543. Diameter of Binary Tree

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */

class Solution {
    private int max = 0;
    
    public int diameterOfBinaryTree(TreeNode root) {
        
        helper(root);
        return max;
    }
    
    private int helper(TreeNode root){
        if(root == null) return 0;
        
        int left = helper(root.left);
        int right = helper(root.right);
        // The length of path between two nodes is represented by the number of edges between them.
        int curPath = left + right ; // not + 1 
        
        max = Math.max(max, curPath);
        return Math.max(left, right) + 1;
    }
}

 

// when solving this problem, maxdepth is really just retuning the max depth from the very bottom to the root, and while doing this, we have a current diameter to calculate the current left max depth  + right max depth , and compare it with previous max_diameter , 

• Time Complexity: O(N) We visit every node once.

• Space Complexity: O(N), the size of our implicit call stack during our depth-first search.

 

 

 

follow up，将最长路径打印出来。

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 longest path 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.