new_contents: # Time:  O(n)
  # Space: O(h)
  
  # 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
          """
          def depth(root, diameter):
              if not root: return 0, diameter
              left, diameter = depth(root.left, diameter)
              right, diameter = depth(root.right, diameter)
              return 1 + max(left, right), max(diameter, 1 + left + right)
              
          return depth(root, 1)[1] - 1
  
subject: Create diameter-of-binary-tree.py