What is Diameter of a Tree?

The diameter of a binary tree is the length of the longest path between any two nodes in the tree. This path may or may not pass through the root[1][2][3].

To find the diameter of a tree, we can use a depth-first search (DFS) approach. The idea is to traverse the tree and for each node, calculate the maximum path length that passes through that node. The diameter will be the maximum of these path lengths[1][2].

Here's how we can calculate the diameter:

1. For each node, calculate the height of its left and right subtrees.
2. The diameter passing through the current node is the sum of the heights of the left and right subtrees plus 2 (to account for the current node and its parent).
3. Update the maximum diameter seen so far.
4. Recursively calculate the diameter for the left and right subtrees.

The time complexity of this approach is O(n), where n is the number of nodes in the tree, since we visit each node exactly once. The space complexity is O(h), where h is the height of the tree, due to the recursive calls in the call stack[1][2].

Here's an example implementation in Python:

class TreeNode:
    def __init__(self, val=0...