Height and Depth of a node in a Binary Tree
Last Updated :
23 Jul, 2025
Given a Binary Tree consisting of n nodes and a integer k, the task is to find the depth and height of the node with value k in the Binary Tree.
Note:
- The depth of a node is the number of edges present in path from the root node of a tree to that node.
- The height of a node is the maximum number of edges from that node to a leaf node in its subtree.
Examples:
Input: k = 25,
Output: Depth of node 25 = 2
Height of node 25 = 1
Explanation: The number of edges in the path from root node to the node 25 is 2. Therefore, depth of the node 25 is 2.
The number of edges in the longest path connecting the node 25 to any leaf node is 1. Therefore, height of the node 25 is 1.
Input: k = 10,
Output: Depth of node 10 = 1
Height of node 10 = 2
Explanation: The number of edges in the path from root node to the node 10 is 1.
The number of edges in the longest path connecting the node 10 to any leaf node is 2.
[Approach 1] Using Recursion - O(n) time and O(h) space
Depth of a node K (of a Binary Tree) = Number of edges in the path connecting the root to the node K = Number of ancestors of K (excluding K itself).
Follow the steps below to find the depth of the given node:
- If the tree is empty, print -1.
- Otherwise, perform the following steps:
- Initialize a variable, say dist as -1.
- Check if the node K is equal to the given node.
- Otherwise, check if it is present in either of the subtrees, by recursively checking for the left and right subtrees respectively.
- If found to be true, print the value of dist + 1.
- Otherwise, print dist.
Height of a node K (of a Binary Tree) = Maximum number of edges from that node to a leaf node in its subtree.
Follow the steps below to find the height of the given node:
- If the tree is empty, print -1.
- Otherwise, perform the following steps:
- Calculate the height of the left subtree recursively.
- Calculate the height of the right subtree recursively.
- Update height of the current node by adding 1 to the maximum of the two heights obtained in the previous step. Store the height in a variable, say ans.
- If the current node is equal to the given node k, print the value of ans as the required answer.
C++
#include <bits/stdc++.h>
using namespace std;
// Structure of a Binary Tree Node
struct Node {
int data;
Node *left, *right;
Node(int item) {
data = item;
left = right = nullptr;
}
};
int findDepth(Node* root, int x)
{
// Base case
if (root == nullptr)
return -1;
int dist = -1;
// Check if x is current node=
if ((root->data == x)
// Otherwise, check if x is
// present in the left subtree
|| (dist = findDepth(root->left, x)) >= 0
// Otherwise, check if x is
// present in the right subtree
|| (dist = findDepth(root->right, x)) >= 0)
// Return depth of the node
return dist + 1;
return dist;
}
int findHeightUtil(Node* root, int x,
int& height)
{
if (root == nullptr) {
return -1;
}
// Store the maximum height of
// the left and right subtree
int leftHeight = findHeightUtil(
root->left, x, height);
int rightHeight
= findHeightUtil(
root->right, x, height);
// Update height of the current node
int ans = max(leftHeight, rightHeight) + 1;
// If current node is the required node
if (root->data == x)
height = ans;
return ans;
}
int findHeight(Node* root, int x)
{
// Store the height of
// the given node
int h = -1;
// Stores height of the Tree
int maxHeight = findHeightUtil(root, x, h);
// Return the height
return h;
}
int main()
{
Node* root = new Node(5);
root->left = new Node(10);
root->right = new Node(15);
root->left->left = new Node(20);
root->left->right = new Node(25);
root->left->right->right = new Node(45);
root->right->left = new Node(30);
root->right->right = new Node(35);
int k = 25;
cout << "Depth: "
<< findDepth(root, k) << "\n";
cout << "Height: " << findHeight(root, k);
return 0;
}
// Structure of a Binary Tree Node
class Node {
int data;
Node left, right;
Node(int item) {
data = item;
left = right = null;
}
}
public class GfG{
int findDepth(Node root, int x) {
// Base case
if (root == null)
return -1;
// Initialize distance as -1
int dist = -1;
// Check if x is current node
if ((root.data == x)
|| (dist = findDepth(root.left, x)) >= 0
|| (dist = findDepth(root.right, x)) >= 0)
// Return depth of the node
return dist + 1;
return dist;
}
int findHeightUtil(Node root, int x, int[] height) {
// Base Case
if (root == null) {
return -1;
}
// Store the maximum height of the left and right subtree
int leftHeight = findHeightUtil(root.left, x, height);
int rightHeight = findHeightUtil(root.right, x, height);
// Update height of the current node
int ans = Math.max(leftHeight, rightHeight) + 1;
// If current node is the required node
if (root.data == x)
height[0] = ans;
return ans;
}
int findHeight(Node root, int x) {
// Store the height of the given node
int[] h = {-1};
// Stores height of the Tree
findHeightUtil(root, x, h);
// Return the height
return h[0];
}
public static void main(String[] args) {
Node root = new Node(5);
root.left = new Node(10);
root.right = new Node(15);
root.left.left = new Node(20);
root.left.right = new Node(25);
root.left.right.right = new Node(45);
root.right.left = new Node(30);
root.right.right = new Node(35);
int k = 25;
GfG tree = new GfG();
System.out.println("Depth: " + tree.findDepth(root, k));
System.out.println("Height: " + tree.findHeight(root, k));
}
}
class Node:
def __init__(self, data):
self.data = data
self.left = None
self.right = None
# Function to find depth of a given node
def find_depth(root, x):
if root is None:
return -1
dist = -1
# Check if x is the current node or
# if it exists in the left or right subtree
if (root.data == x or
(dist := find_depth(root.left, x)) >= 0 or
(dist := find_depth(root.right, x)) >= 0):
return dist + 1
return dist
# Utility function to find height of a given node
def find_height_util(root, x, height):
if root is None:
return -1
# Store the maximum height of left and right subtree
left_height = find_height_util(root.left, x, height)
right_height = find_height_util(root.right, x, height)
# Update height of the current node
ans = max(left_height, right_height) + 1
# If current node is the required node, update height
if root.data == x:
height[0] = ans
return ans
# Function to find height of a given node
def find_height(root, x):
height = [-1] # Using a list to
# store height by reference
find_height_util(root, x, height)
return height[0]
if __name__ == "__main__":
# Construct the tree
root = Node(5)
root.left = Node(10)
root.right = Node(15)
root.left.left = Node(20)
root.left.right = Node(25)
root.left.right.right = Node(45)
root.right.left = Node(30)
root.right.right = Node(35)
k = 25
# Print depth and height of the given node
print("Depth:", find_depth(root, k))
print("Height:", find_height(root, k))
using System;
using System.Collections.Generic;
// Structure of a Binary Tree Node
class Node {
public int data;
public Node left, right;
public Node(int item) {
data = item;
left = right = null;
}
}
class GfG{
int FindDepth(Node root, int x) {
// Base case
if (root == null)
return -1;
// Initialize distance as -1
int dist = -1;
// Check if x is current node
if ((root.data == x)
|| (dist = FindDepth(root.left, x)) >= 0
|| (dist = FindDepth(root.right, x)) >= 0)
// Return depth of the node
return dist + 1;
return dist;
}
int FindHeightUtil(Node root, int x, ref int height) {
// Base Case
if (root == null) {
return -1;
}
// Store the maximum height of the left and right subtree
int leftHeight = FindHeightUtil(root.left, x, ref height);
int rightHeight = FindHeightUtil(root.right, x, ref height);
// Update height of the current node
int ans = Math.Max(leftHeight, rightHeight) + 1;
// If current node is the required node
if (root.data == x)
height = ans;
return ans;
}
int FindHeight(Node root, int x) {
// Store the height of the given node
int h = -1;
// Stores height of the Tree
FindHeightUtil(root, x, ref h);
// Return the height
return h;
}
public static void Main(string[] args) {
Node root = new Node(5);
root.left = new Node(10);
root.right = new Node(15);
root.left.left = new Node(20);
root.left.right = new Node(25);
root.left.right.right = new Node(45);
root.right.left = new Node(30);
root.right.right = new Node(35);
int k = 25;
GfG tree = new GfG();
Console.WriteLine("Depth: " + tree.FindDepth(root, k));
Console.WriteLine("Height: " + tree.FindHeight(root, k));
}
}
class Node {
constructor(data) {
this.data = data;
this.left = null;
this.right = null;
}
}
// Function to find depth of a given node
function findDepth(root, x) {
if (!root) return -1;
let dist = -1;
// Check if x is the current node or
// if it exists in the left or right subtree
if (root.data === x ||
(dist = findDepth(root.left, x)) >= 0 ||
(dist = findDepth(root.right, x)) >= 0) {
return dist + 1;
}
return dist;
}
// Utility function to find height of a given node
function findHeightUtil(root, x, height) {
if (!root) return -1;
// Store the maximum height of left and right subtree
let leftHeight = findHeightUtil(root.left, x, height);
let rightHeight = findHeightUtil(root.right, x, height);
// Update height of the current node
let ans = Math.max(leftHeight, rightHeight) + 1;
// If current node is the required node, update height
if (root.data === x) height.value = ans;
return ans;
}
// Function to find height of a given node
function findHeight(root, x) {
let height = { value: -1 }; // Using an object
// to store height by reference
findHeightUtil(root, x, height);
return height.value;
}
// Construct the tree
let root = new Node(5);
root.left = new Node(10);
root.right = new Node(15);
root.left.left = new Node(20);
root.left.right = new Node(25);
root.left.right.right = new Node(45);
root.right.left = new Node(30);
root.right.right = new Node(35);
let k = 25;
// Print depth and height of the given node
console.log("Depth:", findDepth(root, k));
console.log("Height:", findHeight(root, k));
Time Complexity: O(n)
Auxiliary Space: O(1)
[Approach 2] Using Level Order Traversal - O(n) time and O(n) space
We can calculate the depth of each node using level order traversal by storing the current level as its depth.
To calculate the height of a node k, we find the maximum depth of any leaf node in its subtree.
Then:
Height of node k = (Max depth of leaf in subtree) − (Depth of node k) − 1
Algorithm:
- Initialize height and depth variable with -1;
- Initialize a queue and a level variable with 0 and push the root in the queue.
- When the value of
frontNode is equal to the target k, we stop processing the nodes at that level and clear the queue to only focus on the children of the node k. This ensures that we find the furthest leaf node in the subtree of k. - So the value of depth will be equal to current level.
- After completion we can calculate the value of height using height = level - depth - 1;
- Print the value of height and depth variable.
C++
#include <bits/stdc++.h>
using namespace std;
struct Node
{
int data;
Node *left;
Node *right;
Node(int item)
{
data = item;
left = right = nullptr;
}
};
void findDepthAndHeight(Node *root, int k)
{
if (root == nullptr)
return;
int depth = -1;
int height = -1;
queue<Node *> q;
q.push(root);
int level = 0;
while (!q.empty())
{
int n = q.size();
for (int i = 0; i < n; i++)
{
Node *frontNode = q.front();
q.pop();
if (frontNode->data == k)
{
depth = level;
// Clear the queue after finding the node
while (!q.empty())
{
q.pop();
}
}
// Push left and right children of
// the current node to the queue
if (frontNode->left)
q.push(frontNode->left);
if (frontNode->right)
q.push(frontNode->right);
if (frontNode->data == k)
{
break;
}
}
// Increment the level after processing
// all nodes at the current level
level++;
}
height = level - depth - 1;
cout << "Depth : " << depth << endl;
cout << "Height : " << height << endl;
}
int main()
{
Node *root = new Node(5);
root->left = new Node(10);
root->right = new Node(15);
root->left->left = new Node(20);
root->left->right = new Node(25);
root->left->right->right = new Node(45);
root->right->left = new Node(30);
root->right->right = new Node(35);
int k = 10;
findDepthAndHeight(root, k);
return 0;
}
import java.util.LinkedList;
import java.util.Queue;
class Node {
int data;
Node left, right;
Node(int item) {
data = item;
left = right = null;
}
}
public class GfG{
static void findDepthAndHeight(Node root, int k) {
if (root == null) return;
int depth = -1;
int height = -1;
Queue<Node> q = new LinkedList<>();
q.add(root);
int level = 0;
while (!q.isEmpty()) {
int n = q.size();
for (int i = 0; i < n; i++) {
Node frontNode = q.poll();
if (frontNode.data == k) {
depth = level;
// Clear the queue after finding the node
q.clear();
}
// Push left and right children of the current node to the queue
if (frontNode.left != null) q.add(frontNode.left);
if (frontNode.right != null) q.add(frontNode.right);
if (frontNode.data == k) {
break;
}
}
// Increment the level after processing all nodes at the current level
level++;
}
height = level - depth - 1;
System.out.println("Depth : " + depth);
System.out.println("Height : " + height);
}
public static void main(String[] args) {
Node root = new Node(5);
root.left = new Node(10);
root.right = new Node(15);
root.left.left = new Node(20);
root.left.right = new Node(25);
root.left.right.right = new Node(45);
root.right.left = new Node(30);
root.right.right = new Node(35);
int k = 10;
findDepthAndHeight(root, k);
}
}
class Node:
def __init__(self, item):
self.data = item
self.left = None
self.right = None
def find_depth_and_height(root, k):
if root is None:
return
depth = -1
height = -1
q = [root]
level = 0
while q:
n = len(q)
for i in range(n):
front_node = q.pop(0)
if front_node.data == k:
depth = level
# Clear the queue after finding the node
q.clear()
# Push left and right children of the current node to the queue
if front_node.left:
q.append(front_node.left)
if front_node.right:
q.append(front_node.right)
if front_node.data == k:
break
# Increment the level after processing all nodes at the current level
level += 1
height = level - depth - 1
print(f'Depth : {depth}')
print(f'Height : {height}')
def main():
root = Node(5)
root.left = Node(10)
root.right = Node(15)
root.left.left = Node(20)
root.left.right = Node(25)
root.left.right.right = Node(45)
root.right.left = Node(30)
root.right.right = Node(35)
k = 10
find_depth_and_height(root, k)
if __name__ == '__main__':
main()
using System;
using System.Collections.Generic;
class Node {
public int data;
public Node left, right;
public Node(int item) {
data = item;
left = right = null;
}
}
class GfG{
static void FindDepthAndHeight(Node root, int k) {
if (root == null) return;
int depth = -1;
int height = -1;
Queue<Node> q = new Queue<Node>();
q.Enqueue(root);
int level = 0;
while (q.Count > 0) {
int n = q.Count;
for (int i = 0; i < n; i++) {
Node frontNode = q.Dequeue();
if (frontNode.data == k) {
depth = level;
// Clear the queue after finding the node
q.Clear();
}
// Push left and right children of the current node to the queue
if (frontNode.left != null) q.Enqueue(frontNode.left);
if (frontNode.right != null) q.Enqueue(frontNode.right);
if (frontNode.data == k) {
break;
}
}
// Increment the level after processing all nodes at the current level
level++;
}
height = level - depth - 1;
Console.WriteLine("Depth : " + depth);
Console.WriteLine("Height : " + height);
}
static void Main() {
Node root = new Node(5);
root.left = new Node(10);
root.right = new Node(15);
root.left.left = new Node(20);
root.left.right = new Node(25);
root.left.right.right = new Node(45);
root.right.left = new Node(30);
root.right.right = new Node(35);
int k = 10;
FindDepthAndHeight(root, k);
}
}
// Node structure
class Node {
constructor(item) {
this.data = item;
this.left = null;
this.right = null;
}
}
function findDepthAndHeight(root, k) {
if (root === null) return;
let depth = -1;
let height = -1;
let queue = [];
queue.push(root);
let level = 0;
while (queue.length > 0) {
let n = queue.length;
for (let i = 0; i < n; i++) {
let frontNode = queue.shift();
if (frontNode.data === k) {
depth = level;
// Clear the queue after finding the node
queue = [];
}
// Push left and right children of the current node to the queue
if (frontNode.left) queue.push(frontNode.left);
if (frontNode.right) queue.push(frontNode.right);
if (frontNode.data === k) {
break;
}
}
// Increment the level after processing all nodes at the current level
level++;
}
height = level - depth - 1;
console.log("Depth : " + depth);
console.log("Height : " + height);
}
let root = new Node(5);
root.left = new Node(10);
root.right = new Node(15);
root.left.left = new Node(20);
root.left.right = new Node(25);
root.left.right.right = new Node(45);
root.right.left = new Node(30);
root.right.right = new Node(35);
let k = 10;
findDepthAndHeight(root, k);
OutputDepth : 2
Height : 1
Time Complexity: O(n)
Auxiliary Space: O(n)due to queue data structure.
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem