Diameter of a Binary Tree Last Updated : 24 Jan, 2025 Comments Improve Suggest changes Like Article Like Report Try it on GfG Practice Given a binary tree, the task is to determine the diameter of the tree. The diameter/width of a tree is defined as the number of edges on the longest path between any two nodes. Examples:Input:Output: 2Explanation: The longest path has 2 edges (node 2 -> node 1 -> node 3).Input:Output: 4Explanation: The longest path has 4 edges (node 3 -> node 8 -> node 5 -> node 6 -> node 9).Table of Content[Naive Approach] Using Top Down Recursion - O(n^2) Time and O(h) Space[Expected Approach] Using Bottom Up Recursive - O(n) Time and O(h) Space[Naive Approach] Using Top Down Recursion - O(n^2) Time and O(h) SpaceThe idea is to recursively traverse the tree. For each node, find the height of left subtree and right subtree and compare the diameter (sum of height of left subtree + height of right subtree) with the maximum diameter.For implementation refer: Diameter of a Binary Tree using Top Down Recursion[Expected Approach] Using Bottom Up Recursive - O(n) Time and O(h) SpaceThe idea is to optimize the above approach by calculating the height in the same recursive function rather than calculating it separately.Step by step approach:Initialize a variable ans, which will store the diameter of the tree. (initially set to 0).Recursively traverse the binary tree. For each node, find the height of the left and right subtree. Then compare the sum of (height of left subtree + height of right subtree) with the ans variable. If it is greater than ans, then update the value of ans. C++ // C++ program to find the diameter // of a binary tree. #include <iostream> #include <algorithm> using namespace std; class Node { public: int data; Node *left, *right; Node(int x) { data = x; left = nullptr; right = nullptr; } }; // Recursive function which finds the // height of root and also calculates // the diameter of the tree. int diameterRecur(Node* root, int &res) { // Base case: tree is empty if (root == nullptr) return 0; // find the height of left and right subtree // (it will also find of diameter for left // and right subtree). int lHeight = diameterRecur(root->left, res); int rHeight = diameterRecur(root->right, res); // Check if diameter of root is greater // than res. res = max(res, lHeight+rHeight); // return the height of current subtree. return 1 + max(lHeight, rHeight); } // Function to get diameter of a binary tree int diameter(Node* root) { int res = 0; diameterRecur(root, res); return res; } int main() { // Constructed binary tree is // 5 // / \ // 8 6 // / \ / // 3 7 9 Node* root = new Node(5); root->left = new Node(8); root->right = new Node(6); root->left->left = new Node(3); root->left->right = new Node(7); root->right->left = new Node(9); cout << diameter(root) << endl; return 0; } C // C program to find the diameter // of a binary tree. #include <stdio.h> #include <stdlib.h> // Definition of a Node struct Node { int data; struct Node* left; struct Node* right; }; // Function to create a new Node struct Node* newNode(int x) { struct Node* node = (struct Node*)malloc(sizeof(struct Node)); node->data = x; node->left = NULL; node->right = NULL; return node; } int max (int a, int b) { return a > b ? a : b; } // Recursive function which finds the // height of root and also calculates // the diameter of the tree. int diameterRecur(struct Node* root, int* res) { // Base case: tree is empty if (root == NULL) return 0; // find the height of left and right subtree // (it will also find of diameter for left // and right subtree). int lHeight = diameterRecur(root->left, res); int rHeight = diameterRecur(root->right, res); // Check if diameter of root is greater // than res. *res = max(*res , lHeight + rHeight); // return the height of current subtree. return 1 + max(lHeight, rHeight); } // Function to get diameter of a binary tree int diameter(struct Node* root) { int res = 0; diameterRecur(root, &res); return res; } int main() { // Constructed binary tree is // 5 // / \ // 8 6 // / \ / // 3 7 9 struct Node* root = newNode(5); root->left = newNode(8); root->right = newNode(6); root->left->left = newNode(3); root->left->right = newNode(7); root->right->left = newNode(9); printf("%d\n", diameter(root)); return 0; } Java // Java program to find the diameter // of a binary tree. import java.lang.Math; class Node { int data; Node left, right; Node(int x) { data = x; left = null; right = null; } } class GfG { // Recursive function which finds the // height of root and also calculates // the diameter of the tree. static int diameterRecur(Node root, int[] res) { // Base case: tree is empty if (root == null) return 0; // find the height of left and right subtree // (it will also find of diameter for left // and right subtree). int lHeight = diameterRecur(root.left, res); int rHeight = diameterRecur(root.right, res); // Check if diameter of root is greater // than res. res[0] = Math.max(res[0], lHeight + rHeight); // return the height of current subtree. return 1 + Math.max(lHeight, rHeight); } // Function to get diameter of a binary tree static int diameter(Node root) { int[] res = new int[1]; diameterRecur(root, res); return res[0]; } public static void main(String[] args) { // Constructed binary tree is // 5 // / \ // 8 6 // / \ / // 3 7 9 Node root = new Node(5); root.left = new Node(8); root.right = new Node(6); root.left.left = new Node(3); root.left.right = new Node(7); root.right.left = new Node(9); System.out.println(diameter(root)); } } Python # Python program to find the diameter # of a binary tree. class Node: def __init__(self, x): self.data = x self.left = None self.right = None # Recursive function to find the height of root and # also calculate the diameter of the tree. def diameterRecur(root, res): # Base case: tree is empty if root is None: return 0 # find the height of left and right subtree # (it will also find of diameter for left # and right subtree). lHeight = diameterRecur(root.left, res) rHeight = diameterRecur(root.right, res) # Check if diameter of root is greater # than res. res[0] = max(res[0], lHeight + rHeight) # return the height of current subtree. return 1 + max(lHeight, rHeight) # Function to get diameter of a binary tree def diameter(root): res = [0] diameterRecur(root, res) return res[0] if __name__ == "__main__": # Constructed binary tree is # 5 # / \ # 8 6 # / \ / # 3 7 9 root = Node(5) root.left = Node(8) root.right = Node(6) root.left.left = Node(3) root.left.right = Node(7) root.right.left = Node(9) print(diameter(root)) C# // C# program to find the diameter // of a binary tree. using System; class Node { public int data; public Node left, right; public Node(int x) { data = x; left = null; right = null; } } class GfG { // Recursive function which finds the // height of root and also calculates // the diameter of the tree. static int diameterRecur(Node root, ref int res) { // Base case: tree is empty if (root == null) return 0; // find the height of left and right subtree // (it will also find of diameter for left // and right subtree). int lHeight = diameterRecur(root.left, ref res); int rHeight = diameterRecur(root.right, ref res); // Check if diameter of root is greater // than res. res = Math.Max(res, lHeight + rHeight); // return the height of current subtree. return 1 + Math.Max(lHeight, rHeight); } // Function to get diameter of a binary tree static int diameter(Node root) { int res = 0; diameterRecur(root, ref res); return res; } static void Main(string[] args) { // Constructed binary tree is // 5 // / \ // 8 6 // / \ / // 3 7 9 Node root = new Node(5); root.left = new Node(8); root.right = new Node(6); root.left.left = new Node(3); root.left.right = new Node(7); root.right.left = new Node(9); Console.WriteLine(diameter(root)); } } JavaScript // JavaScript program to find the diameter // of a binary tree. class Node { constructor(x) { this.data = x; this.left = null; this.right = null; } } // Recursive function which finds the // height of root and also calculates // the diameter of the tree. function diameterRecur(root, res) { // Base case: tree is empty if (root === null) return 0; // find the height of left and right subtree // (it will also find of diameter for left // and right subtree). let lHeight = diameterRecur(root.left, res); let rHeight = diameterRecur(root.right, res); // Check if diameter of root is greater // than res. res.value = Math.max(res.value, lHeight + rHeight); // return the height of current subtree. return 1 + Math.max(lHeight, rHeight); } // Function to get diameter of a binary tree function diameter(root) { let res = { value: 0 }; diameterRecur(root, res); return res.value; } // Driver Code // Constructed binary tree is // 5 // / \ // 8 6 // / \ / // 3 7 9 let root = new Node(5); root.left = new Node(8); root.right = new Node(6); root.left.left = new Node(3); root.left.right = new Node(7); root.right.left = new Node(9); console.log(diameter(root)); Output4 Time Complexity: O(n), where n is the number of nodes in tree.Auxiliary Space: O(h) due to recursive calls.Related article:Diameter of an N-ary tree Diameter of a Binary Tree. Visit Course Diameter of a Binary Tree. Find the Diameter of a Binary Tree Comment More infoAdvertise with us Next Article Applications, Advantages and Disadvantages of Binary Tree K kartik Follow Improve Article Tags : Tree DSA Microsoft Amazon Oracle Directi VMWare Cadence India Snapdeal MakeMyTrip Salesforce OYO Philips +9 More Practice Tags : AmazonCadence IndiaDirectiMakeMyTripMicrosoftOraclePhilipsSalesforceSnapdealVMWareTree +7 More Similar Reads Binary Tree Data Structure A Binary Tree Data Structure is a hierarchical data structure in which each node has at most two children, referred to as the left child and the right child. It is commonly used in computer science for efficient storage and retrieval of data, with various operations such as insertion, deletion, and 3 min read Introduction to Binary Tree Binary Tree is a non-linear and hierarchical data structure where each node has at most two children referred to as the left child and the right child. 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