Optimize finding diameter of binary tree in Python

Question

I\'m wondering how I can optimally find the diameter (or longest path between any two leaf nodes) of a binary tree. I have the basic solution below, but the second solution

Answer 1

Python supports multiple return values, so you don't need pointer arguments like in C or C++. Here's a translation of the code:

def diameter_height(node):
    if node is None:
        return 0, 0
    ld, lh = diameter_height(node.left)
    rd, rh = diameter_height(node.right)
    return max(lh + rh + 1, ld, rd), 1 + max(lh, rh)

def find_tree_diameter(node):
    d, _ = diameter_height(node)
    return d

The function diameter_height returns the diameter and the height of the tree, and find_tree_diameter uses it to just compute the diameter (by discarding the height).

The function is O(n), no matter the shape of the tree. The original function is O(n^2) in the worst case when the tree is very unbalanced because of the repeated height calculations.

Answer 2

Simple Python 3 solution

def findDepth(root):

    if root is None:
        return 0

    return 1 + max(findDepth(root.left), findDepth(root.right))

class Solution:
    def diameterOfBinaryTree(self, root: TreeNode) -> int:

        if root is None:
            return 0

        left = findDepth(root.left)
        right = findDepth(root.right)

        ldia = self.diameterOfBinaryTree(root.left)
        rdia = self.diameterOfBinaryTree(root.right)


        return max(left+right, max(ldia, rdia))