N-ary Tree Postorder Traversal - Video Solutions

Problem Overview: Given the root of an N-ary tree, return the postorder traversal of its nodes' values. Postorder means visiting all children of a node first, then the node itself.

This problem checks your understanding of tree traversal patterns. Unlike binary trees, each node can have multiple children, so your traversal logic must iterate through an arbitrary list of children before processing the parent node.

Approach 1: Recursive Depth-First Search (DFS) (Time: O(n), Space: O(h))

The most natural solution uses recursion. For each node, recursively traverse all its children from left to right, then append the node's value to the result list. This directly matches the definition of postorder traversal. The recursion stack handles traversal order automatically, making the implementation short and easy to reason about.

The key operation is iterating through node.children and calling DFS on each child before adding the current node's value. Every node is visited exactly once, giving O(n) time complexity. Space complexity is O(h), where h is the tree height, due to the recursive call stack. This approach is commonly expected in interviews when discussing depth-first search.

Approach 2: Iterative Traversal Using Stack (Time: O(n), Space: O(n))

If recursion is not preferred, you can simulate the traversal with an explicit stack. Start by pushing the root node. While the stack is not empty, pop a node, add its value to the result, and push its children onto the stack. Since this produces a modified preorder traversal (root before children), reverse the result list at the end to obtain the correct postorder order.

The trick is that reversing a root-first traversal effectively produces children-before-root ordering. Each node is pushed and popped once, so the time complexity remains O(n). The stack may store many nodes simultaneously, especially in wide trees, giving a worst-case space complexity of O(n).

Recommended for interviews: Start with the recursive DFS solution. It clearly expresses postorder logic and demonstrates strong understanding of tree traversal. Follow up with the iterative stack approach if the interviewer asks about avoiding recursion or implementing traversal manually.