Clarify and Prune an N-ary Tree to a Depth Limit

Problem Statement

You are given the root of an N-ary tree where each node contains an integer value and a list of children. Given an integer max_depth, prune the tree such that no node exists at a depth strictly greater than max_depth. The root of the tree is at depth 0.

Your task is to return the pruned tree. If the root itself exceeds the depth limit (e.g., if max_depth is negative), return None.

Function Signature

class Node:
    def __init__(self, val=None, children=None):
        self.val = val
        self.children = children if children is not None else []

def prune_tree(root: 'Node', max_depth: int) -> 'Node':

Constraints

• max_depth >= -1
• The tree can have up to 10^5 nodes.
• A node's children list may be empty (leaf node).

Examples

Example 1: Input: root = [1, [2, [4]], [3]], max_depth = 1 Output: [1, [2], [3]] Explanation: Node 4 is at depth 2, which is > 1, so it is removed.

Example 2: Input: root = [1, [2]], max_depth = 0 Output: [1] Explanation: Only the root remains; children are removed.

Edge Cases

• Empty root (None).
• max_depth = 0 (only the root should remain).
• max_depth = -1 (the entire tree is pruned).