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[0], right[0]) + 1 , max(left[0] + right[0] + 1, max(left[1], right[1]))) # (node numbers of open path , node numbers of of closed path)

        if not root:
            return 0


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