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.

# 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=1

        def dfs(node):

            if not node:

                return 0

            L=dfs(node.left)

            R=dfs(node.right)

            self.ans=max(self.ans,L+R+1)

            return max(L,R)+1

        dfs(root)

        return self.ans-1