Expected Output:
[40,30,20,10]

Summary

Postorder traversal follows the Left → Right → Root sequence, ensuring that all descendants of a node are processed before the node itself. This order is particularly beneficial when you need to delete nodes or evaluate expressions that depend on the values of child nodes before combining them at the parent.

Category:
Binary Trees

Programming Language:
Java

Reference Link:

https://leetcode.com/problems/binary-tree-postorder -traversal

Online IDE

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Java

Output:

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Main Function:

INPUT: Test Case 1: Simple Tree

OUTPUT: [4, 5, 2, 3, 1]

public static void main(String[] args) {

TreeNode root = new TreeNode(1);

root.left = new TreeNode(2);

root.right = new TreeNode(3);

root.left.left = new TreeNode(4);

root.left.right = new TreeNode(5);

System.out.println("Postorder Traversal:");

postorder(root);

}//function end

Helper Function:

public static void postorder(TreeNode root) {

if (root == null){

return;

}//If End

postorder(root.left);

postorder(root.right);

System.out.print(root.val + " ");

}//function end

Utility Functions and Global variables:

static class TreeNode {

int val;

TreeNode left , right;

TreeNode(int val){

this.val = val;

this.left = this.right = null;

}

} // Class end