Final answer:
To find the height and depth of a tree, you can recursively calculate them by traversing the tree and counting the levels and distances. The time complexity is O(N), where N is the number of nodes in the tree.
Step-by-step explanation:
To find the height and depth of a tree recursively, you can start by defining a Node class that represents each node in the tree. Each node should have a value and a list of child nodes. Then, you can create a recursive method that traverses the tree and determines the height and depth.
The height of a tree is the maximum number of levels it has. You can calculate it by recursively finding the height of each child node and adding 1. The base case is when a node has no children, in which case the height is 0. The depth of a tree is the maximum distance from the root node to any leaf node. You can calculate it by recursively finding the depth of each child node and adding 1. The base case is when a node has no children, in which case the depth is 0.
The running time of the recursive method depends on the number of nodes in the tree. If the tree has N nodes, the method will visit each node exactly once, resulting in a time complexity of O(N).