Select a Random Node from a Singly Linked List
Last Updated :
23 Jul, 2025
Given a singly linked list, select a random node from the linked list (the probability of picking a node should be 1/N if there are N nodes in the list). You are given a random number generator.
Below is a Simple Solution
- Count the number of nodes by traversing the list.
- Traverse the list again and select every node with a probability of 1/N. The selection can be done by generating a random number from 0 to N-i for the node, and selecting the i'th node only if the generated number is equal to 0 (or any other fixed number from 0 to N-i).
We get uniform probabilities with the above schemes.
i = 1, probability of selecting first node = 1/N
i = 2, probability of selecting second node =
[probability that first node is not selected] *
[probability that second node is selected]
= ((N-1)/N)* 1/(N-1)
= 1/N
Similarly, the probability of other selecting other nodes is 1/N
The above solution requires two traversals of the linked list.
How to select a random node with only one traversal allowed?
The idea is to use Reservoir Sampling. Following are the steps. This is a simpler version of Reservoir Sampling as we need to select only one key instead of the k keys.
(1) Initialize result as first node
result = head->key
(2) Initialize n = 2
(3) Now one by one consider all nodes from 2nd node onward.
(3.a) Generate a random number from 0 to n-1.
Let the generated random number is j.
(3.b) If j is equal to 0 (we could choose other fixed number
between 0 to n-1), then replace result with current node.
(3.c) n = n+1
(3.d) current = current->next
Below is the implementation of the above algorithm.
C++
/* C++ program to randomly select a node from a singly
linked list */
#include<stdio.h>
#include<stdlib.h>
#include <time.h>
#include<iostream>
using namespace std;
/* Link list node */
class Node
{
public:
int key;
Node* next;
void printRandom(Node*);
void push(Node**, int);
};
// A reservoir sampling based function to print a
// random node from a linked list
void Node::printRandom(Node *head)
{
// IF list is empty
if (head == NULL)
return;
// Use a different seed value so that we don't get
// same result each time we run this program
srand(time(NULL));
// Initialize result as first node
int result = head->key;
// Iterate from the (k+1)th element to nth element
Node *current = head;
int n;
for (n = 2; current != NULL; n++)
{
// change result with probability 1/n
if (rand() % n == 0)
result = current->key;
// Move to next node
current = current->next;
}
cout<<"Randomly selected key is \n"<< result;
}
/* BELOW FUNCTIONS ARE JUST UTILITY TO TEST */
/* A utility function to create a new node */
Node* newNode(int new_key)
{
// allocate node
Node* new_node = (Node*) malloc(sizeof( Node));
/// put in the key
new_node->key = new_key;
new_node->next = NULL;
return new_node;
}
/* A utility function to insert a node at the beginning
of linked list */
void Node:: push(Node** head_ref, int new_key)
{
/* allocate node */
Node* new_node = new Node;
/* put in the key */
new_node->key = new_key;
/* link the old list of the new node */
new_node->next = (*head_ref);
/* move the head to point to the new node */
(*head_ref) = new_node;
}
// Driver program to test above functions
int main()
{
Node n1;
Node *head = NULL;
n1.push(&head, 5);
n1.push(&head, 20);
n1.push(&head, 4);
n1.push(&head, 3);
n1.push(&head, 30);
n1.printRandom(head);
return 0;
}
// This code is contributed by SoumikMondal
/* C program to randomly select a node from a singly
linked list */
#include<stdio.h>
#include<stdlib.h>
#include <time.h>
/* Link list node */
struct Node
{
int key;
struct Node* next;
};
// A reservoir sampling based function to print a
// random node from a linked list
void printRandom(struct Node *head)
{
// IF list is empty
if (head == NULL)
return;
// Use a different seed value so that we don't get
// same result each time we run this program
srand(time(NULL));
// Initialize result as first node
int result = head->key;
// Iterate from the (k+1)th element to nth element
struct Node *current = head;
int n;
for (n=2; current!=NULL; n++)
{
// change result with probability 1/n
if (rand() % n == 0)
result = current->key;
// Move to next node
current = current->next;
}
printf("Randomly selected key is %d\n", result);
}
/* BELOW FUNCTIONS ARE JUST UTILITY TO TEST */
/* A utility function to create a new node */
struct Node *newNode(int new_key)
{
/* allocate node */
struct Node* new_node =
(struct Node*) malloc(sizeof(struct Node));
/* put in the key */
new_node->key = new_key;
new_node->next = NULL;
return new_node;
}
/* A utility function to insert a node at the beginning
of linked list */
void push(struct Node** head_ref, int new_key)
{
/* allocate node */
struct Node* new_node = new Node;
/* put in the key */
new_node->key = new_key;
/* link the old list of the new node */
new_node->next = (*head_ref);
/* move the head to point to the new node */
(*head_ref) = new_node;
}
// Driver program to test above functions
int main()
{
struct Node *head = NULL;
push(&head, 5);
push(&head, 20);
push(&head, 4);
push(&head, 3);
push(&head, 30);
printRandom(head);
return 0;
}
// Java program to select a random node from singly linked list
import java.util.*;
// Linked List Class
class LinkedList {
static Node head; // head of list
/* Node Class */
static class Node {
int data;
Node next;
// Constructor to create a new node
Node(int d) {
data = d;
next = null;
}
}
// A reservoir sampling based function to print a
// random node from a linked list
void printrandom(Node node) {
// If list is empty
if (node == null) {
return;
}
// Use a different seed value so that we don't get
// same result each time we run this program
Math.abs(UUID.randomUUID().getMostSignificantBits());
// Initialize result as first node
int result = node.data;
// Iterate from the (k+1)th element to nth element
Node current = node;
int n;
for (n = 2; current != null; n++) {
// change result with probability 1/n
if (Math.random() % n == 0) {
result = current.data;
}
// Move to next node
current = current.next;
}
System.out.println("Randomly selected key is " + result);
}
// Driver program to test above functions
public static void main(String[] args) {
LinkedList list = new LinkedList();
list.head = new Node(5);
list.head.next = new Node(20);
list.head.next.next = new Node(4);
list.head.next.next.next = new Node(3);
list.head.next.next.next.next = new Node(30);
list.printrandom(head);
}
}
// This code has been contributed by Mayank Jaiswal
# Python program to randomly select a node from singly
# linked list
import random
# Node class
class Node:
# Constructor to initialize the node object
def __init__(self, data):
self.data= data
self.next = None
class LinkedList:
# Function to initialize head
def __init__(self):
self.head = None
# A reservoir sampling based function to print a
# random node from a linked list
def printRandom(self):
# If list is empty
if self.head is None:
return
if self.head and not self.head.next:
print("Randomly selected key is %d" %(self.head.data))
# Use a different seed value so that we don't get
# same result each time we run this program
random.seed()
# Initialize result as first node
result = self.head.data
# Iterate from the (k+1)th element nth element
# because we iterate from (k+1)th element, or
# the first node will be picked more easily
current = self.head.next
n = 2
while(current is not None):
# change result with probability 1/n
if (random.randrange(n) == 0 ):
result = current.data
# Move to next node
current = current.next
n += 1
print("Randomly selected key is %d" %(result))
# Function to insert a new node at the beginning
def push(self, new_data):
new_node = Node(new_data)
new_node.next = self.head
self.head = new_node
# Utility function to print the LinkedList
def printList(self):
temp = self.head
while(temp):
print(temp.data,end=" ")
temp = temp.next
# Driver program to test above function
llist = LinkedList()
llist.push(5)
llist.push(20)
llist.push(4)
llist.push(3)
llist.push(30)
llist.printRandom()
# This code is contributed by Nikhil Kumar Singh(nickzuck_007)
// C# program to select a random node
// from singly linked list
using System;
// Linked List Class
public class LinkedList
{
Node head; // head of list
/* Node Class */
public class Node
{
public int data;
public Node next;
// Constructor to create a new node
public Node(int d)
{
data = d;
next = null;
}
}
// A reservoir sampling based function to print a
// random node from a linked list
void printrandom(Node node)
{
// If list is empty
if (node == null)
{
return;
}
// Use a different seed value so that we don't get
// same result each time we run this program
//Math.abs(UUID.randomUUID().getMostSignificantBits());
// Initialize result as first node
int result = node.data;
// Iterate from the (k+1)th element to nth element
Node current = node;
int n;
for (n = 2; current != null; n++)
{
// change result with probability 1/n
if (new Random().Next() % n == 0)
{
result = current.data;
}
// Move to next node
current = current.next;
}
Console.WriteLine("Randomly selected key is " +
result);
}
// Driver Code
public static void Main(String[] args)
{
LinkedList list = new LinkedList();
list.head = new Node(5);
list.head.next = new Node(20);
list.head.next.next = new Node(4);
list.head.next.next.next = new Node(3);
list.head.next.next.next.next = new Node(30);
list.printrandom(list.head);
}
}
// This code is contributed by 29AjayKumar
<script>
// Javascript program to select a random node
// from singly linked list
/* Node Class */
class Node
{
constructor(d)
{
this.data=d;
this.next = null;
}
}
// A reservoir sampling based function to print a
// random node from a linked list
function printrandom(node)
{
// If list is empty
if (node == null) {
return;
}
// Use a different seed value so that we don't get
// same result each time we run this program
//Math.abs(UUID.randomUUID().getMostSignificantBits());
// Initialize result as first node
let result = node.data;
// Iterate from the (k+1)th element to nth element
let current = node;
let n;
for (n = 2; current != null; n++) {
// change result with probability 1/n
if (Math.floor(Math.random()*n) == 0) {
result = current.data;
}
// Move to next node
current = current.next;
}
document.write("Randomly selected key is <br>" +
result+"<br>");
}
// Driver program to test above functions
head = new Node(5);
head.next = new Node(20);
head.next.next = new Node(4);
head.next.next.next = new Node(3);
head.next.next.next.next = new Node(30);
printrandom(head);
// This code is contributed by rag2127
</script>
OutputRandomly selected key is
4
Time Complexity: O(n), as we are using a loop to traverse n times. Where n is the number of nodes in the linked list.
Auxiliary Space: O(1), as we are not using any extra space.
Note that the above program is based on the outcome of a random function and may produce different outputs.
How does this work?
Let there be total N nodes in the list. It is easier to understand from the last node.
The probability that the last node is result simply 1/N [For the last or N'th node, we generate a random number between 0 to N-1 and make the last node as the result if the generated number is 0 (or any other fixed number]
The probability that the second last node is the result should also be 1/N.
The probability that the second last node is result
= [Probability that the second last node replaces result] X
[Probability that the last node doesn't replace the result]
= [1 / (N-1)] * [(N-1)/N]
= 1/N
Similarly, we can show the probability for 3rd last node and other nodes.
Another approach Using rand() Function:
Here in this Approach, we convert linked list to vector by storing every node value and than we apply rand() function on them and return the random node value.
Approach/Intuition:
here given linked list :
- 5 -> 20 -> 4 -> 3 -> 30.
- we traverse over linked list and convert it into vector.
- vector<int>v{5,20,4,3,30};
- than we use rand() function.
- int n=v.size() //size of the vector.
- int RandomIndex=rand() % n;
- and at the end we will return random node value from singly linked list.
Below is the code to implement the above approach:
C++
/* C++ program to randomly select a node from a singly
linked list */
#include <bits/stdc++.h>
#include <iostream>
using namespace std;
/* Link list node */
class Node {
public:
int key;
Node* next;
void printRandom(Node*);
void push(Node**, int);
};
Node* newNode(int new_key)
{
// allocate node
Node* new_node = (Node*)malloc(sizeof(Node));
/// put in the key
new_node->key = new_key;
new_node->next = NULL;
return new_node;
}
/* A utility function to insert a node at the beginning
of linked list */
void Node::push(Node** head_ref, int new_key)
{
/* allocate node */
Node* new_node = new Node;
/* put in the key */
new_node->key = new_key;
/* link the old list of the new node */
new_node->next = (*head_ref);
/* move the head to point to the new node */
(*head_ref) = new_node;
}
void printRandom(Node* head)
{
Node* temp = head;
vector<int> v;
while (temp != NULL) {
v.push_back(temp->key);
temp = temp->next;
}
int n = v.size();
int randIndex = rand() % n;
cout << v[randIndex] << endl;
}
// Driver's code
int main()
{
Node n1;
Node* head = NULL;
n1.push(&head, 5);
n1.push(&head, 20);
n1.push(&head, 4);
n1.push(&head, 3);
n1.push(&head, 30);
// function call
printRandom(head);
// code & approach contributed by Sanket Gode.
return 0;
}
/*package whatever //do not write package name here */
import java.io.*;
import java.util.*;
// Node of Linkedlist
class Node {
int key;
Node next;
Node(int key)
{
this.key = key;
this.next = null;
}
}
class GFG {
// Function to Print Random Values
public static void printRandom(Node head)
{
Node temp = head;
ArrayList<Integer> list = new ArrayList<Integer>();
while (temp != null) {
list.add(temp.key);
temp = temp.next;
}
int n = list.size();
Random rand = new Random();
int randIndex = rand.nextInt(n);
System.out.println(list.get(randIndex));
}
// Drivers Code
public static void main(String[] args)
{
// Making List
Node head = new Node(30);
head.next = new Node(3);
head.next.next = new Node(4);
head.next.next.next = new Node(20);
head.next.next.next.next = new Node(5);
// Calling Function
printRandom(head);
// This Code is Contributed By Vikas Bishnoi
}
}
import random
# Link list node
class Node:
def __init__(self):
self.key = 0
self.next = None
def push(self, head_ref, new_key):
# allocate node
new_node = Node()
# put in the key
new_node.key = new_key
# link the old list of the new node
new_node.next = head_ref
# move the head to point to the new node
head_ref = new_node
return head_ref
@staticmethod
def printRandom(head):
temp = head
v = []
while temp != None:
v.append(temp.key)
temp = temp.next
n = len(v)
randIndex = random.randint(0, n-1)
print(v[randIndex])
# Driver's code
if __name__ == '__main__':
n1 = Node()
head = None
head = n1.push(head, 5)
head = n1.push(head, 20)
head = n1.push(head, 4)
head = n1.push(head, 3)
head = n1.push(head, 30)
# function call
Node.printRandom(head)
using System;
using System.Collections.Generic;
// Node of Linkedlist
public class Node {
public int key;
public Node next;
public Node(int key)
{
this.key = key;
this.next = null;
}
}
public class GFG {
// Function to Print Random Values
public static void printRandom(Node head)
{
Node temp = head;
List<int> list = new List<int>();
while (temp != null) {
list.Add(temp.key);
temp = temp.next;
}
int n = list.Count;
Random rand = new Random();
int randIndex = rand.Next(n);
Console.WriteLine(list[randIndex]);
}
// Drivers Code
public static void Main()
{
// Making List
Node head = new Node(30);
head.next = new Node(3);
head.next.next = new Node(4);
head.next.next.next = new Node(20);
head.next.next.next.next = new Node(5);
// Calling Function
printRandom(head);
}
}
// import random
const val = 7;
// Link list node
class Node{
constructor(){
this.key = 0;
this.next = null;
}
push(head_ref, new_key){
// allocate node
let new_node = new Node();
// put in the key
new_node.key = new_key;
// link the old list of the new node
new_node.next = head_ref;
// move the head to point to the new node
head_ref = new_node;
return head_ref;
}
printRandom(head){
let temp = head;
let v = [];
while(temp != null){
v.push(temp.key);
temp = temp.key;
}
let n = v.length;
let randIndex = Math.floor((Math.random() * (n-1)));
console.log(Math.floor(v[randIndex]/val));
}
}
// Driver's code
n1 = new Node()
head = null
head = n1.push(head, 5)
head = n1.push(head, 20)
head = n1.push(head, 4)
head = n1.push(head, 3)
head = n1.push(head, 30)
// function call
n1.printRandom(head)
// The code is contributed by Nidhi goel.
Complexity Analysis:
Time Complexity: O(n).
Space Complexity:O(n).
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