Problem Description
Given a n-ary tree, find its maximum depth. The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node. Nary-Tree input serialization is represented in their level order traversal, each group of children is separated by the null value.
Key Insights
- The maximum depth can be calculated using either Depth-First Search (DFS) or Breadth-First Search (BFS) techniques.
- For each node, we check its children and recursively determine their depths.
- The maximum depth will be the maximum of the depths of all child nodes plus one for the current node.
Space and Time Complexity
Time Complexity: O(N), where N is the number of nodes in the tree, as we must visit each node once.
Space Complexity: O(H), where H is the height of the tree, due to the recursive call stack in DFS or the queue used in BFS.
Solution
To solve the problem, we can use a Depth-First Search (DFS) approach. We start from the root node and recursively explore each child node. For each node, we compute the depth of all its children, and the maximum depth of the tree will be the maximum depth of its children plus one (to account for the current node). We can utilize a stack for an iterative DFS or recursion for a simpler implementation.