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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
(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.