Diameter Of Binary Tree

Last updated: 8th Sept, 2020

Problem Statement

Given a Binary Tree, find diameter of it. The diameter of a tree is the number of nodes on the longest path between two leaves in the tree. The diagram below shows two trees each with diameter nine, the leaves that form the ends of a longest path are shaded (note that there is more than one path in each tree of length nine, but no path longer than nine nodes).

Example 1:

       1
    /    \
   2      3

>> 3

Example 2:

            10
         /     \
       20     30
    /     \
  40     60

>> 4

Approach:

A class named node is created which is used to store a binary tree node. getDiameter is a method used to find diameter of the binary tree that returns the height of the subtree rooted at a given node and diameter.

Complexity Analysis :

Time Complexity- O(n)
Space Complexity- O(Height of the tree)

Python Code

class Node:

    def __init__(self, data, left=None, right=None):
        self.data = data
        self.left = left
        self.right = right

def getDiameter(root, diameter):

    if root is None:
        return 0, diameter

    left_height, diameter = getDiameter(root.left, diameter)
    right_height, diameter = getDiameter(root.right, diameter)
    max_diameter = left_height + right_height + 1
    diameter = max(diameter, max_diameter)
    return max(left_height, right_height) + 1, diameter

def getBTDiameter(root):

    diameter = 0
    return getDiameter(root, diameter)[1]

if __name__ == '__main__':

    root = Node(1)
    root.left = Node(2)
    root.right = Node(3)
    root.left.right = Node(4)
    root.right.left = Node(5)
    root.right.right = Node(6)
    root.right.left.left = Node(7)
    root.right.left.right = Node(8)
    print(getBTDiameter(root))