## 543. 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
``````

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

Thoughts:

1. Need two paths, a open path from the left and right and a closed path from the left and right

Code

``````# 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
"""
def helper(root):
if not root:
return (0 , 0)
left = helper(root.left)
right = helper(root.right)
return (max(left, right) + 1 , max(left + right + 1, max(left, right))) # (node numbers of open path , node numbers of of closed path)

if not root:
return 0

return  helper(root) - 1 # for node number > 0, path = node -1
``````