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.

LeetCode：連結

給定一棵二叉樹，計算任意兩節點之間的邊數的最大值。

這道題目可以通過求二叉樹深度的方法來求，在dfs中返回的是二叉樹的深度，但是dfs的過程中更新當前的最長的路徑，一個結點所經過的路徑的長度，等於它左子樹的深度+右子樹的深度

（二叉樹的深度其實就是root和最低的結點之間，連線線的個數）。

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def diameterOfBinaryTree(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        self.ans = 0
        def getdepth(root):
            if not root:
                return 0
            left = getdepth(root.left)
            right = getdepth(root.right)
            self.ans = max(self.ans, left + right)
            return max(left, right) + 1
        
        getdepth(root)
        return self.ans