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Select a Random Node from a Singly Linked List
• Difficulty Level : Hard
• Last Updated : 10 Jun, 2021

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 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``#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`

## 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``        ``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 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)`

## 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

 ``

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 3rd 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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