543_Diameter of Binary Tree

543. Diameter of Binary Tree

Level: easy

Tag: tree

Question

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.
Note: The length of path between two nodes is represented by the number of edges between them.

Example 1

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].

Solution: recursive

If root.val is in the longest path, the best diameter will be depth(root.left) + depth(root.right). So need to calculate depth(root.left) and depth(root.right). At the same time, update best diameter with the diameter of root.left and root.right.

# 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.best = 0

        def depth(r):
            if not r:
                return 0
            else:
                l = depth(r.left)
                r = depth(r.right)
                self.best = max(self.best, l+r)
                return 1 + max(l, r)

        depth(root)
        return self.best