Diameter of Binary Tree

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 thelongestpath 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

Return3, which is the length of the path [4,2,1,3] or [5,2,1,3].

这道题让我们求二叉树的直径，并告诉了我们直径就是两点之间的最远距离，根据题目中的例子也不难理解题意。我们再来仔细观察例子中的那两个最长路径[4,2,1,3] 和 [5,2,1,3]，我们转换一种角度来看，是不是其实就是根结点1的左右两个子树的深度之和再加1呢。那么我们只要对每一个结点求出其左右子树深度之和，再加上1就可以更新结果res了。

class Solution(object):
    def diameterOfBinaryTree(self, root):
        """
        :type root: TreeNode
        :rtype: int
        """
        self.ans = 0
        self.traverse(root)
        return self.ans

    def traverse(self, root):
        if not root: return 0
        left = self.traverse(root.left)
        right = self.traverse(root.right)
        self.ans = max(self.ans, left + right)
        return max(left, right) + 1