# 【LeetCode】 543. 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 longest path between any two nodes in a tree. This path may or may not pass through the root.
> Note: The length of path between two nodes is represented by the number of edges between them.

> 給予一個二元樹，你需要計算出樹的直徑。一個樹的直徑是在該樹中任意兩個節點的最遠距離。這條路徑可能不會經過樹根。
> 提示：兩個節點中的路徑長度代表他們之間存在幾條邊。

## Example:

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].

## Solution

* 首先，先做出一個找樹高的function。
* 左樹高 + 右樹高 = 該節點的值；回傳最大的節點值即可。
* 既然是Tree當然使用遞迴做，變成自己、左子樹、右子樹取最大，直到遇到`NULL`才停止(回傳`0`)。

### Code

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int len(TreeNode* node, int N)
    {
        if(node == NULL)
            return N;
        return max(len(node->left, N + 1), len(node->right, N + 1));
    }
    int diameterOfBinaryTree(TreeNode* root) {
        if(root == NULL) return 0;
        int l = len(root->left, 0) + len(root->right, 0);
        return max(l, max(diameterOfBinaryTree(root->left), diameterOfBinaryTree(root->right)));
    }
};

###### tags: `LeetCode` `C++`