# Select a Random Node from a Singly Linked List

• Difficulty Level : Hard
• Last Updated : 27 Jun, 2022

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
(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` `#include` `#include ` `#include` `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` `#include` `#include `   `/* 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

 ``

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 3rd last node and other nodes.

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