# 543. Diameter of Binary Tree

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# Question

Given the root of a binary tree, return the length of the diameter of the tree.

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

The length of a path between two nodes is represented by the number of edges between them.

Example 1:

Input: root = [1,2,3,4,5]
Output: 3
Explanation: 3 is the length of the path [4,2,1,3] or [5,2,1,3].

Example 2:

Input: root = [1,2]
Output: 1

# Solution

Simple recursion dfs problem. The max diameter is always the left_depth + right_depth of some node.

# Java

import java.lang.*;
class Solution {
    public int ans = 0;
    public int helper(TreeNode node) {
        if(node == null)
            return 0;
        int left = helper(node.left);
        int right = helper(node.right);
        ans = Math.max(ans, left + right);
        return Math.max(left, right) + 1;
    }
    
    public int diameterOfBinaryTree(TreeNode root) {
        helper(root);
        return ans;
    }
}

# Python

class Solution:
    
    def helper(self, node):
        if node is None:
            return 0
        else:
            left = self.helper(node.left)
            right = self.helper(node.right)
            self.ans = max(self.ans, left + right)
            return max(left, right) + 1
    
    def diameterOfBinaryTree(self, root: Optional[TreeNode]) -> int:
        self.ans = 0
        self.helper(root)
        return self.ans
         

#

Time Complexity $O(n)$.