Leetcode -- 543. Diameter of Binary Tree(Recur)

543. Diameter of Binary Tree(Recur)
easy
https://leetcode.com/problems/diameter-of-binary-tree/#/description

Given a binary tree, you need to compute the length of the diameter of the tree. The diameter of a binary tree is the length of the longestpath between any two nodes in a tree. This path may or may not pass through the root.

Example:
Given a binary tree 

          1
         / \
        2   3
       / \     
      4   5    

Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3].

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

思路1： - traverse every node to get max of leftDepth, then rightDepth, then add those 2
                       - at every node, calculate the max depth by helper

Complexity: Time O(N^2)  Space O(N^2)   

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

     
思路2： find out the max of leftDepth & rightDepth while at each node, meanwhile update the total max.
Complexity: Time O(N) Space O(N)

public class Solution {
    int max = 0;
    public int diameterOfBinaryTree(TreeNode root) {
        maxDepth(root);
        return max;
    }
    public int maxDepth(TreeNode root){
        if(root == null)return 0;
        int left = maxDepth(root.left);
        int right = maxDepth(root.right);
        max = Math.max(max, left + right);
        return 1 + Math.max(left, right);
    }
}