Check if two nodes are cousins in a Binary Tree
Last Updated :
23 Jul, 2025
Given a binary tree (having distinct node values) root and two node values. The task is to check whether the two nodes with values a and b are cousins.
Note: Two nodes of a binary tree are cousins if they have the same depth with different parents.
Example:
Input: a = 5, b = 4
Output: True
Explanation: Node with the values 5 and 4 are on the same level with different parents.
Input: a = 4, b = 5
Output: False
Explanation: Node with the values 5 and 4 are on the same level with same parent.
Using Depth First Search:
The idea is to check the level of both the given node values using depth first search. If their levels are same, then check if they are children of same or different nodes. If they have same parent, then return false. else, return true.
Below is the implementation of the above approach.
C++
// C++ program to
// check if two Nodes are Cousins
#include <bits/stdc++.h>
using namespace std;
class Node{
public:
int data;
Node* left, *right;
Node(int x) {
data = x;
left = right = nullptr;
}
};
// Recursive function to check if two Nodes are siblings
bool isSibling(Node* root, int a, int b) {
// Base case
if (root == NULL)
return false;
if (root->left != nullptr && root->right != nullptr &&
root->left->data == a && root->right->data == b)
return true;
if (root->left != nullptr && root->right != nullptr &&
root->left->data == b && root->right->data == a)
return true;
return isSibling(root->left, a, b) ||
isSibling(root->right, a,b);
}
// Recursive function to find level of Node with data = value in a
// binary tree
int level(Node* root, int value, int lev) {
// base cases
if (root == NULL)
return 0;
if (root->data == value)
return lev;
// Return level if Node is present in left subtree
int l = level(root->left, value, lev + 1);
if (l != 0)
return l;
// Else search in right subtree
return level(root->right, value, lev + 1);
}
// Returns true if a and b are cousins, otherwise false
bool isCousins(Node* root, int a, int b) {
// 1. The two Nodes should be on the same level in the
// binary tree.
// 2. The two Nodes should not be siblings (means that
// they should
// not have the same parent Node).
if (a == b)
return false;
int aLevel = level(root, a, 1);
int bLevel = level(root, b, 1);
// if a or b does not exists in the tree
if (aLevel == 0 || bLevel == 0)
return false;
if (aLevel == bLevel && !isSibling(root, a, b))
return true;
else
return false;
}
int main() {
// create hard coded tree
// 1
// / \
// 2 3
// / \
// 5 4
Node* root = new Node(1);
root->left = new Node(2);
root->right = new Node(3);
root->left->left = new Node(4);
root->right->right = new Node(5);
int a = 4, b = 5;
if (isCousins(root, a, b)) {
cout << "True" << endl;
}
else {
cout << "False" << endl;
}
return 0;
}
// C program to
// check if two Nodes are Cousins
#include <stdio.h>
#include <stdlib.h>
struct Node {
int data;
struct Node* left, *right;
};
// Recursive function to check if two Nodes are siblings
int isSibling(struct Node* root, int a, int b) {
// Base case
if (root == NULL)
return 0;
if (root->left != NULL && root->right != NULL &&
root->left->data == a && root->right->data == b)
return 1;
if (root->left != NULL && root->right != NULL &&
root->left->data == b && root->right->data == a)
return 1;
return isSibling(root->left, a, b) ||
isSibling(root->right, a, b);
}
// Recursive function to find level of
// Node with data = value in a binary tree
int level(struct Node* root, int value, int lev) {
// base cases
if (root == NULL)
return 0;
if (root->data == value)
return lev;
// Return level if Node is
// present in left subtree
int l = level(root->left, value, lev + 1);
if (l != 0)
return l;
// Else search in right subtree
return level(root->right, value, lev + 1);
}
// Returns true if a and b are cousins, otherwise false
int isCousins(struct Node* root, int a, int b) {
// 1. The two Nodes should be on
// the same level in the binary tree.
// 2. The two Nodes should not be siblings
// (means that they should not
// have the same parent Node).
if (a == b)
return 0;
int aLevel = level(root, a, 1);
int bLevel = level(root, b, 1);
// if a or b does not exist in the tree
if (aLevel == 0 || bLevel == 0)
return 0;
if (aLevel == bLevel && !isSibling(root, a, b))
return 1;
else
return 0;
}
struct Node* createNode(int x) {
struct Node* newNode =
(struct Node*)malloc(sizeof(struct Node));
newNode->data = x;
newNode->left = newNode->right = NULL;
return newNode;
}
int main() {
// create hard coded tree
// 1
// / \
// 2 3
// / \
// 5 4
struct Node* root = createNode(1);
root->left = createNode(2);
root->right = createNode(3);
root->left->left = createNode(4);
root->right->right = createNode(5);
int a = 4, b = 5;
if (isCousins(root, a, b)) {
printf("True\n");
}
else {
printf("False\n");
}
return 0;
}
// Java program to
// check if two Nodes are Cousins
class Node {
int data;
Node left, right;
Node(int x) {
data = x;
left = right = null;
}
}
class GfG {
// Recursive function to check if
// two Nodes are siblings
static boolean isSibling(Node root, int a, int b) {
// Base case
if (root == null)
return false;
if (root.left != null && root.right != null &&
root.left.data == a && root.right.data == b)
return true;
if (root.left != null && root.right != null &&
root.left.data == b && root.right.data == a)
return true;
return isSibling(root.left, a, b) ||
isSibling(root.right, a, b);
}
// Recursive function to find level of Node with
// data = value in a binary tree
static int level(Node root, int value, int lev) {
// base cases
if (root == null)
return 0;
if (root.data == value)
return lev;
// Return level if Node is present in left subtree
int l = level(root.left, value, lev + 1);
if (l != 0)
return l;
// Else search in right subtree
return level(root.right, value, lev + 1);
}
// Returns true if a and b are cousins, otherwise false
static boolean isCousins(Node root, int a, int b) {
// 1. The two Nodes should be on the same
// level in the binary tree.
// 2. The two Nodes should not be siblings
//(means that they should not have
// the same parent Node).
if (a == b)
return false;
int aLevel = level(root, a, 1);
int bLevel = level(root, b, 1);
// if a or b does not exist in the tree
if (aLevel == 0 || bLevel == 0)
return false;
return aLevel == bLevel && !isSibling(root, a, b);
}
public static void main(String[] args) {
// create hard coded tree
// 1
// / \
// 2 3
// / \
// 5 4
Node root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.right.right = new Node(5);
int a = 4, b = 5;
if (isCousins(root, a, b)) {
System.out.println("True");
}
else {
System.out.println("False");
}
}
}
# Python program to check if two
# nodes in a binary tree are cousins
class Node:
def __init__(self, x):
self.data = x
self.left = self.right = None
# Recursive function to check
# if two Nodes are siblings
def isSibling(root, a, b):
# Base case
if root is None:
return False
if root.left is not None and root.right is not None and \
root.left.data == a and root.right.data == b:
return True
if root.left is not None and root.right is not None and \
root.left.data == b and root.right.data == a:
return True
return isSibling(root.left, a, b) or isSibling(root.right, a, b)
# Recursive function to find level of Node with
# data = value in a binary tree
def level(root, value, lev):
# base cases
if root is None:
return 0
if root.data == value:
return lev
# Return level if Node is present in left subtree
l = level(root.left, value, lev + 1)
if l != 0:
return l
# Else search in right subtree
return level(root.right, value, lev + 1)
# Returns true if a and b are cousins, otherwise false
def isCousins(root, a, b):
# 1. The two Nodes should be on the same
# level in the binary tree.
# 2. The two Nodes should not be siblings
# (means that they should not
# have the same parent Node).
if a == b:
return False
aLevel = level(root, a, 1)
bLevel = level(root, b, 1)
# if a or b does not exist in the tree
if aLevel == 0 or bLevel == 0:
return False
return aLevel == bLevel and not isSibling(root, a, b)
if __name__ == "__main__":
# create hard coded tree
# 1
# / \
# 2 3
# / \
# 5 4
root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.right.right = Node(5)
a, b = 4, 5
if isCousins(root, a, b):
print("True")
else:
print("False")
// C# program to
// check if two Nodes are Cousins
using System;
class Node {
public int data;
public Node left, right;
public Node(int x) {
data = x;
left = right = null;
}
}
class GfG {
// Recursive function to check
// if two Nodes are siblings
static bool IsSibling(Node root, int a, int b) {
// Base case
if (root == null)
return false;
if (root.left != null && root.right != null &&
root.left.data == a && root.right.data == b)
return true;
if (root.left != null && root.right != null &&
root.left.data == b && root.right.data == a)
return true;
return IsSibling(root.left, a, b) ||
IsSibling(root.right, a, b);
}
// Recursive function to find level of
// Node with data = value in a binary tree
static int Level(Node root, int value, int lev) {
// base cases
if (root == null)
return 0;
if (root.data == value)
return lev;
// Return level if Node is present in left subtree
int l = Level(root.left, value, lev + 1);
if (l != 0)
return l;
// Else search in right subtree
return Level(root.right, value, lev + 1);
}
// Returns true if a and b are cousins, otherwise false
static bool IsCousins(Node root, int a, int b) {
// 1. The two Nodes should be on the
// same level in the binary tree.
// 2. The two Nodes should not be
// siblings (means that they should
// not have the same parent Node).
if (a == b)
return false;
int aLevel = Level(root, a, 1);
int bLevel = Level(root, b, 1);
// if a or b does not exist in the tree
if (aLevel == 0 || bLevel == 0)
return false;
return aLevel == bLevel && !IsSibling(root, a, b);
}
static void Main() {
// create hard coded tree
// 1
// / \
// 2 3
// / \
// 5 4
Node root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.right.right = new Node(5);
int a = 4, b = 5;
if (IsCousins(root, a, b)) {
Console.WriteLine("True");
}
else {
Console.WriteLine("False");
}
}
}
// JavaScript program to
// check if two Nodes are Cousins
class Node {
constructor(x) {
this.data = x;
this.left = this.right = null;
}
}
// Recursive function to check if two Nodes are siblings
function isSibling(root, a, b) {
// Base case
if (root == null)
return false;
if (root.left != null && root.right != null &&
root.left.data === a && root.right.data === b)
return true;
if (root.left != null && root.right != null &&
root.left.data === b && root.right.data === a)
return true;
return isSibling(root.left, a, b) ||
isSibling(root.right, a, b);
}
// Recursive function to find level of Node with
// data = value in a binary tree
function level(root, value, lev) {
// base cases
if (root == null)
return 0;
if (root.data === value)
return lev;
// Return level if Node is present in left subtree
let l = level(root.left, value, lev + 1);
if (l !== 0)
return l;
// Else search in right subtree
return level(root.right, value, lev + 1);
}
// Returns true if a and b are cousins, otherwise false
function isCousins(root, a, b) {
// 1. The two Nodes should be on the same level
// in the binary tree.
// 2. The two Nodes should not be siblings
// (means that they should not have the same parent Node).
if (a === b)
return false;
let aLevel = level(root, a, 1);
let bLevel = level(root, b, 1);
// if a or b does not exist in the tree
if (aLevel === 0 || bLevel === 0)
return false;
return aLevel === bLevel && !isSibling(root, a, b);
}
// create hard coded tree
// 1
// / \
// 2 3
// / \
// 5 4
let root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.left = new Node(4);
root.right.right = new Node(5);
let a = 4, b = 5;
if (isCousins(root, a, b)) {
console.log("True");
} else {
console.log("False");
}
Time Complexity O(n), where n are the number of nodes in binary tree.
Auxiliary complexity: O(h), where h is the height of the tree.
In a depth-first search (DFS) approach to check if two nodes are cousins, we traverse the tree three times, resulting in a time complexity O(3n).
Using Breadth-First Search :
The idea is to use a queue to traverse the tree in a level-order manner. This allows us to explore all nodes at a given depth before moving deeper. If the two nodes are found at the same level and are not siblings, then we return true, indicating they are cousins. Otherwise, we return false, as this means they either do not share the same depth or are sibling. Please Refer to Check if two nodes are cousins in a Binary Tree using BFS for implementation.
Time Complexity O(n), where n are the number of nodes in binary tree.
Auxiliary Space: O(n), if the tree is completely unbalanced, the maximum size of the queue can grow to O(n).
Check if two Nodes are Cousins | DSA Problem
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