Select a Random Node from a Singly Linked List

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 

1. Count the number of nodes by traversing the list. 
2. 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 off 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

/* 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 off 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

// 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

Python3

# 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#

// 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

Javascript

<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>

Output

Randomly selected key is 
3

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 3^rd last node and other nodes.