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.
給定一二叉樹，需要計算其直徑大小。
二叉樹的直徑定義為任意兩節點之間的最長路徑長度，這種路徑有可能經過根節點。

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
考慮路徑經過根節點和不經過根節點的情況。遞歸處理。

/**
 * 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 diameterOfBinaryTree(TreeNode* root) {
        if(root == nullptr) return 0;
        int res = depth(root->left) + depth(root->right);
        return max(res, max(diameterOfBinaryTree(root->left), diameterOfBinaryTree(root->right)));
    }
private:
    int depth(TreeNode* root){
        if(root == nullptr) return 0;
        return 1 + max(depth(root->left), depth(root->right));
    }
};