Given a singly linked list, select a random node from linked list (the probability of picking a node should be 1/N if there are N nodes in list). You are given a random number generator.

Below is a Simple Solution

1) Count number of nodes by traversing the list.

2) Traverse the list again and select every node with probability 1/N. The selection can be done by generating a random number from 0 to N-i for i’th node, and selecting the i’th node node only if generated number is equal to 0 (or any other fixed number from 0 to N-i).

We get uniform probabilities with 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, probabilities of other selecting other nodes is 1/N

The above solution requires two traversals of 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 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 above algorithm.

## 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

## Python

# 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 linkd list def printRandom(self): # If list is empty if self.head is None: return # 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 current = self.head 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 linked LinkedList def printList(self): temp = self.head while(temp): print temp.data, 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)

Note that the above program is based on outcome of a random function and may produce different output.

**How does this work?**

Let there be total N nodes in list. It is easier to understand from last node.

The probability that last node is result simply 1/N [For last or N’th node, we generate a random number between 0 to N-1 and make last node as result if the generated number is 0 (or any other fixed number]

The probability that second last node is 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 probability for 3^{rd} last node and other nodes.

This article is contributed by **Rajeev**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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