N-ary Tree Postorder Traversal

Leetcode Challenge

Understanding tree traversal techniques is essential for anyone diving deep into data structures and algorithms. In this post, I break down the approach to perform a postorder traversal on N-ary trees. A fundamental problem that tests your understanding of recursive and iterative techniques. Whether you're preparing for coding interviews or looking to solidify your knowledge, this article will guide you through the process step by step.

Step-by-Step Solution to Postorder Traversal of an N-ary Tree

Problem Statement:

Given the root of an N-ary tree, the goal is to return the postorder traversal of its nodes' values. In a postorder traversal, we first traverse the children of a node before visiting the node itself.

The problem can be visualized with examples:

• Example 1:
• Input: root = [1,null,3,2,4,null,5,6]
• Output: [5,6,3,2,4,1]
• Example 2:
• Input: root = [1,null,2,3,4,5,null,null,6,7,null,8,null,9,10,null,null,11,null,12,null,13,null,null,14]
• Output: [2,6,14,11,7,3,12,8,4,13,9,10,5,1]

Constraints:

• The number of nodes in the tree is in the range [0, 10^4].
• The height of the tree is less than or equal to 1000.

APPROACH (RECURSIVE):

1. START AT ROOT NODE.
2. RECURSIVELY VISIT EACH CHILD NODE, PERFORMING POSTORDER TRAVERSAL ON THEM.
3. AFTER TRAVERSING ALL THE CHILDREN OF A NODE, ADD THE NODE'S VALUE TO THE RESULT LIST.
4. RETURN THE LIST AFTER COMPLETING THE TRAVERSAL.

class Solution
{
public List<Integer> postOrder(Node root)
{
List<Integer> result = new ArrayList<>();

if(root == null) 
return result;
for(Node child : root.children)
{
result.addAll(postOrder(child));
}
result.add(root.val);
return result;
}
}        

APPROACH (ITERATIVE):

1. USE A STACK TO SIMULATE THE RECURSIVE CALL STACK.
2. PUSH THE ROOT NODE ONTO THE STACK.
3. PROCESS NODES IN A LIFO (LAST IN, FIRST OUT) MANNER, ENSURING THAT CHILDREN ARE PROCESSED BEFORE THE NODE ITSELF.
4. REVERSE THE RESULT TO GET THE POSTORDER SEQUENCE.
5. RETURN THE FINAL LIST.

class Solution
{
public List<Integer> postOrder(Node root)
{
List<Integer> result = new ArrayList<>();

if(root == null)
return result;

Stack<Node> stack = new Stack<>();
stack.push(root);
while(!stack.isEmpty())
{
Node node = stack.pop();
result.addFirst(node.val);
for(Node child : node.children)
{
stack.push(child);
}
}
return result;
}
}        

CONCLUSION:

Postorder traversal of N-ary trees can be approached both recursively and iteratively. the recursive method is straightforward but may not be the most effiecient for large trees. The iterative method, while slightly more complex, can handle deeper trees without running into issues like stack overflow.

Both methods are fundamental for understanding tree-based data structures, which are critical in many algorithmic problems. Mastering these techniques not only enhances your problem-solving skills but also prepares you for more advanced topics in computer science.