# 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

- 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 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.